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Investigation of several important phenomena associated with the development of Knudsen compressors

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Investigation of several important phenomena associated with the development of Knudsen compressors

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Content INVESTIGATION OF SEVERAL IMPORTANT PHENOMENA ASSOCIATED WITH THE DEVELOPMENT OF KNUDSEN COMPRESSORS By Marcus Paul Young A Dissertation Presented to the FACULTY OF THE SCHOOL OF ENGINEERING UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Fulfillment of the Requirements for the Degree DOCTOR OF PHILOSOPHY (AEROSPACE AND MECHANICAL ENGINEERING) August 2004 Copyright 2004 Marcus Paul Young Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. UMI Number: 3 1 4 5 3 1 7 Copyright 2 0 0 4 by Y oung, M arcus Paul All rights reserved . INFORMATION TO U S E R S T he quality of this reproduction is d ep en d en t upon th e quality of th e copy subm itted. Broken or indistinct print, colored or poor quality illustrations and photographs, print bleed-through, substandard m argins, and improper alignm ent can a d versely affect reproduction. In the unlikely ev en t that the author did not se n d a co m p lete m anuscript and there are m issing p a g e s, th e s e will be noted. A lso, if unauthorized copyright material had to be rem oved, a note will indicate th e deletion. ® UMI UMI Microform 3 1 4 5 3 1 7 Copyright 2 0 0 4 by P roQ u est Information and Learning C om pany. All rights reserved . This microform edition is protected a g ain st unauthorized copying under Title 17, United S ta te s C ode. P roQ u est Information and Learning C om pany 3 0 0 North Z eeb R oad P.O . Box 1346 Ann Arbor, Ml 4 8 1 0 6 -1 3 4 6 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Dedication “Education is the best provision for the journey to old age” Aristotle Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Acknowledgements This research was part of a joint effort between the Aerospace and Mechanical Engineering Department at the University of Southern California and the Micro Devices Lab at the Jet Propulsion Laboratory, California Institute of Technology. The work was sponsored by the National Aeronautics and Space Administration, Office of Aerospace Technology and the USC Department of Aerospace Engineering. A special thanks is extended to Dr. E.P. Muntz for his decade of mentorship and support beginning with my undergraduate studies and continuing all the way through my Ph.D. It was a great honor to be mentored by such a great scientist/engineer/person. I would also like to thank my other committee members, Professor G. Shiflett, Professor D. Shemansky, Professor P. Ronney, and Professor E.S. Kim for their guidance over the course of this work. I would like to thank all of my friends and coworkers at USC who have helped me over the years. Special thanks goes to Dr. Andrew Ketsdever for his many years of advice and mentorship and for sparking my interest in Aerospace Engineering in the very beginning. I would also like to thank Yen- Lin Han for her help and advice, and for continuing the Knudsen Compressor research. Special thanks also goes to Stephen Vargo for blazing the trail for this project with his work. Thanks also goes to Ryan Dougherty, Joseph Polasik, Josh Cripps, and Dave Scharfe. Special thanks to the USC Engineering Machine Shop for their many years of providing us with excellent parts. I would also like to personally thank the many people at the Jet Propulsion Laboratory who have helped with this work. I would like to thank Amy Green for her help with designing and manufacturing the Knudsen Compressor. Thanks also goes to Dr. Steven Jones for providing us with the aerogel for this study and for all of his aerogel related advice. iii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. I would also like to thank my family for their support throughout this entire process. Special thanks goes to my wife, Simone Gao, for her many years of patience, understanding, and gentle prodding. I would also like to thank my parents for instilling in me the values of hard work and dedication and for allowing me to follow my own path. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Table of Contents Dedication ii Acknowledgements iii Tables vii Figures viii Nomenclature xii Abstract xv Chapter 1 Introduction 1 1.1 Background 1 1.2 Applications for Micro/Meso-Scale Gas Roughing Pumps 3 1.3 Applications for High Pressure Gas Sources in MEMS Devices 7 1.4 Basic Application Concerns 9 1.5 Competing Candidate Solutions for Meso-Scale Roughing Pumps 10 1.6 Competing Candidate Solutions for Meso-Scale Gas Compressors 16 1.7 Sample Meso-Scale High-Vacuum Pump 17 Chapter 2 The Knudsen Compressor Concept 19 2.1 Thermal Transpiration Model (Thermal Effusion and Thermal Creep) 19 2.2 Knudsen Compressor Stage Description 23 2.3 Common Transpiration Materials: Aerogels 24 2.4 Knudsen Compressor Powering Options 27 2.5 Radiantly Heated Knudsen Compressor Stage Design 33 Chapter 3 Knudsen Compressor Performance Model 36 3.1 Knudsen Compressor Performance Model Overview 36 3.2 Knudsen Compressor Pumpdown Model 39 3.3 Models for Aerogel Physical and Optical Properties 41 3.4 Transpiration Membrane Temperature Distribution Analysis 46 3.5 Thermal Conductivity Analysis 49 3.6 Outward Cooling Models 51 3.7 Gas Conduction Analysis 54 3.8 Transpiration Analysis 55 3.9 Effects of Carbon Doping Silicon Aerogel Transpiration Membranes 56 3. lORepresentative Optimizations 57 Chapter 4 Low Pressure Transpiration Membrane Considerations 62 4.1 Low Pressure Limit Definition 62 4.2 Representative Low Pressure Knudsen Compressor 64 4.3 Etched Aerogel Transpiration Membranes 65 4.4 Glass Microsphere Transpiration Membranes 67 4.5 Performance Predictions for Low-Pressure Transpiration Membrane 69 Options 4.6 Microsphere Transpiration Membrane Experiments 70 4.7 Microsphere Based Knudsen Compressor Designs 72 V Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. C hapter 5 High Pressure Knudsen Compressor Considerations 75 5.1 Introduction 75 5.2 Gas Particle-Surface Interaction Effects 78 5.3 Increased Surface Interaction Effects 83 5.4 Phonon-Particle Drag in Nanocapillary Flows 85 5.5 Quantum Effects in Nanocapillary Gas Flows 88 5.6 Nanopore Condensation Effects 91 5.7 Basic Design Considerations and Representative Example 93 5.8 Membrane Materials for Operating Knudsen Compressors at P> lOatm 97 Chapter 6 Single Stage Experiments: Transpiration Membrane Temperature 99 Difference and TMPD Measurements 6.1 Conventionally Machined Knudsen Compressor Stage Description 99 6.2 Transpiration Membrane Temperature Difference Measurements 101 6.3 Single Stage Steady-State AP Measurements 105 C hapter 7 Multi-Stage Measurements: Pumping Curve Measurements and 108 Cascading Effects Investigations 7.1 One to Five Stage Cascade Description 108 7.2 Pumping Curve Experimental Process 110 7.3 Summary of Pumping Trace Results 116 7.4 15 Stage Conventionally Machined Knudsen Compressor 122 Chapter 8 Proposed Future Knudsen Compressor Designs 124 8.1 Single Point Knudsen Compressor Optimization 124 8.1. a Knudsen Compressor Optimization - Moderate k 125 8.1. b Knudsen Compressor Cascade Optimization - Moderate k 131 8. l.c Knudsen Compressor Optimization - k = 0 134 8.1.d Knudsen Compressor Optimization - k = 1 137 8.1.e Summary 138 8.2 Manufacturing Techniques for Meso-Scale Radiantly Heated Knudsen 139 Compressors as a Gas Roughing Pump 8.3 Meso-Scale Resistively Driven Knudsen Compressor as a Low 143 Pressure Ratio Pump 8.4 Meso-Scale Waste Heat Driven Knudsen Compressors 144 8.5 Summary 147 Chapter 9 Conclusions 148 Bibliography 150 v i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Tables Table I: Estimated Miniature SEM Roughing Pump Performance Requirements 5 Table II: Pump Information Used for Energy Efficiency Comparison 14 Table III: Low Pressure lOmTorr to lOOmTorr Base Cascade Analysis Results 66 Table IV: Performance Estimates for Glass Microsphere Based Knudsen Compressor 74 Designs Table V: Large Pressure Ratio Cascade Properties 94 Table VI: Small Pressure Ratio Cascade Properties 95 Table VII: Nanopore Materials Compared to a Typical Aerogel 98 Table VIII: Properties of Creare’s Miniaturized Turbomolecular Pump 130 Table IX: Required Properties for the Meso-Scale Gas Roughing Pump 130 Table X: Cascade Optimization Effects 131 Table XI. MEMS Fabricated Radiantly Driven Knudsen Compressor Characteristics 142 Table XII. Resistively Driven Low Pressure Ratio Knudsen Compressor 144 Characteristics v ii Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figures Figure 1: Quadrapole Mass Spectrometer Array (QMSA) from JPL 4 Figure 2: Cyranose® 320 Electronic Nose and NoseChip™ Gas Sensors from Cyrano 6 Sciences Figure 3: High-Pressure Knudsen Compressor Based Actuated Valve and Pressure 8 Regulator Figure 4: KNF Neuberger Diaphragm Pump 11 Figure 5: Honeywell’s Dual Diaphragm Pump Schematic 11 Figure 6: Air Squared Scroll Pumps 12 Figure 7: Scroll Section of the JPL-USC Meso-Scale Scroll Pump 13 Figure 8: Energy Efficiency of Chosen Meso-Scale Pump Technologies 14 Figure 9: Energy Efficiency of Chosen Meso-Scale Pump Technologies to 200 mTorr 15 Figure 10: KNF Neuberger Diaphragm Compressor 16 Figure 11: MIT Centrifugal Engine Compressor 17 Figure 12: Creare’s Ultraminiaturized Turbomolecular/Molecular Drag Pump 18 Figure 13: Thermal Effusion Schematic 20 Figure 14: Transitional Flow Thermal Creep Schematic 22 Figure 15: Illustrative i’th stage of a Knudsen Compressor 24 Figure 16: Comparison of Silicon Aerogel with p=10mg/cc and p=100mg/cc 26 Figure 17: Resistive and Radiant Heating Configurations 28 Figure 18: Resistively Heated Knudsen Compressor Energy Efficiency (Torr Seal) 31 Figure 19: Resistively Heated Knudsen Compressor Energy Efficiency (PMMA) 32 Figure 20: Exploded View of a Single Stage MEMS Radiantly Driven Knudsen 35 Compressor Figure 21: Knudsen Compressor Stage Models 37 Figure 22: Aerogel Microstructure Schematic 42 Figure 23: Aerogel Mean Effective Pore Diameters 43 Figure 24: Aerogel Specific Surface Area 44 Vlll Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 25: Temperature Dependent Specific Extinction Coefficient for Carbon Doped Aerogels 46 Figure 26: Calculated Aerogel Absorption Coefficients 46 Figure 27: One Dimensional Temperature Difference Model Schematic 47 Figure 28: Transpiration Membrane Temperature Profile 49 Figure 29: Relative Membrane Cooling Fluxes 53 Figure 30: Tube Formulation Flow Rates 55 Figure 31: Total Aerogel Thermal Conductivity at P = 760 Ton- 58 Figure 32: Total Aerogel Thermal Conductivity at P = 1 Ton 58 Figure 33: Resistively Heated Energy Efficiency at P = 760 Ton 60 Figure 34: Radiant Heating Energy Efficiency for P = 760 Ton 60 Figure 35: Low Pressure Knudsen Compressor Concept 64 Figure 36: Unit Cell for Simple Cubic (SC) and Face Centered Cubic (FCC) Microsphere Bed Geometries 67 Figure 37: Energy Efficiency for Candidate Membrane Materials 70 Figure 38: Single Stage Knudsen Compressor Based on Glass Microspheres 71 Figure 39: Comparison of Experimental and Analytical Glass Microsphere TMPD 72 Figure 40: Sample Microsphere Knudsen Compressor Stages 73 Figure 41: Pore Sizes Required to Efficiently Operate Knudsen Compressors at Different Pressures 75 Figure 42: Nanopore Potential Models 79 Figure 43: Various N2 on Si02 Gas-Surface Interaction Potentials 81 Figure 44: Gas-Cylinder (N2-Si02 ) Potentials for Various Sized Cylinders 82 Figure 45: Gas-Phonon Coupling Driven Flow for Assumed 87 Figure 46: Gas-Phonon Coupling Driven Flow Verses Temperature 87 Figure 47: Gas-Phonon Coupling Driven Flow for C 02 on C 88 Figure 48: Quantum Ratio for N2 89 Figure 49: Quantum ID Gas Effect Strength, T = 300K 90 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 50: Pore Condensation Effect of CO2 in Cylindrical Pores, T = 200K 91 Figure 51: Porous Glass With Condensed Water Vapor 92 Figure 52: High Pressure Knudsen Compressor Concept 93 Figure 53: High Pressure Knudsen Cascade Pressures 94 Figure 54: Single Stage Radiantly Driven Knudsen Compressor 100 Figure 55: Experimental Setup Used to Measure AT 102 Figure 56: Comparison of Predicted and Observed Transpiration Membrane Temperature 103 Difference Figure 57: Steady State Pressure Difference for Different Configurations 105 Figure 58: Steady-State AP Dependence on Incident Flux 107 Figure 59: Five Stage Knudsen Compressor Experimental Setup 111 Figure 60: Representative 1 Stage Cascade Pressure Trace 113 Figure 61: Pressure Difference Traces for a Single Type II Stage on Air 114 Figure 62: Performance Curves for a Type II Single Stage on Air 115 Figure 63: Venting Traces for a Single Type II Stage on Air 116 Figure 64: Maximum Pressure Difference verses Pressure for Single Type II Aerogel Stage 116 Figure 65: Maximum Flow Rate verses Pressure for a Single Type II Aerogel Stage 117 Figure 66: Comparison of Experimentally Measured and Predicted Gas Flow Conductances for Type II Aerogel 118 Figure 67: Steady-State Pressure Difference for Various Numbers of Stages 118 Figure 68: Maximum Flowrate for Various Numbers of Stages 119 Figure 69: Cascade Gas Flow Conductance for Various Numbers of Stages 120 Figure 70: Maximum Pressure Difference for 5 Stage Knudsen Compressor 121 Figure 71: Maximum Throughput for 5 Stage Knudsen Compressor 122 Figure 72: Fifteen Stage Knudsen Compressor Cascade 123 Figure 73: 15 Stage Cascade Pumpdown Curves 123 Figure 74: Minimization of First Bracketed Term for P = 1 atm of Air 126 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 75: Minimization of First Bracketed Term for P = 1 Torr of Air 127 Figure 76: Minimization of Second Bracketed Term 128 Figure 77: Minimization of Third Bracketed Term 129 Figure 78: Nonoptimal Operation of Perforated Aerogel Stages 132 Figure 79: Aerogel Density Effect on Energy Efficiency 135 Figure 80: Carbon Dope Fraction Effect on Energy Efficiency 135 Figure 81: Aerogel Transpiration Membrane Thickness Effect on Energy Efficiency 136 Figure 82: Powering Flux Effect on the Energy Efficiency 136 Figure 83: k = 1 Energy Efficiency Optimization 138 Figure 84: Manufacturing Process for an Multi-Stage Radiantly Heated Knudsen Compressor 140 Figure 85: False Color View of Single Stage Knudsen Compressor Flow Producer 143 Figure 86: Waste Heat Driven Knudsen Compressor Schematic 146 Figure 87: Approximate Scaling of Candidate Waste Heat Driven Stage Configurations 146 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Nomenclature a Distance From Wall for Molecular Potential Calculations A Stage Cross-sectional Area A p,s Area Representing One Particle on a Distributed Mass Surface c Temperature Dependent Specific Extinction Coefficient C c d Preexponential Factor for Solid Conduction of Carbon Doped Aerogel C s i Preexponential Factor for Solid Conduction of Silicon Aerogel C p o r Porous Material Specific Heat Capacity c Gas Conductance 7 Mean Thermal Speed of a Gas Ca Gas Conductance for an Aperture Cpi Gas Conductance for a Finite Length Tube c, Gas Conductance for Isentropic Flow Through and Aperture Clt Gas Conductance for a Long Tube C m a Gas Conductance for a Free Molecule Flow Through an Aperture C ph Gas-Phonon Coupling Term C total Total Cascade Gas Flow Conductance C v Constant Volume Specific Heat da Aerogel Effective Primary Particle Diameter dg Molecular Diameter dr Glass Microsphere Diameter D Diffusion Coefficient Ei Energy Levels in Nanoporous Membranes fcarb o n Volume Fraction of Carbon in Doped Aerogel Membrane h Dirac’s Constant kam b Thermal Conductivity of the Ambient Gas kb Boltzmann’s Constant kg Thermal Conductivity Component Due to Gas Conduction kg,c Thermal Conductivity of a Continuum Gas k seal Thermal Conductivity of the Aerogel Sealing Material K Absorption Coefficient Knr Knudsen Number Based on Pore Radius kr Thermal Conductivity Component Due to Radiation Transport ks Thermal Conductivity Component Due to Solid Conduction k * .c a rb o n Solid Carbon Thermal Conductivity k g . sp h e re Thermal Conductivity of Material of Glass Microspheres ks.si Thermal Conductivity Component Due to Solid Conduction for Si Aerogel ks ,s ilic o n Solid Silicon Thermal Conductivity kt Total Thermal Conductivity L Pore Wall Interaction Potential Range Li,L2 Length Scales for Rectangular Surface Lx Membrane Thickness ta x ,h e a t Thickness of Membrane Where Heat is Applied Lx Connector Section Thickness Lr Mean Effective Pore Diameter Lr Connector Section Radius Lt Thickness of Aerogel Sealing Material m Particle Mass n Number Density ns Surface Gas Density in Pore N Number of Stages in a Knudsen Compressor Cascade N Number Flow Rate Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Flowrate Produced by i’th Stage Pressure Gradient Driven Number Flow Rate Number Flow Rate Driven by Gas-Phonon Drag N t Temperature Gradient Driven Number Flow Rate Pv Vapor Pressure Near Curved Surface P v o Vapor Pressure p Pressure p 1 7 a v g Average Pressure Pin Heating Power Delivered to the Membrane P+ Pressure of High-Pressure Side of Aperture Qp Capillary Section Pressure Flow Coefficient Q pc Connector Section Pressure Gradient Flow Coefficient Qt Capillary Section Thermal Gradient Flow Coefficient Qtc Connector Section Thermal Gradient Flow Coefficient $(*) Absorbed Energy Flux at the Given Penetration Depth Q Energy Flux Q a e r o g e l Energy Flux Through Aerogel Q s e a l Energy Flux Through Aerogel Seal r Lennard-Jones Separation Distance R Spherical, Cylindrical Pore Radius Ra Rayleigh Number R m Radius of Curvature s Ratio of Particle Distance to Origin to Spherical Pore Radius Sf Glass Microsphere Bed Average Solid Fraction s Average Solid Fraction for Glass Microsphere Bed Sf Free Conduction Shape Factor S. Specific Surface Area of Porous Material t Time Since the Initiation of Pumpdown to Characteristic Heating Time for Transpiration Membrane tsta g e Characteristic Time for Gas Travel Through a Transpiration Membrane T Temperature T am b Ambient Surrounding Temperature Ta v g Average Temperature Tc Temperature of Cold Side of Transpiration Membrane Th Temperature of Hot Side of Transpiration Membrane Tra d Radiation Temperature TMPD Thermomolecular Pressure Difference V Most Probable Molecular Thermal Speed V0 Mean Thermal Speed V Pore Interaction Potential Depth V Volume Flow Rate Vc Chamber Volume on Cold Side of Pump Vh Chamber Volume on Hot Side of Pump Vnol Molar Volume Vp Pair-wise Lennard-Jones Potential w Total Potential X Distance From Free Aerogel Surface ^ T rn a x Location Inside Aerogel of Maximum Temperature Xp Pressure Ratio Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. z Distance From Origin Along Axis a Accommodation Coefficient a„ Power Factor for Aerogel Solid Conduction P Term Dependent on e, y, a 8 Thickness of Interfacial Region 8a V g Glass Micro Sphere Bed Effective Pore Diameter AP Pressure Difference DT Temperature Difference AT0 p t Optimal Temperature Difference Produced in the Resistively Heated Case AX Plate Spacing 8 Term Dependent on y Slj Lennard-Jones Potential Well Depth er Surface Emissivity Upb Effective Packed-Bed Emittance < t> (x ) Radiant Flux at Penetration Depth x ^con Outward Conduction Cooling Flux ^cont Thermal Flux in a Continuum Gas ^contjfe Thermal Flux from a Free Surface in a Continuum Gas ^fin Thermal Flux in a Free Molecule Gas Free Molecule Gas Conduction Thermal Flux from a Free Surface ^inc Incident Radiant Flux <t>out Total Outward Cooling Fluxes ^rad Outward Radiation Cooling Flux •Nr Thermal Flux in a Transitional Gas *Kr,fs Transitional Gas Conduction Thermal Flux from a Free Surface y Ratio of Specific Heats r, Zeroes of the Bessel Function 7 s Surface Tension K Fraction of Maximum Pressure Difference X Optical Depth of Porous Material K n Mean Free Path of Gas Molecules Xph Phonon-Phonon Mean Free Path K Mean Radial deBroglie Wavelength n Porosity Ppor Density of Porous Material Psi.por Density of Pure Silicon Aerogel P t Density of Solid Material in Aerogel P Incremental Energy Absorbed at Penetration Depth x a Stefan-Boltzmann Constant a e Lennard-Jones Potential Equilibrium Separation Distance T Mean Relaxation Time of Gas Particle With Pore Surface To Characteristic Pumpdown Time for Knudsen Compressor Cascade Q Volume of Particle on Surface of Distributed Mass ^seal Aerogel Sealing Inefficiency c Volume Shrinkage Factor for Aerogel K Energy Efficiency Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Abstract The perceived utility of compact, power efficient sensor systems, coupled with recent advances in micro-electro-mechanical systems (MEMS) fabrication capabilities, have encouraged the construction of micro/meso-scale sensors. Viable micro/meso-scale sensors have been demonstrated; however, in many cases micro/meso-scale vacuum pumps are required to complete the sensor systems. The Knudsen Compressor, a micro/meso-scale gas pump based on thermal transpiration, is one proposed technology for a micro/meso-scale gas roughing pump. There are additional potential far term applications for Knudsen Compressors applied as high-pressure gas sources. Knudsen Compressors have important advantages over other proposed micro/meso-scale gas roughing pumps: no moving parts, no oils or other supplementary fluids, quiet and steady operation, easily scalable, and a range of potential heating activation techniques. The primary focus of this thesis is technological and scientific advancements leading to the development of radiantly driven micro/meso-scale Knudsen Compressors as roughing pumps. Considerations for operating Knudsen Compressors near a practical minimum operating pressure, 10 mTorr, and maximum operating pressure, 10 atm, are discussed. Initial experiments and modeling with glass microsphere beds, one possible low-pressure transpiration membrane, are discussed. Several potentially significant flow phenomena are predicted to appear at high pressures. The Knudsen Compressor Performance Model is updated to include: short tube effects, a generalized aerogel transpiration model, radiant heating capabilities, and outward transpiration membrane cooling effects. The model was also altered to provide time dependent pumping simulations. The Knudsen Compressor Performance Model was used to complete optimization studies and to construct several proposed designs for different applications. Transpiration membrane temperature and steady-state pressure measurements were taken for a variety of conditions and typically agree with model predictions to within 15% except in the pressure range of 10 mTorr to 1 Torr where the gas conduction outward cooling mechanism is transitioning to rarefied xv Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. behavior. Pumping curve traces were obtained for single stages and cascades with up to 15 stages. The gas throughput and cascade pressure ratio predicted by the Knudsen Compressor Performance Model typically agreed to within 20% with the experimental measurements indicating that a satisfactory understanding of radiantly driven Knudsen Compressors has been gained during this investigation. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 1 Introduction 1.1 Background There is currently great interest in the development of energy efficient, micro/meso-scale sensor systems with similar detection capabilities as their macro-scale counterparts.1 A driving force for the development of these systems are the multiple potential benefits associated with distributed sensor networks. Instrument networks are envisioned for roles such as chemical/biological weapons detection on the battlefield or around potential terrorist targets, industrial plant process control, and scientific investigations requiring simultaneous spatially distributed measurements. The enabling requirement for these networks is the availability of reliable, energy efficient, compact sensor systems. Recent advancements in MEMS manufacturing capabilities have made it possible to construct functional micro/meso-scale analytical sensors such as mass spectrometers2, spectrometers3, and gas chromatographs.4 Current fully operational versions of these devices tend to be meso-scale (length scale in centimeters), but there is a continual push towards micro-scale systems (length scales < 1cm). From a systems point of view a universal limitation on the availability of these devices is the lack of micro/meso-scale gas roughing pumps to provide the necessary sampling environmental conditions for the sensor elements.5 The large variety of newly developed micro/meso-scale sensors, along with the uncertainty in the appropriate scaling laws for the pressures that are necessary for each device, has made it an ongoing problem to define the minimum pumping requirements for these micro/meso-scale sensor systems. It is clear, however, that pressures lower than atmospheric will be required in many of the micro/meso-scale sensor realizations, therefore micro/meso-scale gas roughing or backing pumps must be developed as an infrastructure technology for distributed sensors systems. Research into micro/meso-scale gas roughing pumps has been based on two fundamentally different philosophies: shrink down current macro-scale pump technologies; or develop new pump technologies based on pumping mechanisms that haven’t been incorporated into macro-scale pumps, but may become more advantageous at small-scales.5 Apart from one exception that is discussed later, all 1 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. existing macro-scale gas roughing pumps employ moving parts. A micro/meso-scale roughing pump based on an existing technology would therefore require moving parts, a difficult requirement to accommodate at even the meso-scale due to: the increased importance of friction at the meso-scale; maintaining typically required clearances (including the effects of manufacturing tolerances, thermal expansion effects, and relative motion) of several micrometers in a device with a characteristic dimension of several centimeters. Viable micro-scale gas roughing pumps will almost surely be solid- state and must be based on pumping mechanisms not currently employed in macro-scale pumps. An exception to this expectation might be a micro-scale cryosorption pump, but these pumps require a source of low temperatures, making their general application to micro/meso-scale systems problematic. It is therefore worthwhile to consider alternative pumping mechanisms as a basis for micro/meso-scale gas roughing pumps. Thermal transpiration is one such mechanism, it is the flow driving mechanism employed in the Knudsen Compressor. The effect of thermal transpiration, or thermal creep has been identified for over a century. In fact, Knudsen demonstrated the first multi-stage thermal transpiration based pump, achieving a pressure ratio of 10, in 1910.6 Since that time, however, they have mainly been laboratory curiosities. Their application in practical devices has been limited by thermal inefficiency and low pumping speeds. Thermal transpiration based pumps are also most advantageous at the micro/meso-scale, but there has been little need for energy efficient micro/meso-scale vacuum pumps until recently. Interest in a particular version of a thermal transpiration pump, the Knudsen Compressor,7 ,8 has been sparked by the availability of the required materials, such as aerogel, and the development of the required manufacturing capabilities, for example MEMS processes such as deep reactive ion etching (DRIE) and anodic bonding. Previous experiments have demonstrated the operation of a resistively heated Knudsen Compressors at pressures from 100 Torr to 1 atm.9 More recently, MEMS Knudsen Compressors based on existing technologies have been shown theoretically capable of efficiently operating to pressures as low as 10 mTorr, while maintaining flow rates consistent with meso-scale 2 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. high vacuum pumps currently under development.1 0 Thus, the Knudsen Compressor appears to be a viable candidate for a solid-state micro/meso-scale gas roughing pump. Using the same transpiration membrane materials, in their small capillary radius limit (a few nanometers), the Knudsen Compressor has also been predicted capable of operating at pressures approaching 10 atm.1 1 This capability could extend the applicability of the Knudsen Compressor to include co-located, compressed gas sources for MEMS applications. Such a possibility would enable a wide range of MEMS devices because of the available large pneumatic forces,1 2 as well as applications such as distributed cooling for low temperature micro-detectors.1 3 In many cases the low-pressure gas can be drawn, as needed, from the local environment. Initial indications are that different realizations of the Knudsen Compressor are capable of operating as energy efficient micro/meso-scale gas roughing pumps and as co-located micro-scale sources of high-pressure gas. 1.2. Applications for Micro/Meso-Scale Gas Roughing Pumps A micro/meso-scale gas roughing pump is an enabling infrastructure technology for many micro/meso- scale sensor systems. As such it is not necessary to develop the Knudsen Compressor as the pumping component for specific sensor systems because the development of many sensor systems has not yet begun due to the lack of existing micro/meso-scale vacuum pumps. It is, however, useful to identify and consider several representative micro/meso-scale sensor systems to determine if the Knudsen Compressor can satisfy the performance requirements for some sensor systems currently being developed. Mass spectrometers have been shrunk to the meso-scale1 4 (scale length in cm) and there is a current drive to shrink them to the micro-scale (scale length < 1cm).1 5 Both scales of mass spectrometers have operating pressure requirements that indicate that they will require both roughing and turbomolecular pumps to operate efficiently. One example of the current state of the art in functional small mass spectrometers is the Quadrapole Mass Spectrometer Array (QMSA) from JPL shown in Figure l .1 4 3 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Hp 200LX Board Figure 1. Quadrapole Mass Spectrometer Array (QMSA) from JPL1 4 The mass spectrometer body is roughly 6 inches in length, indicating that it is a large meso-scale system. The primary identified application for the QMSA is part of an integrated portable tool (TGA- Trace Gas Analyzer) for use by astronauts on the International Space Station (ISS). One version is currently aboard the ISS and is being used by astronauts for leak detection. Additional suggested applications include use on planetary exploration missions and cabin air monitoring for manned missions. The QMSA is a highly sensitive small-scale sensor, which has experimentally identified and quantified constituents up to 150 amu. The QMSA system maintains high vacuum using two ion pumps, but has no roughing pumps. A meso-scale gas roughing pump would extend the applicability of meso-scale mass spectrometers such as the QMSA. Small meso-scale mass spectrometers with millimeter length scales are currently under development.1 5 The pumping performance of the required meso/micro-scale gas roughing pump has not been clearly identified due to the low maturity level of the technology. It is clear that the roughing pump must adhere to the same length scales (few centimeters / millimeters) and mass scales (few kilograms / fraction of a kilogram) as the device itself. The pump should also operate in the pressure range of typical full-scale roughing pumps, from atmospheric pressure down to the required foreline pressure of the high vacuum pump employed in the system. The required pumping specifications for the QMSA are not readily available, but a high vacuum pump designed to operate with miniature mass spectrometers such as the QMSA, the 4 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. ultraminiaturized turbomolecular / molecular drag pump developed by Creare1 6 and detailed in Section 1.7, has been discussed in the literature and a Knudsen Compressor designed to operate with the Creare pump has been designed and is presented in Section 8.2. Another potential application for the Knudsen Compressor is a gas roughing pump for a miniature scanning electron microscope1 7 (SEM), under development at JPL, for operation in the Martian surface atmosphere. The miniature SEM ultimately requires high vacuum for operation, but also requires a miniature roughing pump to initially evacuate the sampling chamber and to provide a foreline pressure of 0.75 mTorr for the ion pumps incorporated in the current design. The prototype design of the miniature SEM was not completed by the publication date of this work, but several performance requirements for the system roughing pump have been identified. The miniature roughing pump must have a mass of a few kg and consume no more than a few watts of power. The current flight instrument design has an estimated pumpdown volume of 10-20 cm3. Initial estimates indicate that the instrument must be evacuated to steady operating pressures in roughly 1 hour corresponding to a pumping speed of roughly IE-3 LPM. During the operation phase samples of the Martian soil will be brought into the sensor for analysis. The soil samples will also include a volume of less than 0.1 cm3 of local atmospheric gas. The Martian atmosphere has an average surface gas pressure of 5 Torr composed of 95.3% C 0 2, 2.7% N2, 1.6% Ar, and traces of oxygen and water.1 8 The estimated required performance of the roughing pump for the miniature SEM is summarized in Table I. System Characteristic Requirement Mass Several kg Power Several watts Pressure Range 0.75 mTorr to 6 Torr Pumpdown Time Constant 720 s Operational Gases C 02, N2, Ar, 0 2, H2 0 Table I. Estimated Miniature SEM Roughing Pump Performance Requirements1 7 The required foreline pressure of 0.75 mTorr is less than the power efficiency defined practical minimum operating pressure of lOmTorr. The difficulty associated with this requirement is partially relaxed by the low ambient pressure on Mars. 5 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The current state of the art high performance miniature mass spectrometer system has been shrunk the size of a desktop computer.1 9 Further miniaturization efforts are currently underway, but complete high performance mass spectrometer systems are likely to be meso-scale for the foreseeable future. An alternate gas sensor technology that scales more easily to the micro-scale is chemiresistor or “chemical nose” technology. Meso-scale chemiresistor based gas sensor systems operate at atmospheric pressure, but require a gas flow to increase the sample delivery rate to the sensor, and therefore require meso- scale low pressure ratio gas pumps. A portable gas detector employing chemiresistor technology, the Cyranose® 320, and the sensor itself, the NoseChip™, both manufactured by Cyrano Sciences, are shown in Figure 2.2 0 6“ Snout Accessary Plus Purge Inlet On/Off Switch Sun Button LCD Display Exhaust Screen Contrast RS232/USB Connectors Power Supply Figure 2. Cyranose® 320 Electronic Nose and NoseChip™ Gas Sensors from Cyrano Sciences2 0 Each chemiresistor sensor consists of a pair of electrical contacts that are bridged by a composite film. Typically the film for each sensor is made of a composite of a nonconducting polymer and conductive carbon black particles. When the film absorbs vapor-phase analytes and swells, the conductive pathways in the film are broken and the resistance of the composite film changes. The Cyranose® 320 uses arrays of 32 sensors, each containing a unique polymer with unique resistance change responses to different analytes. Chemiresistor based technology, like that used in the Cyranose® 320, operates at Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. atmospheric pressure. Low pressure ratio gas pumps increase the sensitivity of chemiresistor technology by increasing the rate at which the gas is brought to the chemiresistor sensors. The meso- scale Cyranose® gas detector uses a meso-scale diaphragm pump to provide the required gas flow. Efforts are underway to further miniaturize chemiresistor based gas sensors for applications such as wearable gas detectors.2 1 Quantitative sensitivity enhancements as a function of gas flowrate have not yet been determined for these devices, making it difficult to estimate the required pump performance. A Knudsen Compressor has been designed to operate as a low pressure ratio gas pump for a chemiresistor based detector with nominal performance requirements and is detailed in Section 8.3. It is concluded that the Knudsen Compressor is not competitive from simply an energy efficiency standpoint to diaphragm pumps when applied as meso-scale low pressure ratio gas pumps. Diaphragm pumps, however, seem to be limited to the meso-scale indicating that as the chemiresistor sensors are shrunk into the micro-scale it is clear that they will require micro-scale gas pumps employing new technology such as the micro-scale Knudsen Compressor. 1.3. Applications for High Pressure Gas Sources in MEMS Devices Several representative applications for a high-pressure (1 atm to 10 atm) Knudsen Compressor have been previously suggested.1 1 The specific applications that have been identified center around using a MEMS fabricated micro/meso-scale Knudsen Compressor as a co-located source of high-pressure gas (greater than 1 atm.) for MEMS valves, actuators, and fluid flow devices. Some representative devices for this application are shown in Figure 3. A normally open valve driven by a Knudsen Compressor is illustrated in Figure 3 a. In the non-powered position the diaphragm is in its relaxed state allowing maximum flow. As more power is supplied to the Knudsen Compressor a differential pressure is built up across the deflection diaphragm, deflecting it into the tube flow and lowering the flow rate. At full power the deflection diaphragm seals against the valve seat, shutting off the flow in about 30 ms. Figure 3b shows as an example a MEMS pressure regulator using a Knudsen Compressor to maintain the required pressure difference for driving liquid samples in a laboratory-on-a-chip context. The control electronics regulate the high-pressure side of the device to minimize the effects due to changes 7 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. in ambient conditions and driven loads. Both of these devices are only concepts that are meant to illustrate the possibilities that exist with the availability of micro-scale gas compressor technologies. Tube Flow Deflection Diaphragm High Pressure Knudsen Compressor Ambient Atmosphere Valve Seat a Pressure Sensors Control Electronics Ambient Atmosphere High Pressure gas to drive fluid flow in Lab-on-Chips High Pressure Knudsen Compressor b Figure 3. High-Pressure Knudsen Compressor Based Actuated Valve and Pressure Regulator Specific systems requiring micro-scale gas compressors have not yet been identified for the high pressure Knudsen Compressor making it difficult to investigate the details of its applicability, but performance estimates for the device can still be made. Relying only on existing materials and technologies, MEMS Knudsen Compressors can be constructed that provide compressed gas up to pressures of about 10 atm while making use of ambient gases as the working medium.1 1 The theoretical performance of Knudsen Compressors operating from 1 atm up to 10 atm was evaluated with the Knudsen Compressor Performance Model developed as a result of the research completed in Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. this thesis. In one design, further detailed in Section 5.7, a 27 stage Knudsen Compressor provides a pressure increase from 1 atm to 10 atm at a flow rate of 2xl0'3 atm-cm3 /s. The compressor occupies a volume of 40 mm3 and has a power requirement of 0.25W. The apparent ultimate high-pressure limit for the Knudsen Compressor is 100 atm. The pressure range between 10 atm. and 100 atm. requires nanometer and smaller size capillaries in the transpiration membrane. Several physical effects have been predicted to become important at these small dimensions. Experimental validation of the predicted effects at high pressures is required. Generally, existing materials with sub-nanometer capillaries have thermal conductivities that are much higher than for the lower pressure Knudsen Compressors, leading to inappropriate power consumption for MEMS devices; for now, the practical upper limit on the pressure to which a MEMS Knudsen Compressor can operate is around 10 atm. 1.4. Basic Application Concerns Volume limitations associated with micro/meso-scale devices often lead to designs that integrate several functions. Knudsen Compressors have several features that make them attractive candidates for integration with sensor systems. Knudsen Compressors can be built using the same layered manufacturing approach that is common with MEMS fabrication processes. They are also easily scaled and staged devices with simple stage configurations. These factors indicate that it may be possible to integrate the Knudsen Compressor directly with the sensor in one package. The Knudsen Compressor requires only a temperature difference across the transpiration membrane to induce the thermal transpiration effect, driving the pump. A variety of energy delivery mechanisms can be envisioned to both generate and maintain the temperature difference across the transpiration membrane. Previous experimental Knudsen Compressors relied on resistive heating of one side of the transpiration membrane, while the other side was cooled or thermally grounded. The current work focuses on radiantly heating the transpiration membrane by illuminating one side and thermally grounding the other side. The radiant flux required to drive typical Knudsen Compressor designs is consistent with the solar flux at the Earth’s surface, making solar driven micro/meso-scale gas pumps 9 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. or compressors a possibility. Another interesting possibility is using available waste heat to drive the pump. By thermally connecting a Knudsen Compressor to both the hot waste side and the heat sink side of a system it is possible to drive the Knudsen Compressor, providing an integrated micro/meso- scale gas roughing pump or compressor that requires no additional power. General considerations for waste heat driven Knudsen Compressors are given in Section 8.4. At operating pressures above an atmosphere the transpiration membrane’s pore diameters required for efficient operation are in the range of several nanometers. New flow effects are predicted at these small diameters and are discussed in Chapter 5. These new physical effects are gas dependent and can possibly be employed to add species dependent screening and separating capabilities to the high- pressure Knudsen Compressor. 1.5. Competing Candidate Solutions for Meso-Scale Roughing Pumps The current state of the art in meso-scale vacuum pump technology has been achieved by shrinking macro-scale pump technologies. Two different technologies have been successfully shrunk down to the meso-scale: diaphragm pumps and scroll pumps. An example of the state of the art in meso-scale diaphragm pumps available for application as a gas roughing pump is the KNF Neuberger diaphragm dump shown in Figure 4.2 2 The diaphragm pump has a length scale of 10cm, nominally consumes 35 Watts of power, has a pumping speed of 5 L/s, and reaches an ultimate pressure of 1.5 Torr. Diaphragm pumps are available with characteristic length scales down to 5cm, but they have very limited ultimate pressures (-300 Torr). 10 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 4. KNF Neuberger Diaphragm Pump2 2 Honeywell is currently developing the smallest published meso-scale diaphragm pump, the Dual Diaphragm Pump (DDP), shown schematically in Figure 5.2 3 D riv in g signals Cross Section ^ Outlet D m pluugm G V V 3a. Bom diaphragms down, tower port seated 2. Lower rtephragm ptAed down, upper pod remains sealed. 1. Pump stroke Initialed, bods diaphragms puMed towards top. 2a. Lower diaphragm down, upper port and lower port sealed. l i f e ! * — U < Diaphragm la. Puiro stroke comptetad. upper port sealed. 3 Upper daphrafprt pulled dowi, upper port opened, lower port sealed. ‘ Otapiwegm molon ' Air M ow „23 Figure 5. Honeywell’s Dual Diaphragm Pump Schematic The DDP measures 1.5cm x 1.5cm x 0.1cm, and is manufactured using an injection molding process. The pump is driven by the controlled electrostatic actuation of two thin structured diaphragms in a sequence, shown in Figure 5, to first fill and then expel the chamber volume. The DDP has a pumping speed of 30sccm at a power consumption 8mW. It is, however, only able to maintain a pressure 11 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. difference of 14.7 Torr per stage, making it strictly a low pressure ratio gas pump. The small pressure difference attainable by the DDP is consistent with the trend observed with other diaphragm pumps, which have more limited pressure difference capabilities with decreasing physical dimensions below 10cm. A performance comparison of a Knudsen Compressor and the DDP employed as low pressure ratio pumps is given in Sections 8.1.c and 8.3. Scroll pumps are dry vacuum pumps that have found many applications in the semiconductor industry and other fields where oil vapor in a system would be detrimental. Scroll pumps have been successfully shrunk to the same length scale as diaphragm pumps. Examples of the state of the art in commercially available meso-scale scroll pumps are the Air Squared scroll pumps shown in Figure 6.2 4 Figure 6. Air Squared Scroll Pumps2 4 The smallest Air Squared scroll pump has a length scale of 10cm, consumes roughly 30W of power, has a pumping speed of 7 L/s, and can reach an ultimate pressure of 10 mTorr. The physical dimensions, power consumption, and throughput are all similar to the meso-scale diaphragm pumps, but the achievable ultimate pressure is lower by several orders of magnitude. The limit in scalability of scroll pumps is illustrated by a meso-scale scroll pump that has been recently proposed by JPL and USC.2 5 The scroll section of the pump is shown in Figure 7. 12 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 7. Scroll Section of the JPL-USC Meso-Scale Scroll Pump2 5 The diameter of the scroll section is 1.2cm. The internal scroll shown on the left revolves on a circular path. This traps gas between the two scrolls and continuously moves the trapped gas towards the outlet (in the middle of the scroll on the left). The gas is compressed along the way to provide the outlet pressure. The required manufacturing processes are currently being demonstrated for the JPL-USC scroll pump. The main concern for the viability of the meso-scale scroll pump is the manufacturing tolerances required to provide sufficient sealing and the resultant lifetime of the scrolls.2 5 Initial performance estimates made using an analytical performance model, experimentally validated with full scale scroll pumps, indicate that the gap spacing (including both manufacturing tolerances and the effects of the rotation of the stages) must be held under 2pm for the pump to be viable. These manufacturing tolerances can not be met with current technologies and is the main focus of the development work with the pump. Because of the required micrometer sized clearances at even the meso-scale it appears unlikely that scroll pumps will be scaled to the micro-scale. Both scroll pumps and diaphragm pumps have been proven as acceptable choices for 10cm scale gas roughing pumps. There are efforts underway to develop versions of both types of pumps with a characteristic length scale of roughly 1 cm. One technique that can be used to compare the broad range of meso-scale gas pumps is to compare the energy efficiency, or energy per molecule of upflow 13 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. between two specified pressures. Figure 8 shows the energy efficiency for different available meso- scale scroll pumps and diaphragm pumps compared to a Knudsen Compressor designed to operate as a backing pump for the Creare ultraminiaturized turbomolecular / molecular drag pump detailed in Section 1.7. The pumps operate between pressures of 7.6 Torr and 760 Torr. More details of the specific pumps compared in Figure 8 are given in Table II. The Knudsen Compressor used for the comparison is detailed in Section 8.2. 1.00E-15 ^ 1.00E-16 o E 3 j 1.00E-17 O ■ o a 1.00E-18 1.00E-19 0.1 1 10 100 1000 10000 100000 V (cm3 ) Figure 8. Energy Efficiency of Chosen Meso-Scale Pump Technologies I I I + I I Diaphragm Pumps Scroll Pumps ■ Knudsen Compressor © o ©o Pump Pump Type Volume (cm3 ) Energy Efficiency (J/molecule) Knudsen Compressor Transpiration 1 IE-16 KNF N84.4'" Diaphragm 960 2.5E-18 BOC Edwards BLAB 10-8“ Diaphragm 5200 1.16E-17 BOC Edwards BLAB 20-8'* Diaphragm 7000 6.8E-18 BOC Edwards BLAB 34-8“ Diaphragm 9300 7.9E-18 Air Squared P10H10“ Scroll 960 9.55E-19 Varian TriScroll 300'“ Scroll 39000 5E-19 Varian TriScroll 6002/ Scroll 47000 3.39E-19 Varian SH-1002' Scroll 17000 8.25E-19 BOC Edwards ESDP12“ Scroll 34000 3.6E-19 BOC Edwards XDS5“ Scroll 21000 6.7E-19 BOC Edwards XDS10“ Scroll 21000 3.65E-19 Table II Pump Information Used for Energy Efficiency Comparison The two dashed lines bound the meso-scale volume range where both scroll pumps and diaphragm pumps are under development. Scroll pumps have a better energy efficiency at the meso-scale when 14 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. operating between 7.6 and 760 Torr. Both scroll pumps and diaphragm pumps produce similar flow rates for a given power at atmospheric pressures, but diaphragm pumps are typically limited to ultimate pressures of several Torr, while meso-scale scroll pumps reach ultimate pressures of 10s of mTorr. The Knudsen Compressor used for this comparison was sized to have a volume (1cm3 ) that is three orders of magnitude smaller than the currently available meso-scale vacuum pumps. One cubic centimeter also appears to be close to the lower size limit to which both scroll pumps and diaphragm pumps can be shrunk. The Knudsen Compressor is predicted to have roughly the same energy efficiency over the entire volume range in Figure 8. The Knudsen Compressor would consume roughly an order of magnitude more power, at a volume of 1000cm3, than the diaphragm pumps and two orders of magnitude more power than the scroll pumps. The Knudsen Compressor is not very competitive, under only energy efficiency considerations, for this pressure range at a volume of 1000cm3 , but would be the only pump available at a volume of 1cm3. Figure 9 shows the energy efficiency comparison of several commercially available scroll pumps with the Knudsen Compressor operating from atmospheric pressure to a pressure of 200 mTorr. 1.00E-14 1.00E-15 o § 1.00E-16 o 2 *5 1.00E-17 ■ o 1.00E-18 1.00E-19 0.1 1 10 100 1000 10000 100000 V (cm 3) Figure 9. Energy Efficiency of Chosen Meso-Scale Pump Technologies to 200 mTorr At higher pressure ratios the Knudsen Compressor becomes more competitive with other technologies at the meso-scale, and may even be the most energy efficient choice. In general it appears that the 0 % © © © Scroll Pumps □ Knudsen Compressor 15 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Knudsen Compressor is more competitive, from energy efficiency considerations, when operating at high pressure ratios and small volumes and would be the only viable micro-scale gas roughing pump. 1.6. Competing Candidate Solutions for Meso-Scale Gas Compressors Current state of the art meso-scale gas compressors are similar in both size and design to state of the art meso-scale gas roughing pumps. Gas compressors with length scales of 5-10cm are commercially available while gas compressors with length scales of roughly 1 cm are under development. One example illustrating the state of the art in available meso-scale gas compressors is a diaphragm based compressor from KNF Neuberger shown in Figure 10.2 2 Figure 10. KNF Neuberger Diaphragm Compressor2 2 The KNF Neuberger diaphragm compressor has a length scale of 8cm, a maximum pressure difference of 22 PSI, a maximum flowrate of 6 LPM, and consumes 16 Watts of power. Slightly more compact (length scale of 6cm) diaphragm compressors are also available from KNF Neuberger, but their maximum pressure differences are much more limited (7.3 PSI). Several compressors with length scales of roughly 1cm (all with moving parts) are currently under development. They are being developed for more specialized purposes than their 10cm length scale counterparts. One such compressor is being developed by MIT as part of their micro power generation research and is shown in Figure l l . 2 8 The compressor has a diameter of 8mm and has a tip speed of 500m/s providing a predicted pressure ratio of 4:1. The compressor is designed to operate at rotational 16 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. speeds in excess of one million rpm. This design, requiring tip clearances of 2pm, has not yet been experimentally tested at this scale, but clearly demonstrates the high angular speeds and small tolerances required for meso-scale compressors. Figure 11. MIT Centrifugal Engine Compressor Meso-scale gas compressors are being developed with length scales down to 1cm. The difficulties encountered during the development process are the same as for the development of meso-scale gas roughing pumps and indicate that gas compressors at smaller scales will require fundamentally different designs. The Knudsen Compressor as a solid-state gas compressor with a predicted attainable pressure of 10 atm is one promising candidate for a micro/meso-scale gas compressor. 1.7. Sample Meso-Scale High-Vacuum Pump Many micro/meso-scale gas sensor systems require high vacuum (pressures between 10'3 and 10'7 Torr) during operation. These systems will require both micro/meso-scale gas roughing/backing pumps and high vacuum pumps to achieve and maintain these pressures. It is useful therefore to identify micro/meso-scale high-vacuum pumps under development and to determine the compatibility of the Knudsen Compressor with these pumps in providing an entire pumping system. Creare has developed a meso-scale turbomolecular/molecular drag pump as a candidate meso-scale high-vacuum 17 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. pump.1 6 Creare’s ultraminiaturized turbomolecular / molecular drag pump (also called the “C-Cell” Turbo Drag Pump for obvious reasons) is shown in Figure 12. Figure 12. Creare’s Ultraminiaturized Turbomolecular/Molecular Drag Pump1 6 The “C-Cell” Turbo Drag Pump uses advanced technology such as hybrid ceramic bearings to allow it to reach the required rotational speeds of 200,000 rpm while maintaining a lifetime of several months of continuous operation. The pump has a pumping speed of 4 L/s on air and can reach an ultimate pressure of near 10'8 Torr while supporting foreline pressures in excess of 10 Torr. The pump has a diameter of 3.4cm, is 8cm long, and has a mass of 130 grams. Extensive efforts in minimizing the power consumption of the pump have resulted in a pump that consumes 2 Watts of power for foreline pressures under 1 Torr and 7 Watts for a foreline pressure of 10 Torr. A Knudsen Compressor designed to operate as a backing pump for the C-Cell Turbo Drag Pump in terrestrial applications appears attractive and is detailed in Section 8.2. One advantage of the C-Cell Turbo Drag Pump arises from the capability of operating at foreline pressures of 10 Torr, it allows the pump to operate directly in the Martian atmosphere. The pressure range from 1 Torr to 7 Torr consumes the dominant fraction of the power (6 of 7 Watts total) for Martian applications. As detailed later, the Knudsen Compressor operates efficiently in this pressure range indicating that it may be possible to lower the power consumption by employing a Knudsen Compressor as the roughing pump (operating from 7 Torr to 1 Torr) in Martian applications. 18 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 2 The Knudsen Compressor Concept It has been shown in Chapter 1 that it is worthwhile considering new flow driving mechanisms for both micro/meso-scale gas roughing pumps and micro/meso-scale gas compressors. One such flow driving mechanism, thermal transpiration, or thermal creep, was identified as a promising candidate. Thermal transpiration, a rarefied gas effect, drives a flow (in the direction of the temperature gradient) when a temperature difference is maintained across the ends of a tube containing at least a partially rarefied gas. Thermal transpiration is most easily realized in micro/meso-scale gas pumps and compressors by maintaining temperature differences across transpiration membranes made from porous materials, such as aerogel, with pore diameters sized such that the gas in the capillaries is rarefied. The transpiration membrane is the most critical component of the Knudsen Compressor and requires special consideration including: minimizing the thermal conductivity, maximizing the porosity, and properly sizing the characteristic pore dimensions. Many different techniques can be used to build and maintain the temperature difference across the transpiration membrane and two of them, resistive heating and radiant heating, are discussed in Section 2.4. The required flow rate can be obtained by adjusting the cross-sectional area of the stages or the temperature difference across the transpiration membrane in the stages. Many stages, some designs employ upwards of one hundred, can be connected in series to obtain the required pressure ratio. These stages are aligned in a planer fashion to simplify the manufacturing process and allow radiant versions to be driven by a single light source. 2.1. Thermal Transpiration Model (Thermal Effusion and Thermal Creep) The term thermal transpiration refers to two physical mechanisms, thermal effusion through a rarefied orifice and thermal creep in a rarefied tube. Thermal eflusion can be understood by considering two chambers, separated by a free-molecule orifice, as shown in Figure 13. If the two chambers are maintained at different temperatures thermal effusion will take place through the orifice. 19 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 13. Thermal Effusion Schematic Assume that at a time t=0 n!=n2, T]=T2, and therefore Pi=P2, where n, T, and P, are the number density, temperature and pressure, respectively. At the next instant set Ti < T2. Thermal effusion will cause a gas flow through the orifice from chamber 2 (hot side) to chamber 1 (cold side) due to the decreased average thermal speed of the molecules in chamber 1. The net flow rate, defined positive from hot to cold, is given by ^ ( r r - r r ) 0 ) where m is the molecular mass. By instantaneously decreasing Ti (n! = n2 at t = 0) the pressure in chamber 1 would also be decreased. At the initial instant the pressure ratio would be given simply by the ratio of the temperatures as shown by A Pi ,= o (2) At time t > 0 the flow driven by thermal effusion will increase the number density in chamber 1 while decreasing the number density in chamber 2. At intermediate times there will be both a net flow rate, from hot to cold, and a number density difference between the two chambers. When t-> oo the steady- state condition is reached where the reduction in flux from the lower temperature in side 1 is balanced by an increase due to a higher number density, providing no net flow rate, and the steady-state maximum pressure ratio is given by A Pi (3) 20 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Under thermal transpiration considerations a tube separating two chambers that is filled with a gas that has completely specular wall reflections is equivalent to the free-molecule orifice described above. The particle-wall interactions that occur in a specular tube do not change the energy or tangential momentum of the gas particles. The particles exiting one side of the tube have the same properties as when they entered the other side of the tube. The temperature gradient along the tube has no effect on the flow because the temperature information is not communicated to the molecules as they travel through the tube and reflect specularly with the wall. The net flow is produced by different fluxes of gases entering the different ends of the tube. The pressure ratio and net flow rate relationships for thermal transpiration in a specular tube are the same as for the free molecule orifice case. Thermal creep occurs in free molecule or rarefied tube flows with diffuse gas reflections with the surface. In this case the temperature gradient along the axis of the tube drives a gas flow through the tube in the direction of the temperature gradient. The temperature gradient driven flux for a gas under free molecule conditions in a tube, assuming fully diffuse surface reflections, is given by where vQ is the mean thermal speed and Lr is the mean pore radius. The corresponding pressure gradient driven return flux is given by Imagine a case when gas in a tube is under free molecule conditions, a temperature gradient is maintained along the axis of the tube, and the tube separates two chambers that have the same pressure at a time t=0. At this instant there is no pressure gradient and there is a maximum net flux from the cold end of the tube to the hot end of the tube with the flux given by Equation 4. As time advances a pressure difference is built across the chambers attached to both ends of the tube due to the net gas flow from the cold end to the hot end. At the time, t = oo, the temperature gradient driven flux (4) (5) 21 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. is balanced by the pressure gradient driven return flux providing the steady-state condition of maximum pressure difference and no net flow rate. The thermomolecular pressure difference (TMPD) is defined as the normalized pressure difference produced by a normalized temperature difference, which for free molecule conditions is given by A P TMPD = = — (6) AT 2 T avg Thermal creep does not occur in continuum flows so the temperature gradient driven gas flux in continuum flows is 0. The absence of thermal creep in continuum gases produces a TMPD of 0 for continuum flows. In transitional flows the TMPD varies between 0 and !4 The TMPD for transitional flows is given by the ratio of the temperature gradient driven flow coefficient to the pressure gradient driven flow coefficient as given by TMPD = Q - (7) Qp The thermal creep effect for transitional flows is illustrated in Figure 14. TubewaU Z y. 'y ' / / / / / / / / / / / / Z . Z . / , , / JL —.------------------------------------------------ ----------creep flow pi " p* P2 = P, «*— slow Return Hot How " * 1 l 2 Thennal creep flow Figure 14. Transitional Flow Thermal Creep Schematic9 Transitional thermal creep flow is driven from the cold end of the tube towards the hot end of the tube as in the case of free molecule thermal creep flow. Under free-molecule conditions the thermal creep flow would fill the entire tube. As shown in Figure 14 the thermal creep effect, under transitional gas conditions, drives gas flows in tubes close, within roughly one mean free path, to the surface. 22 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Once a pressure difference has been established a pressure return flow will occur, balancing the thermal creep flow. Practical realizations of Knudsen Compressors operate with a Knudsen number of roughly one, transitional flow conditions, in the transpiration membrane to minimize the energy consumption per unit throughput. The thermal creep effect can drive a net gas flow and sustain a pressure difference, the requirements for a gas pump or compressor, simply by maintaining a temperature difference across the ends of a tube full of at least a partially rarefied gas. 2.2. Knudsen Compressor Stage Description The Knudsen Compressor incorporates thermal transpiration in porous membranes as the pump driving mechanism. The Knudsen Compressor, first suggested by Pham-Van-Diep et al2 9 and demonstrated by Vargo et al7 ’ 8 , is a modern version of the original thermal transpiration compressor described by Knudsen6 in 1910. A series of individual stages are used to provide the required pressure ratio in a Knudsen Compressor. A single stage of a Knudsen Compressor is shown schematically in Figure 15. Also shown in Figure 15 are the temperature, T, and pressure, p, variation along the stage. Each stage has a capillary section where the temperature increases, causing a pressure increase due to the rarefied gas dynamic phenomenon of thermal transpiration. The capillary section is followed by a connector section, with a significantly larger radius than the individual capillaries of the capillary membrane. The connector section is designed to make use of the fact that no thermal transpiration occurs in continuum tube flow. The connector section operates with the gas flow closer to the continuum regime so that the pressure is approximately constant while the temperature is lowered to its original value entering the stage. Each capillary section is reminiscent of the single thermal transpiration element used by Reynolds3 0 in his experiments reported in 1879. The compressor's potential applicability has been significantly expanded since Knudsen’s 1910 investigations by the recent, serendipitous availability of small pore size membranes formed from materials with extremely low thermal conductivities. 23 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (i-l)th Stage ith Stage (i+ l)th Stage Lx,i LX,i y y////////////////m v////////////////m m ////////////y m W //////////////M Capillary Section LR,i Ccnnector Section / \ Tavg TL,i (pi-l)Eff Figure 15 Illustrative i’th stage of a Knudsen Compressor 2.3. Common Transpiration M aterial: Aerogels The transpiration membrane properties are critically important to the overall Knudsen Compressor performance making the choice of an appropriate membrane the first step in designing a Knudsen Compressor. Three evaluation parameters can be used to determine the effectiveness of a candidate transpiration membrane material: effective pore diameter, gas conductance or porosity, and thermal conductivity. It has been shown that for minimum energy operation, the effective pore diameter of the membrane for an individual stage should be sized such that the gas flow in the pores has a Knudsen number of roughly one.3 1 The transpiration membranes must have sufficient porosity to allow efficient mass flow through the membrane. Materials with sufficiently low thermal conductivities (10s of mW/mK) are required to minimize the power required to maintain the temperature difference across the transpiration membrane, since it is the temperature difference that 24 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. drives the pump. Aerogel is one material that satisfies these three requirements and has been identified for application as a transpiration membrane in Knudsen Compressors. Previously investigated resistively driven Knudsen Compressors employed silicon aerogel as the transpiration membrane material.9 The current investigations into radiantly driven Knudsen Compressors employ carbon doped silicon aerogel as the transpiration membrane material. Radiantly driven Knudsen Compressors have the added requirement of efficient absorption of the incident radiation (high extinction coefficient). Doping the silicon aerogel with small amounts of carbon increases the specific extinction coefficient and decreases the thermal conductivity, both of which are critical for optimizing radiantly driven Knudsen Compressors. Aerogels are porous materials with extreme properties: porosities that can exceed 95%, solid density as low as 3 mg/cc, sound velocity ~ 100 m/s, evacuated thermal conductivity ~ 5 mW/mK, specific surface area ~ 1000 m2 /g, and dielectric constant ~ 1.1.3 2 Aerogels also typically have mean effective pore diameters of tens of nanometers, which satisfies the Knudsen Compressor transpiration membrane requirements for gas pressures around 1 atm. Aerogels can be made from a variety of different base materials (silicon, carbon, titanium, resorcinol formaldehyde (RF)), can be doped with an even wider range of materials (carbon, laser dyes, organic materials), and can be made in densities from 3mg/cc to the solid density of the material (densities > -150 mg/cc typically corresponds to xerogels). This wide range of available aerogels broadens the potential applicability of devices employing them. All of these factors make aerogels an obvious candidate for a Knudsen Compressor transpiration membrane material. Silicon aerogel is the most common aerogel type and is the type used in the current study. The wide range of available aerogel types makes it difficult to fully optimize the choice of an aerogel for different applications. Fundamental properties of aerogeld can range over orders of magnitude with different aerogel materials, densities, and manufacturing processes. The microstructure of the aerogel has been shown to be dependent on the aerogel density and the aerogel manufacturing 25 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. procedure.3 3 Figure 16 compares SEM pictures for silicon aerogel with a density of 10 mg/cc (a) to a silicon aerogel with a density of 100 mg/cc, both manufactured using a TEOS based two step acid catalyzed process.3 4 Figure 16. Comparison of Silicon Aerogel with p=10mg/cc and p=100mg/cc' The microstructure changes drastically between these two aerogel densities manufactured using the same process. It is also clear from Figure 16 that the porous nature of aerogel is not physically represented by the parallel array of cylindrical pores assumed in most aerogel gas flow and thermal transpiration models. The first aerogel produced, silicon aerogel, is also the most common aerogel. Silicon aerogel is always made using a sol-gel procedure, but many different specific techniques exist. The formation of aerogels, in general, involves two major steps. The first step is to form a wet gel or a solid porous network that is filled with a liquid. The second step is to dry the wet gel to form an aerogel. The balanced chemical equation for the formation of a silica gel from one of the common precursors, Tetraethyloxysilane (TEOS), is32: S i ( O C H 2C H 3)4 (liq.) + 2 F I2O (Hq.) = S i 0 2 (solid) + 4 H O C H 2C H 3 (ijq.) ( 8 ) The above reaction is typically performed in ethanol, with the final density of the aerogel dependent on the ratio of the silicon (from the TEOS) to the alcohol and water. The reaction is impractically slow at standard conditions. Acid or base catalysts are typically added to the formulation to speed up the reaction. Once a solid gel is formed in the solution the wet gel is removed from its mold. The gel 26 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. is kept covered by alcohol at all times to prevent evaporation of the liquid contained in the pores of the gel. Evaporation produces a liquid solid interface meniscus in the pores creating high surface tension on the fragile porous structure, causing it to shrink and crack. The aerogel is then allowed to age, typically for several days. After aging the gel, the water still contained within its pores must be removed prior to drying. This step involves a solvent exchange process where the water is exchanged with other liquids with lower surface tension, acetone or hexane for example. The specific solvent is dependent on the drying procedure chosen. The final, and most critical, process in making silicon aerogels is supercritical drying. If the wet gel is dried very carefully under ambient conditions then a xerogel will be formed. Xerogels are similar to aerogels, but have an increased density due to the shrinkage that occurs under ambient drying conditions. The surface tension in the meniscus between the liquid and vapor phase in the pores causes the porous structure to shrink. If, however, the wet gel is dried under supercritical conditions there is no clearly defined gas and liquid states and hence there is no meniscus and much less shrinkage will occur. Silicon based aerogels were chosen over other types of aerogels for the current realization of the radiantly driven Knudsen Compressor because of their availability and broad range of possible characteristics. The aerogels were doped with a small amount of carbon (typically under 10%) to minimize the total aerogel thermal conductivity by limiting the radiation transport through the aerogel and to absorb the incident radiation, providing the temperature difference. 2.4. Knudsen Compressor Powering Options Once the transpiration membrane has been chosen for a given application, the energy delivery technique or method used to establish and maintain the temperature difference across the transpiration membrane must be chosen. Previous performance estimates for the MEMS Knudsen Compressor have been made assuming the limit of both minimum volume and power consumption.7 ,8 ,9 The minimum volume assumption was realized by neglecting the volume of the packaging and other secondary equipment such as control electronics and light sources. The only volume considered was 27 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the volume taken up by the transpiration membrane and the open part of the connector section. The minimum power consumption approximation was realized by considering only the thermal power conducted through the transpiration membrane and ignoring inefficiencies such as energy conversion inefficiencies, energy delivery inefficiencies, and outward cooling flux losses. At this stage in the development of the Knudsen Compressor it is appropriate to begin making performance estimates for the entire system when optimizing the design for both minimal required volume and power per unit upflow. Estimates for the system volume, total power consumption, and performance must be made to prove the operation of the entire Knudsen Compressor system and to fully compare different candidate heating configurations. There are two obvious approaches to maintaining a temperature gradient across the transpiration membrane in the Knudsen Compressor, resistive heating (including both wire bonded systems and inductively coupled systems) and radiant heating (including powered light sources and direct solar illumination). The two configurations are shown schematically in Figure 17. Incident Radiation Resistive Heater JBL Thermal Guard Aerogel Thermal Guard grogel Seal Aerogel Thermal G u a rd ^ gel geal^ t e r o | Figure 17. Resistive and Radiant Heating Configurations The resistively heated configuration is modeled by an aerogel transpiration membrane that is sandwiched between two perforated thermal guards that are each at uniform temperatures. The aerogel edges are sealed by a thin layer of material. The wire bonded version requires a thin film heater deposited on the top thermal guard because the aerogel, which can have thin film heaters deposited directly on it, is not strong enough to support a wire bonded to the heater. The inductively coupled version does not require a top thermal guard because it doesn’t have a wire bonded directly to 28 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the thin film heater. The radiantly heated configuration doesn’t use a thermal guard on the hot side. The temperature difference is maintained by directly illuminating the aerogel with radiant energy. The radiant energy is absorbed in the aerogel itself and is released into the thermal guard on the cold side of the aerogel transpiration membrane. Additional more exotic heating techniques such as combustion driven heating have been suggested3 5 , but are not appropriate for Knudsen Compressors employed in gas roughing pumps and gas compressors. Another alternative configuration, waste heat driven Knudsen Compressors, discussed in more detail in Section 8.4, could potentially provide micro/meso-scale gas compressors/pumps that require no electrical energy to operate. Resistive heating requires thin film heaters deposited on either the hot side of the aerogel membrane itself (for the inductively heated case) or on a thermal guard placed on the hot side of the transpiration membrane (for the wire bonded case). Previous single-stage experimental versions used wire-bonded resistive heating9 because it was simple to implement in a single-stage device and because it has no conversion inefficiency and no distributed absorption losses because all of the thermal energy is absorbed in a silicon wafer on the surface of the membrane. Employing the resistive heating technique in a multistage packaged device, however, requires vacuum rated electrical feedthroughs and wire bonding for each individual stage. A multistage Knudsen Compressor based on radiant heating appears to be easier to manufacture because it does not require wiring. A radiantly heated Knudsen Compressor only requires an optical path from the light source, current configurations have it located outside the pump body, to the hot side of the aerogel transpiration membrane. The manufacturing processes required to construct a radiantly driven Knudsen Compressor represent a subset of the required manufacturing processes for a resistively driven Knudsen Compressor making radiantly heated Knudsen Compressors an obvious step in the development of a multistage resistively heated Knudsen Compressor. A simple comparison can be made to estimate the relative energy efficiency of resistively and radiantly heated Knudsen Compressor configurations based on existing materials and manufacturing 29 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. capabilities. At this stage in the Knudsen Compressor development it is practical to begin considering four energy inefficiencies: outward cooling inefficiency, energy delivery efficiency, distributed absorption inefficiency for optically driven pumps, and the sealing inefficiency that arises from the thermal energy losses through the finite sealing areas around the aerogel transpiration membrane. The outward cooling inefficiency is predicted to represent as high as 80% of the delivered energy, in Section 3.6, for the current configurations, but the energy inefficiency is the same for both radiantly driven configurations and resistively driven configurations and is not considered when comparing the relative energy efficiency of the different configurations. The dominant inefficiency associated with the wire-bonded resistively heated configuration is the energy loss through the material used to seal the outside of the aerogel. The thickness of the sealing material can be minimized to limit this loss, but a finite thickness is required for structural purposes (for the wire-bonded case). The sealing energy efficiency can be calculated from e _ Q aerogel / m 7) 7) f s aerogel ~^~x£seal Where Qa e r o g e , is the thermal flux traveling through the aerogel and Qs e a l is the thermal flux traveling through the sealing ring. The energy flux through the aerogel is given by Q aerogel ( 10) Lx Where kto ta i is the total thermal conductivity of the aerogel, A is the aerogel cross-sectional area, and Lx is the aerogel thickness. The energy flux through the sealing ring for a square aerogel transpiration membrane cross-section is given by Q s e a l ^ seal (4 ^ + 4 L ,4 a ) ^ - (11) Where kse a | is the thermal conductivity of the sealing material and Lt is the thickness, measured outward from the aerogel side, of the sealing ring. Estimates can be made of the sealing energy efficiency for different candidate sealing materials and thickness. The first material chosen is Torr Seal® Epoxy which is used to seal the sides of the aerogel in the conventionally machined Knudsen 30 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Compressor cascades used in this study. Figure 18 shows the thermal fluxes through both the aerogel transpiration membrane and the sealing epoxy and the sealing energy efficiency verses the sealing ring thickness. Typical values are used for the calculation: k ^ = 17mW/(mK), A = 1cm2, AT = 40K, Lx = 1mm, kse a i (Torr Seal®) = 435 mW/(mK). 1 0 0 1 0 1 f ** o 0 . 1 a °Cu 0.01 0.001 0.0001 1 E -06 1.E -05 XQdot_aerogel (W) X Qdot_seal (W) o Sealing Efficiency 1.E -0 4 U(m ) 1.E -03 1.E-C >» o c .© '5 E > * o> 1- < u c 1 1 1 o > c « A Figure 18. Resistively Heated Knudsen Compressor Energy Efficiency (Torr Seal) For the typical characteristics used in the calculation it appears that a sealing energy efficiency of 50% is achieved at a sealing ring thickness of 100 pm. The typical sealing ring thickness achieved when using Torr Seal epoxy is greater than 1 mm providing sealing energy efficiencies of roughly 5%, which is obviously too low for application in energy efficient designs. It is useful at this point to make a similar estimate for the best candidate material identified for possible use in the transpiration membrane sealing ring, polymethylmethacrylate (PMMA). PMMA is a solid material that can be patterned with x-ray lithography and has one of the lowest thermal conductivities of any solid material at 180 mW/(mK). The results for the sealing energy efficiency for PMMA sealing rings for the same conditions as in Figure 18 are shown in Figure 19. For a sealing energy efficiency of 25% the required PMMA thickness is 600pm. This size of PMMA sheath can be easily manufactured. There are several problems with implementing this configuration, however. PMMA sheaths are solid seals. It is very difficult to cut the aerogel membranes to the tolerances required for an adequate fit within a 31 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. solid seal. The PMMA sheath and aerogel section would still require a method to bond it to the cold thermal guard. For both of these reasons it appears that the resistively heated configuration sealed with PMMA would be very difficult to implement. A more practically implemented design would be to deposit a thin film of material along the outside edge of the aerogel after it had already been bonded to the thermal guard or grown in place. Inductively coupled configurations with no structural requirement on the sealing ring and no top thermal guard appears to be a more energy efficient configuration. 10 ■ a a 0.01 0.001 0.0001 t o ^ - — J t . XQdot_aerogel (W) XQ dot_seal (W) o Sealing Efficiency \ ^ °Oo ° u oo °Nw > X J O O C O O O O O C O O O O O O O * * * * 1 1 0 .9 0.8 0 .7 0.6 0 .5 0 .4 0 .3 0.2 0.1 0 1.E -0 6 1.E -05 1.E -0 4 U(m) 1 .E -0 3 1.E -0 2 >. o c o '5 h > > o > a) c U J o> c « (8 Figure 19. Resistively Heated Knudsen Compressor Energy Efficiency (PMMA) The radiantly heated Knudsen Compressor configuration also suffers from several energy inefficiencies. The dominant predicted energy inefficiency is the energy delivery inefficiency. This inefficiency is comprised of both the electrical to radiant energy conversion losses and the energy losses due to the nonzero fraction of the produced light that doesn’t hit the aerogel transpiration membrane. These inefficiencies aren’t a concern for the solar driven configuration, but are used in the comparison made here. Different light source types have different energy conversion efficiencies. One typical light source, a high power red LED, is used here for comparison.3 6 The energy conversion efficiency is roughly 20% for the red high power LED. For the current configuration it is estimated that roughly 80% of the emitted light could be intercepted by the aerogel transpiration 32 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. membrane. This value is obtained by assuming that a fraction (typically 15%) of the emitted light is either reflected or absorbed as it passes through the transparent cover on the pump body on the way to the transpiration membrane and another fraction that makes it into the pump body, but does not strike the aerogel. This provides an energy delivery efficiency using the current state of the art high-power LED and the current design of the Knudsen Compressor of 16%. Future improvements could be achieved if the light source energy conversion efficiencies are increased towards their limiting quantum efficiency (-40%), by better collection of the emitted light, and by optimizing the transparent cover of the pump body. Both configurations have similar predicted energy inefficiencies under the limitations of the current Knudsen Compressor design, available materials, and manufacturing processes. The radiantly driven configuration was chosen for this study because it had not yet been investigated and it is easier to manufacture. The manufacturing steps required for the radiantly driven Knudsen Compressor also represent a subset of the required manufacturing processes for a resistively driven Knudsen Compressor. 2.5. Radiantly Heated Knudsen Compressor Stage Design There are a variety of different considerations for the design of a radiantly driven Knudsen Compressor including: limited manufacturing capabilities and existing materials, thermal management, fluid flow concerns, and optical access to the hot side of the transpiration membrane. These concerns are briefly discussed in this section along with a design of a single stage of the radiantly driven MEMS Knudsen Compressor. The stage design described in this section is the MEMS equivalent of the single stage conventionally machined Knudsen Compressor detailed in Section 6.1. Additional more complete designs incorporating knowledge gained from the current work are detailed in Chapter 8. 33 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The most practical technique for manufacturing micro/meso-scale Knudsen Compressors is by using MEMS m anufacturing processes. M EM S manufacturing techniques can produce the required feature sizes, fabricate a large number of Knudsen Compressor stages at one time, and allow for potential high-level integration with the support electronics and the device employing the Knudsen Compressor. Using M EM S techniques, however, limits the available materials to those that are consistent with M EM S processes, such as anodic bonding which limits the material choices to silicon, pyrex, and kovar. M EM S processes are also most applicable to planer configurations. The gas flow and pressure difference in Knudsen Compressors are driven by maintaining a temperature gradient across the thermal transpiration membrane. Thermal management is, therefore, a critical consideration in the design of an efficient Knudsen Compressor. The thermal design of the transpiration membrane is the most important thermal consideration. Thermal resistance from the top of the transpiration membrane to the heat sink must be maximized to limit the outward cooling losses due to outward radiation transport and gas conduction from the free surface of the transpiration membrane. The thermal resistance through the transpiration membrane must also be maximized to increase the temperature difference produced by an incident radiation flux. The thermal resistance from the cold side of the transpiration membrane to the heat sink must be minimized for efficient removal of the thermal energy from the device. The Knudsen Compressor must also be designed to maximize the gas conductance through the device, but still maintain sufficient tube lengths to allow the gas temperature sufficient time to adjust to local wall imposed temperatures. The device must also provide optical access to the hot side of the transpiration membrane. Additional work, including the work described in this thesis, is required to fully implement these considerations into a Knudsen Compressor design. An initial design can, however, be made. 34 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 20 shows an exploded view of a single stage of the MEMS fabricated, radiantly driven Knudsen Compressor designed under the considerations listed above. A 2mm thick 8% carbon doped silicon aerogel (80mg/cc) transpiration membrane, shown in false color for clarity, is grown directly on a silicon thermal guard. The transpiration membrane has a nominal cross-sectional area of 1cm2. No sealing ring is employed in the current design for simplicity. The silicon thermal guard is perforated, using the deep reactive ion etch (DRIE) process, under the aerogel transpiration membrane to allow gas to flow through it. The silicon thermal guard is anodically bonded to a pyrex top cavity. Pyrex allows optical access to the hot side of the transpiration membrane and is consistent with the anodic bonding process. The bottom side of the silicon thermal guard is bonded to a thin pyrex bonding union. The bonding union is an intermediate layer required to bond silicon to kovar. The pyrex bonding union is then bonded to a kovar bottom cavity. Kovar is used in the bottom cavity because it has a higher thermal conductivity than pyrex. The blue arrow shows the gas flow through the stage inlet, from the cold to hot side of the aerogel transpiration membrane, through the cavities and out the stage exhaust. The design employs a planer configuration to be consistent with MEMS manufacturing capabilities. The internal 180° turns that the gas undergoes (2 per stage) decrease the gas conductance through the stage, but not noticeably, relative to the gas conductance of the aerogel transpiration membrane, except for the low-pressure stages. Similar stages can be added in series to achieve the required number of stages for the desired pressure ratio. Pyrex Top Cavity Silicon Thermal Guard Aerogel Transpiration Membrane Pyrex Bonding Union Kovar Bottom Cavity Figure 20. Exploded View of a Single Stage MEMS Radiantly Driven Knudsen Compressor 35 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 3 Knudsen Compressor Performance Model The candidate micro/meso-scale pump applications detailed in Chapter 1 were used to provide estimates for the required mass, volume, power, pressure ratio, and throughput for Knudsen Compressors. A performance model, previously developed and validated,9 was updated and improved to estimate performance parameters for a variety of different stage configurations. The results helped to determine the suitability of the Knudsen Compressor for several candidate applications. The Knudsen Compressor Performance Model was also used to perform transpiration membrane energy optimizations for several configurations. A large number of physical variables are required to adequately describe a Knudsen Compressor, even at the most basic level, requiring a computational model to estimate the performance of competing Knudsen Compressor designs. The updated computational model discussed in this chapter was written in a Fortran 90 code. 3.1. Knudsen Compressor Performance Model Overview The Knudsen Compressor Performance Model treats each stage of a Knudsen Compressor cascade individually. As discussed earlier, each stage is composed of two parts, the transpiration membrane (capillary section) and the connector section. Both the transpiration membrane and pump body (connector section) are important in Knudsen Compressor designs, but the transpiration membrane plays the dominant role in defining the Knudsen Compressor’s performance. It is the main focus of the current Knudsen Compressor Performance Model. The physical models, for both gas flow and transpiration membrane properties, are shown in Figure 21 for both the aerogel and glass microsphere transpiration membranes. The physical model for the thermal properties of the aerogel transpiration membrane is detailed in Section 3.5 while the model for the glass microspheres transpiration membrane is detailed in Section 4.4. 36 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Capillary Section Connector Section Figure 21. Knudsen Compressor Stage Models The capillary section is modeled as a disc with a certain fraction, II, of its cross-sectional area taken up by capillaries, all with a mean effective pore radius, Lr, and a thickness, Lx. The capillary section is followed by the connector section that is composed of a single capillary with a radius LR and a length Lx. For all of the configurations considered in this study the radius of the capillary section disc is the same as the connector section radius, LR . The temperature is assumed to be uniform over any cross-section parallel to the membrane face (a one dimensional thermal model). The cold-side temperature (physically the thermal sink temperature or the temperature of the pump body) is assumed constant for an entire cascade. The effects of the thermal guards, described in more detail in Chapter 4, on the gas flow and transpiration properties have not yet been included in the model. The thermal guards have pore radii that are orders of magnitude larger than the pores in the aerogel, for all the configurations described in this work, and have small temperature differences across them so their effect is likely to be small except near the low-pressure limit (10s of mTorr). Predictions made using the performance model detailed in this chapter indeed indicate that the effects of the thermal guards could not be experimentally measured in the current investigations, so it is warranted to neglect them in the current Knudsen Compressor Performance Model. Modeling the transpiration membrane as a dense array of straight capillary tubes, with circular cross- sections, with a certain fraction of the cross-sectional area of open tube, is physically unrealistic. The experimental membranes have been more akin to thin, low-density layers of granular materials with a 37 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. distribution of pore sizes. The first membranes7 were standard Supor-100, polyethersulfane filters. The most recent membranes are aerogel structures.8 ,9 For both types extensive comparisons have been made to transitional rarefied flow characteristics and to the maximum thermomolecular pressure differences as a function of pressure. The remarkable result is that the theoretical predictions from the capillary array model can be adjusted to fit quite satisfactorily all of the observed characteristics, by using a self-consistent set of; an effective capillary radius, and membrane porosity. The details of the comparisons have been presented in previous publications.7 ,8 ,9 The conclusion is that while the model membranes bear little physical resemblance to the actual membranes, the model captures the essence of the observed behavior and is thus extremely useful for design and investigative studies. These comments apply to flows up to 1 atm. pressure and likely will be shown to be valid to pressures as high as 10 atm, providing the capillary radius remains larger than a few nanometers. The physical stage characteristics (pp o r, fc a rb o n , Lx, Lx, and LR ) and the incident radiation flux (tjw) are individually defined for a set number of stages (N) in the Knudsen Compressor Performance Model. Performance calculations can be completed for Knudsen Compressors based on bulk aerogel, perforated aerogel, and glass microsphere bed transpiration membranes. The working gas specie and the gas pressure on the low-pressure side of the initial (lowest pressure) stage is specified as an input. The Knudsen Compressor Performance Model is not currently capable of making predictions for multiple gas species. The model described in this section is used to calculate the pump characteristics for one point on the pumping curve, corresponding to a single set of specifications for gas throughput and pressure difference. The location on the pumping curve is identified through the specification of the mass flow rate for the initial stage. A modified code allowing the detailed investigation of the Knudsen Compressor performance over the entire pumpdown curve is described in Section 3.2. A preliminary step of the Knudsen Compressor Performance Model is to calculate the mean effective pore diameter for transpiration membranes of each stage, which can be specified individually by specifying the aerogel density for each stage. The cascade performance calculation first evaluates the 38 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. lowest pressure stage because it typically has the lowest maximum flow rate for a given radiant flux. The working gas properties for the first stage, corresponding to the input gas specie, number density, and the cold side temperature, are then calculated. A more accurate method would be to use the average properties for the stage, but this requires an iterative process because the temperature and pressure differences across the membrane are not yet known since they are what are being calculated. This approximation introduces small errors for the calculations described in the present work because of the small relative temperature and pressure differences experienced across a stage. The temperature difference across the transpiration membrane stage is then calculated based on the incident radiant flux to the exposed membrane surface, the membrane properties, and the gas properties. The corresponding maximum pressure difference and maximum gas flow rate are then calculated for the first stage. The actual pressure difference across the stage is set as a fraction, k (an input), of the maximum pressure difference. Setting the fraction of the maximum pressure difference defines the flow rate for the initial stage and, through conservation of mass, the entire cascade. The same process can be used to estimate the pressure loss and throughput loss due to the reverse transpiration effects in the connector section, but this additional complexity was not required for the design and experimental cases described in this work. The exhaust pressure from the initial stage is set as the input pressure for the second stage and the entire process is repeated for the specified number of stages. The flow rate produced by each subsequent stage is matched to the flow rate of the initial stage and the corresponding fraction of the maximum pressure difference is then calculated for the following stages based on the flowrate. 3.2. Knudsen Compressor Pumpdown Model An additional Knudsen Compressor Performance Model code was constructed to model the entire pumping curve for a given Knudsen Compressor cascade operating between two known volumes. Many potential Knudsen Compressor applications require repeated pumpdowns making it important to understand the performance of the Knudsen Compressor over an entire pumping cycle, including both the pumpdown and venting process. The single point optimized designs detailed in section 8.1 39 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. provide a design that minimizes the energy required to operate at a given pumping curve condition, but further investigations are required to determine the effect of the single point optimization on the entire pumping curve. An updated formulation was required for the pumping curve model because the nested iterative processes used in the technique described above led to instabilities when implemented into a pumpdown analysis, typically near the maximum pressure ratio for a high pressure ratio cascade. The single pumping curve condition formulation described above calculated the throughput produced by the initial stage and then matched the throughput for the subsequent stages by adjusting the stage k. The surrounding stages were not considered when calculating the throughput produced by each individual stage. This model essentially assumes that the flow produced by each stage is stopped at the start of the next stage and then the next stage produces the same flow. A different cascade formulation was used that calculates the throughput addition provided by a single stage as if the other stages were not on, but in this case considering the conductance of the other stages. The total throughput is then given as the sum of the throughputs produced by each individual stages as given by N A T = $ > ( = 1=1 Where C totai is the total conductance for the cascade, Qt and Qp are the temperature gradient flow coefficient and the pressure gradient flow coefficients, respectively, for the transpiration membrane and Qtc and Qp c are the temperature gradient flow coefficient and the pressure gradient flow coefficients, respectively for the connector section. Without any additional assumptions it would be difficult to implement this technique and calculate the k for each individual stage. The single pumping curve condition formulation provided satisfactory results, by comparison with experimental results described in Chapters 6 and 7, under the assumption that all stages produced the same throughput. This allows us to make the corresponding assumption with the current formulation that all stages produce the same fraction of the net throughput at any given pumpdown condition. This assumption allows the fraction of the maximum pressure difference, k , for each stage to be calculated. 40 z r ^ total i khT AT Q, AT T O avf* z-stn ( 12) Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. An additional benefit of using the new formulation is that it allows any combination of stages to be turned off at any time during the process allowing the calculation of the vent up portion of the pumpdown process as well. The new formulation still does not provide accurate calculations for cascades of large numbers of stages or with large temperature differences across each stage because of the necessary assumptions. The pumpdown formulation code starts at a time, t=0, with the condition of no pressure difference and maximum net throughput. At this condition all of the stages are at the same pressure and the throughput for each stage can be calculated. The code then calculates the pressure difference across the pump that builds up over a specified time step, sized to be small compared to the estimated time constant for the process. The pressures for the individual stages in the cascade are then updated. The throughput at the new pressure difference is calculated and the process repeated to provide the entire pumpdown curve. Comparisons are made between the pumping curve predictions made from the Knudsen Compressor Performance Model and the experimentally measured pumping curves in Chapter 7. There is satisfactory agreement for all of the cascades studied in this investigation. 3.3 Models for Aerogel Physical and Optical Properties The Knudsen Compressor Performance Model’s code begins by calculating the properties for the transpiration membrane of each stage. The previously developed performance model code was only valid for Knudsen Compressors with transpiration membranes made from a “typical” aerogel.9 The process for estimating the properties of aerogel transpiration membranes is described in this section, while the process for estimate the properties of glass microsphere bed membranes is described in Section 4.4. The aerogel transpiration membrane model makes predictions for silicon aerogel that can be doped with a small amount of carbon (<15%). The aerogel density and carbon dope fraction are inputs for the computational model. They can be set individually for each stage in a Knudsen Compressor cascade. Aerogel properties are heavily dependent on aerogel density, carbon dope fraction and even the manufacturing process. The method for calculating aerogel properties is 41 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. therefore only approximate since it was compiled from various sources, but it allows an understanding of the general scaling of aerogel properties and the capability of making Knudsen Compressor performance estimates. Aerogel is typically described as a porous network of beads of particles chained together in a random network as shown in Figure 22.3 3 M«woparosity 2 T in * o 50 n m Mleroparoelty * Z nro Figure 22. Aerogel Microstructure Schematic There are two characteristic length scales that are defined in describing the microstructure of aerogels. The first length scale is the effective primary particle diameter, da. This property represents the typical diameter of the solid, Si02 for silicon aerogel, beads in the random lattice. The aerogel primary particle diameter can be measured using electron microscopy. It is heavily dependent on the specific aerogel manufacturing technique, making it difficult to estimate the primary particle diameter for different conditions analytically, but is usually assumed to be between 2 and 5 nm.3 2 An average aerogel primary particle diameter of 3.5 nanometers is used for all of the calculations described in this report. The second length scale defined for aerogels is the mean effective pore diameter, Lr. Aerogels are an open lattice porous material, but it is still useful to define a mean effective pore diameter to use in gas conductance and thermal conductivity calculations. It has been shown that, for silicon based 42 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. aerogel, that the mean effective pore diameter of the aerogel transpiration membrane can be given by3 7 Where pp o r is the density of the aerogel and the solid material density, pt, is the density of solid Si02, 2.57 g/cc. Figure 23 shows the mean effective pore diameter predicted by this model as a function of the silicon aerogel density for various primary particle diameters, ft also shows the characteristic length scale ratio. 1.E-06 a da = 2nm O da = 3.5nm x da = 5nm ♦ Lr/da 1.E-07 1 & 1.E-08 - 1.E-09 - 1.E-10 0.001 0.01 0.1 p a (g/cc) Figure 23. Aerogel Mean Effective Pore Diameters The silicon aerogel density defines the characteristic length scale ratio, Lr/da, for the aerogel. As the aerogel particle diameter increases for a constant aerogel density the pore size must increase by the same factor to compensate. As the mean effective particle diameter increases, for a constant aerogel density, there are less aerogel “particles” and the length scale between particles must increase, which increases the effective aerogel pore diameter. An aerogel primary particle diameter of 3.5nm is assumed in the later calculations with the understanding that it has an associated uncertainty. This uncertainty results in a corresponding uncertainty of a similar magnitude in the aerogel pore diameter. The calculated mean effective pore radii for aerogels encountered in this study range from 20. lnm, for 80mg/cc silicon aerogel, to 15.1 nm, corresponding to the 120 mg/cc silicon aerogel. The estimated 43 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. range of effective pore radii from simply the uncertainty in the primary particle diameter is 11.1 to 27.9 nm for the 80 mg/cc silicon aerogel and 8.6 to 21.6 nm for the 120 mg/cc silicon aerogel. While this range is probably highly exaggerated, it does give some idea of the magnitude of the uncertainty in this model. The porosity of the aerogel transpiration membrane is given by3 8 n = l - ^ ~ (14) P, The aerogels used in this study ranged in porosity from 96.9% to 95.3% corresponding to the 80mg/cc and 120 mg/cc aerogel, respectively. Another parameter that is useful in describing aerogels is the specific surface area or amount of surface area per unit mass of the aerogel. The specific surface area for the type of silicon aerogel used in this study has been previously experimentally measured using a gas adsorption analyzer.3 4 A summary of the experimental results and the best linear curve fit are shown in Figure 24. 90 0 S s — 2 .3 5 2 8 p P o r + 4 9 6 .6 3 80 0 700 6 0 0 - „ -5 0 0 - E r 4 o o - 30 0 - 200 100 100 150 Figure 24. Aerogel Specific Surface Area3 4 The experimental measurements of the specific surface area obviously contains a great deal of uncertainty. The aerogel specific surface area data is also only available over a limited aerogel 44 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. density range. At veiy high aerogel densities there are many aerogel particles, providing a limited number of accessible pores to the gas. The specific surface area should trend towards zero as the density approached the solid density of the material. This trend is not yet seen in the data provided here implying that this trend will not be captured in performance calculations employing this model. The data is only strictly appropriate over a limited range of aerogel densities, pp o r = 40 mg/cc to 140 mg/cc. The linear curve fit is used in the performance model. This limited range, however, includes the aerogel densities encountered experimentally in this study and the optimal aerogel densities identified in this study. In Figure 24 the experimental measurements clearly show the uncertainty in this model. Aerogel optical properties are dependent on the aerogel manufacturing process, the aerogel density, and level of the carbon doping. The aerogel optical property of interest for the radiantly driven Knudsen Compressor is the absorption coefficient, K, which quantifies how opaque the aerogel is to the incident radiation. It is possible to make only rough estimates for the absorption coefficient of the aerogel for various aerogel densities and carbon dope fractions based on limited published information. Effects due to changes in microstructure associated with different manufacturing techniques are not represented in the Knudsen Compressor performance model indicating that the current performance model predicts average optical properties (over different microstructures). In general the absorption coefficient of a porous material can be represented as a product of the temperature dependent specific extinction coefficient and the material density as shown by K = C(T )Ppor (15) The temperature dependent specific extinction coefficient, c(T), for various levels of carbon doping of silicon aerogel is shown, recreated from previous work, in Figure 25.3 9 The Knudsen Compressor performance model interpolates between the published data points to estimate the specific extinction coefficient for different aerogel types. 45 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 12 0 i 1 0 0 - _ 8 0 - o> .x: ^ 6 0 - ° 4 0 - 2 0 - n - ♦ 0% Carbon ■ 5% Carbon • 10% Carbon • i • i • i • • • • • • • • ■ • ■ : : ♦ * . . " ■ ■ " ................................................... ♦ * ♦ ♦ U 1 1 1 1 1 1 1 0 5 0 100 1 5 0 2 0 0 2 5 0 3 0 0 T (K ) Figure 25. Temperature Dependent Specific Extinction Coefficient for Carbon Doped Aerogels3 9 Figure 26 shows the absorption coefficients for various carbon dope fractions of silicon aerogel calculated from this model. The aerogel used in this study, pp o r = 80 mg/cc with 8% C and pp o r = 120 mg/cc with 8% C, have absorption coefficients of 6900 1/m and 10,300 1/m respectively. 5 0 0 0 0 4 0 0 0 0 'g 3 0 0 0 0 20000 10000 0 x 0% Carbon x 4% Carbon + 8% Carbon o 12% Carbon 9 * X a . v x x * X » » ^ X - x * V , X X O X x * x * * * * * * * * * * * X X * 1 00 2 0 0 3 0 0 p (m g /c c ) 4 0 0 5 0 0 Figure 26. Calculated Aerogel Absorption Coefficients 3.4 Transpiration Membrane Temperature Distribution Analysis The first step taken by each stage performance calculation in the Knudsen Compressor Performance Model is to estimate the temperature difference maintained across the transpiration membrane by the 46 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. incident radiant flux. Modifications were required to the previous version of the Knudsen Compressor Performance Model to accommodate radiant heating configurations. Previous generations of Knudsen Compressors were heated by passing electrical current through a thin film resistive heater deposited on the perforated silicon thermal guard on the hot side of the aerogel.9 The previous performance model employed a “typical” aerogel thermal conductivity and neglected outward cooling mechanisms. The Knudsen Compressor configuration investigated in this study employs radiant heating requiring that the optical properties of the aerogel be incorporated into the performance model. The model was also updated to predict; the variation of thermal conductivity with aerogel density, carbon dope fraction, and gas pressure; include outward cooling models, and model the distributed absorption of the incident radiant energy. The temperature difference across the transpiration membrane is modeled using a one-dimensional model as shown in Figure 27. L ig h t S o u r c e x = 0 x=L ^ ^rad 1 4 ^ ^ co n / / / Sample i^ kt = kr + ke + ks Th Cold Sink Figure 27. One Dimensional Temperature Difference Model Schematic A radiant flux is incident on the free side, x=0, of the transpiration membrane. The radiant flux is absorbed throughout the transpiration membrane. The cold side of the membrane, x=Lx, is held at a constant temperature due to its intimate thermal contact with the cold sink (physically the Knudsen Compressor body). The absorbed energy can either escape outward through the x=0 surface by gas conduction and outward radiation transport or pass through the aerogel transpiration membrane to the cold sink by gas conduction, solid conduction, and radiation. The outward cooling mechanisms represent inefficiencies because only energy traveling through the transpiration membrane maintains a temperature difference across it. 47 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The temperature difference maintained across the transpiration membrane is calculated using an iterative process. The first step is to assume a hot side transpiration membrane temperature, Th. The total aerogel thermal conductivity corresponding to the average of Th and Tc is then calculated. The outward thermal fluxes, due to gas conduction and radiation, are calculated based on the assumed hot side temperature. Outward radiation cooling from within the aerogel is not yet included in the model by assuming that all of the outward radiation is from the hot side temperature. The outward cooling flux is maintained by the absorbed radiation flux that is being absorbed throughout the transpiration membrane. The radiant flux traveling through an optically thick membrane at a penetration depth x is given by Lambert’s exponential absorption law, (16) Where (Iw is the incident radiant flux. The depth within the transpiration membrane that yields the same absorbed flux as the total outward cooling fluxes is given by In f j. '' t <Pou, \ 'P in e J (17) l llldA ^ Where (Iw is the total outward cooling flux. The temperature profile from the hot side of the transpiration membrane, x=0, to the location of the maximum temperature in the transpiration membrane, xT m a x , due to the exponential radiation absorption and the average total thermal conductivity, kt, is given by T(x) = Th + — {/>ou‘ V ' h K k ,y M k. (18) Where kt is the total thermal conductivity of the transpiration membrane. The temperature profile from the location of the maximum temperature, x=xT m a x, to the cold side of the aerogel transpiration membrane, x=Lx, is given by T(x) = Tm ax ( * - x rmax) + ! ^ ( e -&- » -e-**) (19) 48 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 28 shows the predicted temperature profile for the aerogel transpiration membrane used in the 15 stage Knudsen Compressor at atmospheric pressure of air for various incident radiant fluxes. 7 5 0 70 0 6 5 0 6 0 0 ~ 5 5 0 h 5 0 0 4 5 0 4 0 0 35 0 30 0 0.0 0 E + 0 0 5.0 0 E -0 4 1.00E -03 1.5 0 E -0 3 2 .0 0 E -0 3 x (m) *x X v ■ 50 mw/cmA 2 ♦ 100 mw/cmA 2 ▲ 500 mw/cmA 2 x 1000 mw/cmA 2 Xv AA A. X Xx A Aa» X Xv Aaaa£ x> ------------------- Figure 28. Transpiration Membrane Temperature Profiles It appears that the maximum temperature occurs at roughly 1/8 of the way through the aerogel transpiration membrane for the entire range of incident fluxes. The initial increase in temperature represents an inefficiency because it leads to reverse transpiration in the membrane. The total stage pressure difference and gas throughput are calculated using the temperature difference from the hot side to the cold side of the transpiration membrane. 3.5 Thermal Conductivity Analysis Models of carbon doped silicon aerogel’s thermal conductivity have been created by others in an effort to minimize the total thermal conductivity of aerogel for applications in thermal insulation layers.4 0 ,4 1 These models separate the total thermal conductivity into three independent components that represent the thermal conductivity due to gas conduction (kg), solid conduction (ks ), and radiation transport (kr) as shown by k,=ks +kg +kr (2 0 ) 49 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. It has been previously shown that the thermal conductivity due to gas conduction will be decreased by adding the solid material of the aerogel, which hinders the motion of the particle through the porous material.4 2 The thermal conductivity due to gas conduction between two plates is given by k \+2PKn ) 3 and s are given by . . *’ L (21) (22) y +1 a 4 where kg,0 is the thermal conductivity for the gas under continuum conditions, Kn is the Knudsen Number, a is the accommodation coefficient and y is the ratio of the specific heats. The thermal conductivity defined in Equation 21 is an effective thermal conductivity. It depends on the plate spacing through the Knudsen Number. The expression provides the correct asymptotes for both the free molecule and continuum limits and has been shown to provide adequate values for transitional cases. The thermal conductivity for a continuum gas is given by4 2 kgc =0.461-£wcfcvAm (23) Where n is the number density of the gas, c1 is the mean thermal speed of the gas molecules, cv is the constant volume specific heat, and X m is the mean free path of the gas particles. Adding the solid structure of the aerogel to the gas decreases the thermal conductivity by lowering the mean free path, and hence the Knudsen Number, of the gas molecules as given by4 2 A- = h s 7 “ (24> j r a 42n7id^ + 2 , S r p o r * 411 Where dg is the molecular diameter. Adding the solid material increases the second term in the denominator in Equation 24, which lowers the mean free path, lowering the thermal conductivity. It has been experimentally shown that the solid conduction fraction of the thermal conductivity for silicon aerogel can be approximated by4 3 =cslPX (25) 50 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where c3 1 is a constant for a given aerogel type and a a is roughly 1.4 - 1.6. Simple expressions can be written for the radiation component of the thermal conductivity as shown by4 0 These expressions are only approximate, but allow the total thermal conductivity for different silicon aerogel densities and carbon dope fractions to be calculated. 3.6 Outward Cooling Models The model described in Section 3.5 can be used to estimate the amount of energy that is traveling through the aerogel transpiration membrane for a given temperature difference. Typical total thermal conductivities encountered in this study are around 10-15 mw/mK. Because of this low thermal conductivity and the nominal aerogel transpiration membrane thickness of 2mm two outward cooling mechanisms, gas conduction from the free aerogel surface and outward radiation transport, become important when modeling the thermal properties of the transpiration membrane. The outward radiation flux from a solid surface is given by Where er is the emissivity of the surface and T^b is the ambient temperature of the surroundings. This is clearly a simplification for porous materials, but the distributed emission from within the porous material has not yet been considered in the model. The gas conduction from the free surface may transition to free convection transport in cases with large transpiration membrane areas (>lcm2 ), high pressures (>100s of Torr), and high temperature differences (>50K), but this effect is not included in the current thermal model because of the (26) where (27) (28) 51 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. difficulty in predicting the location of the transition. The thermal flux due to continuum gas conduction between two plates is given by =kg,c^ (29) Where AX is the spacing between the two plates. The free molecule thermal flux between two plates is <30) An analytical fit that has the correct asymptotes used for transitional thermal flux between two plates is given by < t > , r = *co n ‘ (31) ,r 1 + lfiKn Where p is given from Equation 22. The continuum gas conduction from a free surface is defined in a similar manner by4 4 (32) Where A is the surface area and SF is a shape factor, which for a free surface is given by SF = ^ for Li > L2 (33) Inf 4 — \ ) Where Li and L2 are the length scales of a rectangular surface. The free molecular thermal transport from a free surface to the surrounding gas is given by ^fin.fi = - Ta m b ] (34) V IW T am b It is reasonable to then provide a transitional function that fits both asymptotes by <35) 52 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where the value of % is adjusted to provide the correct fit to the free molecule value, q is 3.2 for N2 and 2.1 for He. Figure 29 compares the outward cooling mechanisms: gas conduction from the free surface and radiation, to the total inward cooling flux for the nominal aerogel stages used in this investigation (pp o r = 80mg/cc, fc a rb 0 n = 8%, Lx = 2mm) verses pressure for N2 with an incident radiation flux of 100 mw/cm2. 50 50 4 0 ■ E 30 o | 2 5 - •=-20 - 30 • Outward Gas Conduction ■ Outward Radiation A Inward Total DT (K) 10 - 4 0 0 P (Torr) 6 0 0 8 0 0 200 Figure 29. Relative Membrane Cooling Fluxes The relative importance of the different cooling mechanisms changes for different operating conditions, but from this analysis it is clear that all of the cooling mechanisms, conduction through the membrane, gas conduction outward into the surroundings, and radiation transport outward can all be of the same magnitude and none of them can be neglected. The gas conduction outward and the radiation outward provide no temperature difference across the membrane and represent losses. For these conditions between about 25% and 45% of the absorbed energy travels through the membrane, providing the temperature difference. Further optimization of the membrane towards lower total thermal conductivities will have limited effect on the overall performance of the pump because a large fraction of the absorbed thermal energy is being lost outwards. Further performance increases may be gained by reducing the outward cooling fluxes in later designs. 53 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.7 Gas Conduction Analysis The gas conductance for gas flows through porous media is analogous to the conductance in electronic circuits and is given by4 5 C = V ^ - (36) AP where the volume flow rate, V , is analogous to the current in electronic circuits and AP/Pa v g is analogous to the voltage in electronic circuits. The gas conductance for long tubes is given by (37) 1 The gas conductance for gas flow through an aperture is given by C „= C ma+(C ,-C m a)j l-1 .0 5 “2* " 'j (38) Where the gas conductance for isentropic flow through an aperture is given by C | = m A P 2r (x_x ^ 1 /2 _r-\K p ) The gas conductance for free molecule flow through an aperture is given by (39) Cma= A J ^ - (40) V 2 n-m An approximation for the gas conductance for a finite length tube with correct long tube and aperture asymptotes is given by c " = f e + ^ } (41) The finite length tube conductance expression is required for low-pressure transpiration membranes using perforated aerogel. Figure 30 compares the finite tube length model flowrate to the long tube model flowrate and lists the aperture flowrate for the conditions of Ta v g =300K, AT=80K, Pa v g =100 Pa, Lr=5xl0'7 m, N2, A=lcm2. 54 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 .E-02 -i X Finite Tube Long Tube 1.E-03 - Aperture 1.E-04 1 .E-05 - m 1.E-06 ^ 1.E-07 1.E-08 - 1.E-09 - 1.E-10 0.0001 0.001 0.01 0.1 D/L 10 100 Figure 30. Tube Formulation Flow Rates The long tube and finite tube formulations provide the same flowrate for diameter to length ratios under approximately 0.1. At diameter to length ratios above 10 the aperture value matched the finite tube length value. Intermediate diameter to length ratios will require the finite tube length gas conductance formulation. 3.8 Transpiration Analysis One figure of merit for the performance of a transpiration membrane is the thermomolecular pressure difference (TMPD), which is the normalized maximum pressure difference produced by a normalized temperature difference as given by The Knudsen Compressor Performance Model treats the transpiration membrane as a substrate with an array of parallel cylindrical holes, all with the same equivalent radius, Lr, through it. The pressure difference and net mass flow rate through a transpiration membrane modeled in this way are given by TMPD = (42) (43) 55 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Where Q t and Qp are the thermal gradient and pressure gradient driven flow coefficients4 6 ’ 4 7 ,4 8 ,4 9 , respectively. The parameter k , the fraction of the maximum pressure difference, ranges in value from 0 to 1 and represents the operating point on the pumpdown curve. The maximum flow rate (AP = 0) corresponds to k = 0 that would occur at the beginning of the evacuation of a chamber, and k = 1 represents the maximum pressure difference condition (no net flow rate) that occurs when a chamber has been evacuated and is being maintained at the minimum sustainable pressure of the pump. Similar expressions can be written for the pressure difference and flow rates in the connector section, but are neglected in the current study due to the low Knudsen Number (Kn<.01) experienced in the connector section of the compressors throughout the study. 3.9 Effects of Carbon Doping Silicon Aerogel Transpiration M embranes Doping silicon aerogel with carbon has several effects on the overall performance of an aerogel based transpiration membrane. Carbon doping at low levels (<15%) has very little effect on the gas conductance and transpiration properties of the aerogel transpiration membrane and no modifications to the Knudsen Compressor Performance Model are required. However, it has several effects on the thermal properties of the aerogel transpiration membrane. The concept of doping silicon aerogel with small amounts of carbon was originally derived to increase the absorption coefficient of the aerogel in the wavelength range of 3 - 8 pm, greatly reducing the radiation transport through the aerogel and the total thermal conductivity.4 0 Doping with carbon, however, also increases the solid conduction fraction of the energy transported through the transpiration membrane due to the stronger carbon bonds. Whether the net effect is to reduce or increase the total thermal conductivity depends on the aerogel density, level of carbon doping, and the properties of the gas that is filling the pores. Doping silicon aerogel with carbon has two effects on the solid conduction component of the transpiration membrane’s thermal conductivity. Adding carbon causes the aerogel to shrink due to the increased bond strengths. This tends to increase the density of the aerogel above its nominal pure 56 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. silicon value. Adding carbon also tends to increase the solid conduction due to the participation of the carbon particles in the energy transport. The exponent shown in Equation 25 is not altered by adding carbon to the silicon aerogel. The effect of the carbon is seen in both the density and the coefficient. The density effect is given by4 0 P * r = ^ F ( l + / « * J (44) < r .,40 The coefficient in front of the exponential is modified by k . ) (45) . | , * ^s,carbon J carbon « ^ s,silicon , Where fc a rb o n is the carbon dope fraction, ps ijP o r is the density of the silicon aerogel, C is the shrinkage factor, kS ) C a rb o n is the thermal conductivity of solid carbon, and kS i 3 ,ilc o n is the thermal conductivity of solid silicon. The effect of adding carbon to the optical properties and hence the radiation transport component of the total thermal conductivity is included through the modification of the specific extinction coefficient as shown in Figure 25. 3.10 Representative Optimizations It is useful at this point to conduct some optimization calculations for the aerogel transpiration membrane to understand the rough effects of changing different parameters on the transpiration membrane performance and to choose an initial optimized aerogel for the experimental portion of the investigation. Different transpiration membrane optimizations can be realized depending on the specific configuration and the efficiency parameter of interest. One optimization possibility is to minimize the total thermal conductivity of the aerogel membrane by adjusting the aerogel density and carbon dope fraction. This technique was used in previous work in determining the optimal aerogel for insulation purposes.4 0 Figures 31 and 32 show the total thermal conductivity for various levels of carbon doped silicon aerogel for air pressures of 760 Torr and 1 Torr, respectively. 57 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. -■ Silicon A ero g el • 4% Carbon Doped Silicon Aerogel A — 8% Carbon Doped Silicon Aerogel A — 12% Carbon Doped Silicon Aerogel SeriesS 0.01 0.1 Aerogel Density (g/cc) 0.001 0.01 Figure 31. Total Aerogel Thermal Conductivity at P = 760 Torr 0.01 - Si Aerogel 4% C 8% C 12% C 0.001 0.001 0.01 0.1 Aerogel Density (g/cc) Figure 32. Total Aerogel Thermal Conductivity at P = 1 Torr The dashed lines correspond to aerogel densities when the aerogel can no longer be considered optically thick indicating that significant errors will appear in the calculation for kr and thus for kt. At high aerogel densities the thermal gas conduction and radiation components of the thermal conductivity are decreased due to the solid structure of the aerogel. The solid component of the thermal conductivity is, however, increased by increasing the amount of solid material. As the aerogel density is decreased the solid conduction component of the thermal conductivity decreases and the gas conduction and radiation components increase. At low aerogel densities the total thermal 58 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. conductivity is due mostly to the radiation and gas conduction transport. There is, therefore, some intermediate aerogel density that will provide a minimum thermal conductivity for a given gas pressure. The minimum thermal conductivity for an atmospheric pressure of Nitrogen, 15.7 mw/(mK), occurs for an aerogel density of 100 mg/cc and carbon dope fraction of 8%. The minimum thermal conductivity for a pressure of 1 Torr of Nitrogen, 4 .5 mw/(mK), occurs for an aerogel density of 50 mg/cc and carbon dope fraction of 8%. The total thermal conductivity at 1 Torr is less than for 760 Torr because of the decrease in the gas conduction component of the thermal conductivity. The minimum thermal conductivity for lower gas pressures occurs at lower aerogel densities because of the decrease in the gas conduction component of the total thermal conductivity, which becomes relatively more important at low aerogel densities. Knudsen Compressors can be designed with varying aerogel densities for different stages in the cascade to optimize each stage individually under thermal conductivity considerations. Under power consumption considerations it is more useful to minimize the power required per unit throughput of the pump instead of simply the membrane thermal conductivity. This type of optimization requires consideration of not only the total thermal conductivity, but also the gas conductance through the membrane. The models for the outward cooling mechanisms employed in the Knudsen Compressor Performance Model do not depend on the aerogel density and carbon dope fraction. The energy efficiency described in this section considers only the energy conducted through the transpiration membrane. The energy efficiency, power per unit throughput for resistive heating (the optimal heating method where all of the thermal energy goes through the entire membrane thickness) is shown at a pressure of 760 Torr in Figure 33. The minimum energy consumption (maximum energy efficiency) occurs at lower aerogel densities than for the optimized thermal conductivity because the energy efficiency also involves the gas conductance, which increases with decreasing energy density. The maximum energy efficiency for an atmospheric pressure of air, 2.5E- 19 J/molecule, occurs at an aerogel density of 20 mg/cc and a carbon dope fraction of 8%. 59 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. E-16 n ■ ■ Silicon Aerogel -•----- 4% Carbon Doped Silicon Aerogel — 8% Carbon Doped Silicon Aerogel -*— 12% Carbon Doped Silicon Aerogel InvalidO 1E-17 - E-18 : o> E-19 0.01 0.001 Aerogel Density (g/cc) Figure 33. Resistively Heated Energy Efficiency at P = 760 Torr. For the radiant heating case studied in this work it is also important to consider the exponential absorption and distributed heating effects. Figure 34 shows the energy efficiency for the distributed absorption configuration. E-16 -■ Silicon Aerogel -•----- 4% Carbon Doped Silicon Aerogel ■ A— 8% Carbon Doped Silicon Aerogel -•— 12% Carbon Doped Silicon Aerogel Invalid SI E-17 - E-18 - O ) E-19 0.001 0.01 0.1 Aerogel Density (g/cc) Figure 34. Radiant Heating Energy Efficiency for P = 760 Torr The maximum energy efficiency, 3.7E-19 J/molecule, occurs for an aerogel density of 60 mg/cc and a carbon dope fraction of 8%. The distributed energy absorption configuration has a lower energy 60 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. efficiency than the surface heating technique due to the distributed absorption inefficiency described above. The maximum efficiency occurs at a higher density because the amount of energy absorbed by radiant heating increases with energy density. Further device optimization is discussed in Chapter 8 when describing the proposed future designs. The nominal aerogel chosen for the experimental investigations in this work is a silicon aerogel with a density of 80 mg/cc and a carbon dope fraction of 8%. The higher density aerogel was chosen for its increased strength over the 60mg/cc aerogel. 61 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 4 Low Pressure Transpiration Membrane Considerations Knudsen Compressors have been suggested as candidates for both micro/meso-scale gas roughing pumps1 0 (760 Torr to 10 mTorr) and micro/meso-scale gas compressors (latm to ~ 10 atm)1 1 . Initial experimental versions of the Knudsen Compressors, operating at pressures near atmospheric pressure, used 520pm thick sheets of low-density silicon aerogel as the transpiration membrane.9 Aerogel was chosen for its high porosity (>95%) and low thermal conductivity (17 mW/(m*K) at atmospheric pressure). Recent results from volume and power optimization studies indicate that it is most efficient to operate the Knudsen Compressor such that the gas flow through the transpiration membrane has a Knudsen number of roughly one.3 1 The typical silicon aerogel used in the previous work happened to have the right mean effective pore diameters for applications at around atmospheric pressure. Many applications of the Knudsen Compressor operating as a gas roughing pump have input pressures of 10s of mTorr, requiring transpiration membrane pore diameters of millimeters under energy efficiency considerations. Although aerogel can be made with a variety of pore diameters by adjusting the aerogel density, mean effective pore diameters of the millimeter scale are not possible. This section first identifies the minimum predicted operational pressure for meso-scale Knudsen Compressors under efficiency considerations and then outlines the design changes, both in the transpiration membrane and the pump body, that are required to achieve these pressures. 4.1 Low Pressure Limit Definition The practical Knudsen Compressor low-pressure operational limit was defined through energy efficiency considerations.1 0 The process begins by assuming that the Knudsen Number in the connector section must be less than that in the capillary section (optimized under power and volume considerations when Kn = 1) to minimize the reverse transpiration that occurs while the stage temperature is dropped to its initial value. This requirement indicates that, if the Knudsen Number in the capillary section is held at roughly one for energy efficiency considerations, the Knudsen Number 62 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. in the connector section must surely be held under one. The minimum operational pressure is then defined when the maximum connector section radius is defined. For a meso-scale Knudsen Compressor with a connector section radius of 1cm the minimum operation pressure is definitely greater than roughly 0.4 mTorr. Another consideration defining the low-pressure limit of the Knudsen Compressor is that the transpiration membrane must have pore Knudsen Numbers, based on the pore radius, of roughly one. The membrane must also maintain a reasonable length to mean effective pore radius ratios, Lx /Lr, for the molecules to have sufficient collisions with the walls. A nominal membrane thickness for current Knudsen Compressor realizations is 1mm. For an Lx /Lr of 8 this corresponds to an Lr of 0.125 mm. This provides a practical low-pressure pumping limit of roughly 3 mTorr. A more thorough analysis detailed in Section 8.1 indicates that the Knudsen Compressor low-pressure operational limit is probably closer to 10 mTorr, although experimental validation is still required. This minimum operation pressure would be sufficient for application for macro-scale gas roughing pumps and it is reasonable to assume that it is also acceptable for meso- scale gas roughing pumps. The minimum operational pressure for the Knudsen Compressor is inversely proportional to its characteristic dimension indicating that micro-scale Knudsen Compressors will have higher low-pressure limits. Previous Knudsen Compressors used low-density silicon aerogels, having pore diameters of roughly 40 nm, which are inappropriate for application at low pressures because of energy efficiency considerations. Two candidate transpiration membrane options for low pressures have been identified. One option for a low-pressure transpiration membrane is to use the same base aerogel, but to etch optimally sized capillaries through the aerogel with the diameters depending on the operational pressure.1 0 The capillaries can be etched by using either femtosecond laser machining5 0 or by using standard MEMS etching processes that have been optimized for working with aerogels51. Both processes have proven capable of producing characteristic dimensions down to roughly 20pm. Bulk aerogel can be made with mean effective pore diameters up to roughly lOOnm (according to the model detailed in Section 3.3), for an aerogel with a density of 10 mg/cc. Although a gap exists in available 63 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. pore diameters between bulk aerogel and etched aerogel membranes, the range of possible diameters from both of these technologies is sufficient for application as transpiration membranes in low- pressure Knudsen Compressors. Another possibility for low-pressure transpiration membranes is a membrane from an array of glass microspheres. Analytical predictions for both low-pressure transpiration membrane options are discussed in this chapter along with some initial experimental measurements of thermal transpiration properties through glass microsphere beds. 4.2. Representative Low Pressure Knudsen Compressor Special care must also be taken in the physical design of the meso-scale Knudsen Compressor when operating at low pressures to reproduce the thermal conditions assumed in the cascade analysis described in Chapter 3 to avoid a reduction in performance. A schematic of a single stage of a Knudsen Compressor designed for low-pressure applications is shown in Figure 35. Next Stage — P revious Stage Cold Thermal G uard \ ^ T ranspiration Membrane Connector Section H ot Therm al G uard Therm al A djustm ent Material Figure 35. Low Pressure Knudsen Compressor Schematic The primary pump body consideration when operating Knudsen Compressor stages at low pressures is ensuring that the gas entering the hot side of the aerogel transpiration membrane is at the hot side 64 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. temperature, Th, to avoid reverse transpiration effects and a reduction in performance. At high pressures the continuum gas above the hot side of the transpiration membrane is at the hot side temperature because of molecular collisions. At low pressures the gas above the hot side of the transpiration membrane may not be continuum making it possible for cold gas to enter the hot side of the aerogel transpiration membrane causing a reverse transpiration effect. The relative importance of the reverse transpiration effect at low pressures has not been experimentally determined making this discussion a qualitative one. One possible technique for ensuring hot gas entering the hot side of the thermal guard is to add a thermal adjustment material on all of the surfaces that have direct line of sight to the hot side of the aerogel transpiration membrane. Under free molecule flow, with fully accommodating particle surface interaction, this would ensure that all particles hitting the hot side of the transpiration membrane were already hot avoiding any reverse transpiration. At continuum conditions the thermal adjustment material would not be required indicating that at some intermediate transitional flow condition the thermal adjustment material may become advantageous over the current design with no thermal adjustment material. Additional energy would be required to maintain the thermal adjustment material at an elevated temperature making experimental measurements and trade studies required to determine the quantitative possibilities of the thermal adjustment material. The other features of Knudsen Compressor stages designed to operate at low pressures would require no major modifications from stages designed to operate at high pressures. 4.3. Etched Aerogel Transpiration M embranes One candidate low-pressure Knudsen Compressor transpiration membrane material is perforated aerogel, made by etching optimally sized capillaries through an aerogel substrate. Two different processes have been demonstrated, by others, that can be used to etch holes though aerogel: laser machining and aerogel MEMS processes. Laser machining of aerogel is a proven technology that can produce feature sizes down to roughly 20p.m.5 0 Aerogel MEMS processing techniques, including pattern etching, have also recently been demonstrated to have similar capabilities.5 1 Further 65 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. investigations are required to determine which of these techniques are more advantageous, although at an initial glance it appears that the parallel capabilities of MEMS processing techniques would be quite an advantage over the laser machining process which would etch each hole individually. The Knudsen Compressor Performance Code was used to make a comparison of the characteristics of a Knudsen Compressor cascade based on a 8% carbon doped low-density silicon aerogel with one based on a similar membrane with optimized holes etched through it and the results are shown in Table III.1 0 The cascades are designed to operate from lOmTorr to 100 mTorr. The stage dimensions were held constant for each of the cascades because of manufacturing concerns. A temperature difference of 100K was assumed across all of the aerogel transpiration membranes. The membranes are 500 pm thick and have a diameter of 1cm. The connector section also had a diameter of 1cm. and a length of 4cm. The power efficiency is defined as the energy per unit throughput required for the specified pressure range. The volume efficiency is the pump volume per pumped molecule. Low Density 8% Carbon Doped Si Aerogel (base case) Low Density 8% Carbon Doped Si Aerogel with Optimally Sized Holes Number of Stages 24 34 Pressure Ratio 10 10 Flow Rate (#/s) 6xl01 3 3xl01 6 Power Eff. (J/molecule) 2.5xl0'1 4 7xlO'1 ? Volume Eff. (m3 /molecule) 1.8xl0'1 8 6.7x1 O '2 0 Table HI. Low Pressure lOmTorr to lOOmTorr Base Cascade Analysis Results A relatively large number of stages, 24, are required to produce the design pressure ratio of 10 for the base design case employing low-density silicon aerogel due to the inefficiency of the Knudsen Compressor near the lower pressure limit. Etching optimally sized holes in the aerogel decreases the pressure rise capabilities of each stage, requiring more stages to produce the required pressure rise due to the decrease in the Knudsen number, but increases the conductance of the membrane by several orders of magnitude, providing an increase for both the power and volume efficiency of greater than an order of magnitude. Low-density aerogel membranes with optimally sized holes etched through them have predicted volume and power efficiencies that are attractive despite the increase in the number of stages required to achieve a particular pressure ratio. 66 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.4 Glass Microsphere Transpiration Membranes Another candidate technology for transpiration membranes at low pressures is beds of microspheres made from glass or other materials. The thermal conductivity of glass microsphere membranes can approach that of aerogel because of the limited contact areas between the microspheres. Different sphere bed geometries can be realized depending on the manufacturing procedure used in fabricating the microsphere membrane. The different geometries have different mean effective pore diameters, porosities, and thermal conductivities. The simple cubic (SC) and face centered cubic (FCC) pore geometries shown in Figure 36 represent the entire range of porosities for ordered sphere arrangements.5 2 Figure 36. Unit Cell for Simple Cubic (SC) and Face Centered Cubic (FCC) Microsphere Bed Geometries5 2 The first pattern, simple cubic, represents the highest porosity, n = 47.64%, among the ordered packing patterns. Each side of the unit SC cell has the length of the glass microsphere diameter. The face centered cubic pattern has the lowest porosity among the non-random packing patterns. Each The equivalent pore diameter, obtained from geometric considerations, for beds of microspheres is given by5 2 side of the unit cubic cell has the length of -Jl times the glass microsphere diameter. (46) 67 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Where dgr is the sphere diameter. This provides an average pore diameter of 8a v g = 0.607dgr for the SC arrangement and 8a v g = 0.234dgr for the FCC arrangement. Microspheres are commercially available with diameters of 20nm to above 1mm.5 3 This indicates that microsphere membranes can be made with effective pore diameters from roughly lOnm to greater than 1mm. It appears, for air at a mean temperature of 350K, that it is possible to make glass microsphere based transpiration membranes to efficiently operate from roughly 10 atm (for an effective pore diameter of lOnm) to below lOOmTorr (for an effective pore diameter of 0.5mm). It also appears that glass microsphere transpiration membranes have sufficient porosity, between roughly 25% and 50%, to allow efficient mass flow through the membrane. The minimal contact area between each successive layer of microspheres produces an overall thermal conductivity that approaches that of aerogel.5 2 Glass microsphere membranes appear to satisfy all of the requirements for low-pressure transpiration membranes and are considered another candidate material for use as transpiration membranes in Knudsen Compressors. The thermal conductivity through a bed of spheres has been estimated previously by Kaganer for use in granular insulation layers.5 2 His model assumes that the particles of the granular materials are hard spheres with a constant diameter. Planes passing through the centers of the spheres perpendicular to the outward normal of the membrane are assumed to be isothermal. Ignoring radiation, Kaganer expressed the gaseous and solid fraction of the thermal conductivity of a bed of spheres surrounded by a continuum gas as ' k- ^ re f ^ r e f k +k —k g 1 S " ’gtC 5.8(1- n )2 v K 111 s,sP ^ere | r e f + 1 (47) where Krtf = 1 - yks, and kS i S p h e re is the solid thermal conductivity of the sphere material. A similar expression is obtained for a bed of microspheres surrounded by a transitional gas by replacing kg c with 68 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. where y = f / C y and a is the accommodation coefficient. Klein considered radiation scattering on uniform diameter spheres to get the following expression for the fraction of the thermal conductivity due to radiation, kr = 4dgr(X £pb T 3 (49) ■ * / 1~ Epb where a is the Stefan-Boltzmann constant, E p b is the effective packed-bed emittance, S f is the average solid fraction. The total thermal conductivity is then given by kt - k g +k3+kr (50) A capillary tube model5 5 has been used to model the gas flow through a packed bed of microspheres. The pores in the microsphere bed are modeled as an array of capillary tubes with uniform diameter. This allows the same gas flow and thermal transpiration models to be used for the glass microsphere beds as for the aerogel based transpiration membranes. 4.5 Performance Predictions for Low-Pressure Transpiration Membranes Options A comparison of the performance of a single stage of three different transpiration membrane materials operating over the identified mean pressure range is shown in Figure 37. The three membrane materials are low density Si aerogel, low density Si aerogel with optimally sized pores (varying with mean pressure) etched through it, and a bed of microspheres sized to provide optimal pore dimensions (varying with mean pressure). As shown in Figure 37 the unetched low-density aerogel is naturally optimized for operation at pressures just above 1 atmosphere and is a competitive technology in that pressure range. Bulk aerogel quickly becomes unattractive at lower gas pressures and by a pressure of 10 Torr is more than an order of magnitude less efficient than both of the other candidates. For this comparison it is assumed that aerogel MEMS processes are limited to feature scales greater than roughly 10pm. Etched hole diameters are unpractical above 1mm so the available pore diameters for 69 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. transpiration membrane Knudsen Number optimization are between 10pm and 1mm. This indicates that there is a limited pressure range where fully optimized pore diameters are available. Outside of this range the power efficiency is calculated by using the “best available” pore diameter or 1mm for low pressures and 10 pm for higher pressures. It appears that etching properly sized holes in bulk aerogel can produce transpiration membranes to efficiently operate down to lOmTorr. Microspheres with diameters above 1mm are available, but diameters this large lead to impractical designs. A limit of 1mm is therefore placed on the largest microsphere diameter for this study. At lower pressures 1mm is used as the microsphere diameter. Glass microsphere membranes have a wide pressure range of potential application (10 mTorr to above 1 atm) and appear to be efficient enough to warrant further investigation. 1 .E-17 t^ = = = = = = = = ^ -------------------------------------- S- (.J/mol) N 1.E-18 1.E-19 -I- - - - - - - - - - - - - - - - , - - - - - - - - - - - - - - - - - , - - - - - - - - - - - - - - - - , - - - - - - - - - - - - - - - - - , - - - - - - - - - - - - - - - - 0.01 0.1 1 10 100 1000 P(torr) Figure 37. Energy Efficiency for Candidate Membrane Materials 4.6 Microsphere Transpiration Membrane Experiments An experimental single stage Knudsen Compressor based on a glass microsphere transpiration membrane has been constructed to test the thermal transpiration properties of the glass microsphere beds and is shown, in false color, in Figure 38. Figure 38 also shows an image of the experimental setup for the tests. The glass microspheres used in this investigation had a diameter of 1mm. The 70 a Low Density Si Aerogel A x microsphere (nonoptimal) A microsphere (optimal) A • etched aerogel (nonoptimal) A ------ etched aerogel (optimal) A A • A :: % A X \ 4k x% 1 1 i Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. microspheres were housed between two aluminum thermal guards with arrays of 0.5mm diameter holes conventionally machined through them. The glass microspheres could be added or subtracted to adjust the thickness of the glass microsphere bed. A 1mm thick Teflon® sealing ring surrounded the microsphere bed. An aluminum evacuation chamber with a volume of 8cm3 was placed directly underneath the thermal guard on the cold side of the microsphere bed. Figure 38. Single Stage Knudsen Compressor Based on Glass Microspheres The device was placed in a vacuum chamber (volume of roughly 1500cm3 ) that was evacuated to a pressure below 0.1 mTorr and then refilled with a given pressure of a pure gas. Helium was used for the results described in this section. A temperature difference was maintained across the microsphere bed by resistively heating the hot thermal guard and placing the evacuation chamber in intimate thermal contact with the vacuum chamber (heat sink). The steady temperature difference maintained across the glass microsphere bed produced a steady-state pressure difference, measured by a differential baratron, between the evacuation chamber and the larger vacuum chamber. An experimental run would start at the highest pressure for the run (typically 10 Torr) and then the vacuum chamber pressure was slowly decreased through a control valve to the pumping system, allowing the measurement of the differential pressure dependence on the mean pressure. The temperature difference was measured using thin film thermocouples placed in contact with the hot and cold aluminum thermal guards. The measurement of the temperature and pressure differences allowed the determination of the thermo-molecular pressure differences, TMPDs, for different 71 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. operating conditions. Figure 39 shows a typical experimentally determined TMPD for helium compared to analytical predictions made from the model described above. X Experimental — Analytical 0.01 Pressure (Torr) Figure 39. Comparison of Experimental and Analytical Glass Microsphere TMPD The experimental TMPD is consistently less than the predicted value from the performance model. One possible explanation is that the effective diameter of the pores, defined for gas flow purposes, in the glass microsphere membrane model may not be correctly defined for thermal transpiration effects. Further investigation with different microspheres and working gases are required to clear up the discrepancy. 4.7 M icrosphere Based Knudsen Compressor Design Recently a variety of methods for manufacturing synthetic opals, or 3 dimensional arrays of glass microspheres, have been demonstrated.5 6 ,5 7 The synthetic opals are used as photonic crystals5 8 and as test beds to study the fundamental physical problem of phase transitions analogous to molecular phase transitions.5 9 The most common microsphere array assembly procedures are solvent evaporation, sedimentation, and electrostatic interaction. Each different assembly technique produces different sizes of arrays, different array geometries, and have varying amounts of defects. Microsphere self- assembly is a required manufacturing technique for Knudsen Compressors employing spheres with 72 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. diameters smaller than the limiting hole dimension for the thermal guards, « 10p.m. Coincidentally, many microsphere self-assembly techniques are found not effective for sphere diameters above 10 pm.5 7 Self assembled microsphere beds were not fabricated as part of this work, but it appears that a sufficient number of techniques are available for this process to assume that it is a proven technology. Microsphere based stages have been designed for both high-pressure and low-pressure operation for comparison. The first cascade, a single stage of which is shown on the left, operates from 50 Torr to 500 Torr and requires microsphere self-assembly due to the small microsphere dimensions required in the design. The second design shown on the right is sized to operate from 50 mTorr to 500 mTorr and does not require microsphere self-assembly since it employs larger diameter microspheres that can be contained using a top thermal guard. Sample designs for a stage of both microsphere based Knudsen Compressor cascades are shown in Figure 40. _______________ I Hot Thermal M / / Guard 11IIIIIIIIJIIIIIII llini III IT T T T Radiant Heating Thin sealant layer FCC Bed of microspheres (not shown to scale) : FCC Bed of microspheres :(not shown to scale): Cold Thermal Guard Figure 40. Sample Microsphere Knudsen Compressor Stages Glass microspheres with diameters of 0.75 mm and 0.344 pm were chosen as optimal pore diameters for the low-pressure and high-pressure cases, respectively. The glass microspheres for the low- pressure case will be self assembled using the sedimentation technique. The glass microspheres for the high-pressure case will be contained in all dimensions. Blackened microspheres are available and are employed in both designs to minimize the radiation component of the thermal conductivity.5 3 The temperature difference in both arrangements is maintained by radiant heating. The high-pressure cascade using direct radiant heating of the microspheres themselves while the low-pressure cascade using radiant heating of the hot-side thermal guard. Both microsphere membranes require thin sealing rings on the outside to stop gas leakage out of the sides of the membranes. Table IV summarizes the predicted performance of the two designs on Nitrogen. The mean temperature for both cascades is 73 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 350K and the temperature difference is 100K. For both designs the capillary membrane diameter and connector section radius is 4mm, the capillary section thickness is 1cm and the connector section thickness is 3 cm. P = 50-500 Torr (self assembled) P = 50-500 m Torr (not self assembled) Flowrate (U/s) 6.1E16 4.6E15 Number of Stages 32 46 Power Eff. (J/molecule) 5.4E-17 3.4E-17 Table IV. Performance Estimates for Glass Microsphere Based Knudsen Compressor Designs The flowrate for the high-pressure case is only one order of magnitude more than for the low-pressure case because while the pressure is three orders of magnitude higher the gas conductance through the transpiration membrane also decreases. It has been recently suggested that an energy efficiency on the order of l.E-17 J/molecule for a pressure ratio of 10 is sufficient for some purposes5 indicating that both designs may be suitable for application. Microspheres exist in a broad range of materials and with diameters of 20nm and larger. Manufacturing techniques exist to make beds of glass microspheres over the entire desired pressure range for a meso-scale gas roughing pump. Initial performance estimates indicate that beds of glass microspheres can perform nearly as efficiently as low density perforated Si aerogels. Glass microspheres appear to be the most efficient candidate technique at pressures below roughly 100 mTorr. Results from initial experimental investigations show a discrepancy with the thermo- molecular pressure difference (TMPD) predicted using the analytical model. Possible explanations for the discrepancy include fundamental physical considerations and design considerations not included in the computational model indicating that further investigations are required to determine the true performance capabilities of glass microsphere membranes in Knudsen Compressors. Both perforated aerogels and glass microsphere beds appear to be sufficiently attractive candidates for low- pressure Knudsen Compressor transpiration membranes to warrant further investigations. 74 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 5 High Pressure Knudsen Compressor Considerations 5.1 Introduction Several potential high-pressure (>1 Atm) Knudsen Compressor applications, the micro-scale pneumatically actuated valve and the micro-scale pressure regulator, were detailed in Section 1.3. There have not been, however, any experimental investigations of Knudsen Compressors operating at mean pressures above 1 atm. Before conducting high-pressure Knudsen Compressor experiments, it is useful to estimate the performance of high-pressure Knudsen Compressors using the performance model validated at lower pressures, and to identify possible additional effects that may occur at high pressures. The high-pressure operational limit of the Knudsen Compressor is defined from the requirement that the capillary section must operate in the transitional rarefied flow regime. This requires that the radius of the capillaries (Lr) are on the order of or less than the molecular mean free path (k) of the working gas31, ie Kn=X/Lr > 1. Figure 41 shows the required capillary radii for a range of pressures of various gases at 300K to operate at Kn = 1. 1.E+00 -i -H e -N 2 C 02 l.E-01 - l.E-02 - l.E-03 - l.E-04 - ^ l.E-05 - l.E-06 - l.E-07 - 1.&08 - l.E-09 - l.E-10 - l.E-11 l.E-03 l.E-02 l.E-01 1.E+00 l.E+Ol l.E+02 l.E+03 1E-+04 l.E+05 l.E+06 l.E+07 P (Torr) Figure 41. Pore Sizes Required to Efficiently Operate Knudsen Compressors at Different Pressures Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Knudsen Compressors must employ transpiration membranes with effective pore radii below about 50nm to operate efficiently at Nitrogen pressures above 1 atm. At pressures above 10 atm the pore radii must be scaled to below 5nm. The Knudsen Compressor Performance Model detailed in Chapter 3 has not been experimentally validated for pressures above an atmosphere, but certainly it should provide reasonable performance predictions for high-pressure Knudsen Compressors. However, at pressures above 10 atm., corresponding to pore radii below 5nm, additional flow effects are anticipated, making it unwise to apply the current performance model for configurations with gas pressures above 10 atm. Some of the new flow effects for transpiration flows in pores with radii below 5nm have not yet been observed in definitive experiments, but models predicting these effects can be used to make initial estimates for Knudsen Compressor stage performance. Nanocapillary flows recently have been analyzed and several potentially significant new flow effects have been identified.6 0 ,6 1 ,6 2 At radii of several nanometers and below the molecules in a capillary spend a significant amount of time interacting with the walls’ force fields, thus increasing the near wall number densities. One result can be an increase in the thermally driven flow above the classical thermal gradient driven transpiration. Another physical effect that may become noticeable for nanometer size thermal transpiration capillaries is a coupling of the gas flows near the walls to the phonon flux in the wall material. The coupling occurs when the mean travel distance of the molecules along the tube axis between collisions with the capillary’s wall is on the order of the phonon mean free path in the solid, leading to an enhancement of the collisional coupling between phonon and molecule flows.6 0 ,6 2 Phonon-molecule drag will be most pronounced for crystalline structures and may not be seen in random amorphous materials such as aerogels. Drag due to phonon-molecule coupling could counteract the potential for the increased efficiency mentioned above for thermally driven flows due to near wall gas density increases. For low enough temperatures, which enhances the coupling, the phonon drag could even drive the flow in the opposite direction. 76 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. There are also two quantum effects predicted for flows in nanometer-size capillaries at room temperature.6 1 In certain cases the zero point energy of the molecules can overcompensate for the potential energy from the well formed by the capillary’s walls. The number of molecules in the capillary is reduced by a Boltzmann factor, leading to a screening effect. This effect could be used to differentially pump different molecules in a high-pressure MEMS Knudsen Compressor, based on their deBroglie wavelength in the radial direction and their interaction strength with the walls. The other quantum effect that has been predicted to become important in nanoporous flows occurs when the first molecular excited state in the nanopore is high compared to the thermal energy of the molecules. If this condition is met almost all of the gas will be in the ground state and thus it will behave as a one-dimensional gas. All of these effects, which are due to the necessarily smaller dimension of the capillary radius at high pressures, increase the complexity of the physical processes driving the compressor. There are two figures of merit used to characterize the gas flow properties of a transpiration membrane in a Knudsen Compressor. The first is the maximum flow rate produced by the transpiration membrane. The second is the maximum normalized steady state pressure difference that can be produced divided by the normalized temperature difference across the membrane, the ratio is known as the thermomolecular pressure difference (TMPD). The maximum flow rate occurs when the net sum of all the flows from different physical sources is maximized. In the previous transitional flow analysis it was simply a balance between the temperature gradient driven thermal transpiration up flow and pressure gradient driven return flow. The maximum flow rate through channels with radii above 5 nm occurs when the pressure difference across the membrane is zero, so that there is no pressure driven return flow. The analysis for transpiration membranes with capillary radii smaller than several nanometers will require modified expressions for the thermally driven upflows and the return flows, and an additional term for molecule-phonon coupling. 77 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. For Knudsen Compressors operating below roughly 10 atm. there are two parameters that determine the TMPD; the gas Knudsen Number and the accommodation coefficient of the capillary wall. As the capillary radius becomes on the order of several nanometers it is predicted that the mean temperature of the tube will also become important. Once the capillary radius has been shrunk to a size such that a molecule spends nearly all of its time interacting with the wall then the flow becomes two- dimensional (2D) and new temperature effects become important. The gas flow can become one dimensional if the molecules are always interacting with the wall. At high temperatures the TMPD asymptotes to Vi. As the temperature is decreased the increased interaction time with the wall makes the thermal transpiration effect more efficient. As the mean temperature decreases even further the phonon drag due to molecule-phonon coupling may become relatively more important. This effect is most pronounced when the mean free path of the gas-surface interaction is similar to the mean free path of the phonon-phonon collisions in the solid lattice. Beenakker et al. have shown that the TMPD maximum occurs at roughly 240K for gases like Ar and N2.6 0 ,6 1 They have also shown that the crossover to negative TMPD, driven by molecule-phonon coupling, occurs at roughly 140-180K. If these temperature effects on TMPD are found experimentally for the nonideal capillary structure in aerogel then it may be possible to adjust the mean temperature of the high pressure Knudsen Compressor to operate at the TMPD maximum. 5.2 Gas Particle-Surface Interaction Effects The increased importance of the gas-surface interactions in pores with diameters under 5nm requires a gas surface interaction potential model. Previous analysis has employed different interaction potentials for different cylindrical pore sizes.6 0 ,6 1 For larger pore diameters where the interaction potentials from the different sides of the tube do not overlap significantly an interaction potential is defined with a range, L, from the pore wall and a depth, V . Smaller pores where the interaction potentials from the opposite sides of the pore overlap significantly are modeled as circular square well potentials. Figure 42 illustrates the range of possible parameters for the two model potentials 78 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. compared to the corresponding cylindrical pore van der Waals potential for N2 on Si02, which is described below. 1000 500 1000 500 -500 g-1000 3 -1 5 X | -2000 “--2500 -3000 -3500 -4000 -500 •1000 “■ -1500 -2000 -2500 0 0.5 1 ■ 1 -0.5 0.5 -0.5 -0.3 -0.1 0.1 0.3 Position (nm) Position (nm) Figure 42. Nanopore Potential Models It is clear that both models are approximate when compared to the van der Waals potential which, in itself is approximate, and that calculations based on these models are only qualitative until they can be validated experimentally. The Lennard-Jones potential is used to estimate the molecular potential due to the van der Waals forces between the gas particle and the pore surface. The simplifying assumption of continuously distributed mass on the pore surface is used in calculating the gas surface interaction potential. For completeness three types of surfaces are considered here: spherical, flat, and cylindrical. Performance estimates for nanoporous materials in Knudsen Compressors made later in this chapter are all based on cylindrical pores. The pair-wise Lennard-Jones potential used to calculate the particle-surface interaction potential, which in turn is used to estimate the properties of the simplified potentials shown in Figure 42, is given by Where r is the separation distance, c t 0 is the equilibrium separation distance, e,j is the depth of the potential well, m=12, and n=6. Assuming additivity the total potential for the gas particle is the sum of the potentials to each particle in the pore surface given by W = < 52> i 79 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Using an infinitesimal formulation this can be rewritten as W = J Vp (r)da (53) p ,s surface As pointed out by Derycke an analytical solution to this equation exists for the Lennard-Jones potential in spherical pores (no such solution exists for cylindrical pores) as shown by6 3 1 W = -E m ra v -3 m(h - 2)(w - 3) ^ r E is an energy scaling term and is given by * ;(* )- / _ \ m -3 a Where Q is the volume of a surface particle. The geometric factor is given by (n -3 ) Where s=r/R. (n -4 X l-s ) r ( v > rt- 4 ( s > n-3 1 + ------ +1 u - * j U-5J (54) (55) (56) For a molecule-infinite wall interaction with a continuously distributed mass and employing the Lennard-Jones potential, the total potential for the particle is given by — 00—00 P> » 2 a 6 . dxdy (57) Where a is the distance from the wall. This integral can be solved to yield the analytical solution shown by W = _ 4 ^ f a 1-So*a6 .} Ap_ , 20 a 1 (58) No analytical solution exists for the potential in cylindrical pores indicating that the integral must be evaluated numerically. The potential integral for cylindrical pores is given by W ■ Su I n 0 0 ssA 0 — 00 p ,s - 2 a. RdzdO (59) 80 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The integral can then be written as 2suR V l a 1 2 2 a 6 w = — — f f-7--------------—-------------- xT-7----------------- 5 ----------T ^ dddz (60> d p,s o o \R2 +a2 + z 2 + 2a/?sin(#)) \R2 +a2 + z2 + 2a/? sin(#)) Figure 43 compares the potentials from a molecule-molecule interaction, molecule-flat wall interaction, a molecule-cylinder interaction, and a molecule-sphere interaction for N2 on Si02. Both the cylindrical and spherical pores have a radius of 0.5nm and the cylindrical pore is infinite in length. Molecular + Flat Wall Cylindrical Spherical 2.E+03 — 1.E+03 — S'1.E+03 + 4 + H ^++-t^4-44+++ + / 3.En)3 4.E+03 5.EKJ3 -6.E+03 0.00 0.05 0.10 0.15 Distance to Centerline (nm) 0.20 0.25 Figure 43. Various N2 on S i02 Gas-Surface Interaction Potentials The potential well depth for a gas particle-flat wall interaction is increased over the molecule- molecule potential because there is more than one particle forming the surface, which is treated as a continuous mass distribution, interacting with the free particle. The potential minimum appears closer to the surface for the case of the particle-infinite surface interaction than for the particle-particle interaction. This is an artifact that is due to the continuous mass distribution assumption made for the particle-surface interactions. The particle-cylinder potential has a deeper potential minimum than the particle-flat wall interaction potential because of the increased amount of mass close to the particle from the curvature of the cylindrical pore. The particle-sphere interaction potential is the deepest minimum because this condition represents the most mass close to the particle when it is near the surface. All of these gas-surface interaction potentials described here are only approximate due to the 81 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. distributed mass assumption, which is an obvious approximation for pores with a diameter of lnm, but they can be used to estimate the equivalent potential properties assumed in the simplifying potentials employed by the nanoporous flow models. In order to calculate the simplified interaction potentials used in the nanoporous flow models their properties must be estimated from the integrated Lennard-Jones potentials for the gas-cylinder interaction pair. This is difficult to do in any systematic way due to the approximate nature of both potentials. Figure 44 shows the gas-cylinder interaction potential for various sized Si02 cylinders with N2. -4000 X X X X ------R = 0.5nm + 70 II LOnm ------ R = 2.0nm x R = 5.0nm ------ R = 10.0nm 2 4 6 Distance From Centerline (nm) 10 Figure 44. Gas-Cylinder (N2 -Si02 ) Potentials for Various Sized Cylinders The potential well depth is deepest for the R=0.5nm case due to the potential overlap and trends to the particle-flat wall value with increasing pore size. For the 0.5 nm pore radius case the gas particle is always interacting with the wall and a circular square well potential can be approximated from the potential. For the 2.0 nm pore radius case the potential nears zero on the centerline indicating that for pores of this size the potential with a constant depth for a given range from the pore surface can be used. For the cylinder with a radius of lOnm it is clear that the particle-wall interaction time is small compared to the particle ffee time and additional nanoporous effects should play a very small role in 82 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. determining the overall flow properties. These sizes are rough guidelines of when each of these models are appropriate although the flow models representing each regime do not correctly asymptote to each other. 5.3 Increased Surface Interaction Effects There are two flow regimes defined for nanoporous flows based on the percentage of time that a molecule is interacting with the pore wall. 2D flows are defined as tube flows where a molecule is almost always interacting with the wall. The simplified potential model used for the 2D flow case is the model with a constant depth for a given range from the pore surface. ID flows are defined as nanoporous gas flows where a molecule is always interacting with the wall. The simplified potential used to model ID gas flows is the circular square well potential. All of the estimates for additional flow effects in nanoporous flows described here assume a free molecular flow or Kn » 1. Results from kinetic theory can be used to calculate the pressure gradient driven gas fluxes for fully accommodated flow in large tubes as shown by Where n is the gas number density, v is the most probable thermal speed, and Lr is the mean effect pore radius. The similar temperature gradient driven flux, due to the thermal transpiration effect, is given by (61) (62) The TMPD for free molecule gas flows in large tubes is given by (63) 83 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. For the 2D nanoporous gas flow case (analytically predicted to occur in pores with diameters of several nanometers) the pressure gradient driven flux expression is modified to include the quantum screening effect and reduced dimensionality as shown by Where L is the range of the potential, and x is the mean relaxation time of molecules by phonons and surface defects. The expression for the temperature gradient driven flux due to the thermal transpiration effect is modified by the same effects and also by increased surface interactions and is given by The thermomolecular pressure difference is no longer constant and now depends on the potential well depth and the gas temperature. It is evident from this expression that the TMPD does not necessarily asymptote to the large tube limit of 1/2, indicating that the model is very approximate and can’t be used to determine the onset of nanoporous flow effects. The expression for the pressure gradient driven flux in the ID case, modified by the same effects as in the 2D case and even further reduction in the dimensionality, is given by The temperature gradient driven flux caused by the thermal transpiration effect is given by (64) (65) The TMPD for 2D nanotube flows is then given by (66) (67) (68) The TMPD for ID nanotube gas flows is then given by 84 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. f r~r > P\ /( I P )n V T ) V T J k J (69) Which is the same as in the case of 2D nanotube flows. It should be noted that the potential well depth for the ID case is the depth of the circular square well potential while the potential well depth for the 2D case is the depth for the potential for just a given distance away from the wall. It is also worth noting that although the individual pressure and temperature gradient driven flux terms differ for 2D and ID tubes, the TMPD is the same. 5.4 Phonon-Particle Drag in Nanocapillary Flows Initial analytical investigations into nanoporous gas flows have indicated that at low temperatures, primarily for materials with a crystalline structure, phonon drag due to molecule-phonon coupling can become important when modeling gas flows through nanoporous materials.6 1 It has been predicted that the phonon drag effect becomes important when the mean distance that a molecule travels between successive collisions with the wall is similar to the mean free path of the phonon-phonon collisions (Hp h ). The phonon-gas coupling effect is predicted from initial nanoporous gas flow models, but hasn’t been observed experimentally, although a similar mechanism, phonon-electron coupling in semiconductors has been observed as is an important physical mechanism in the modeling of semiconductor heat transfer.6 4 Beenakker et al. have introduced a simple analytical expression to predict the gas flux due to the gas-phonon coupling effect in nanoporous gas flows.6 1 Using the framework of kinetic theory to model the interaction of the gas molecules with a phonon gas Beenakker et al. estimated that the gas flux due to the molecule-phonon coupling is6 1 ,6 2 Nph=~2xLrnsvCphAph^ (70) Where Cp h is a term of order 1 and X p h is the phonon mean free path. The surface density of the molecules in the nanoporous gas flow is given by v n,= nLekb T (71) 85 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The most probable molecular thermal speed is given by v = 2 kbT (72) m The order of magnitude of the other required terms was estimated by amorphous ~ ^ ’ ( ^ > * 1 L. ) w t v , l/l .) ,«10nm P " ' amorphous ' P ' crystal (73) (74) rv « 0.1 -l.Onm (75) The total TMPD due to the balance of the thermal transpiration effect, pressure driven return flow, and gas-phonon coupling effect is given by As shown again here, the TMPD can either be increased or decreased depending on the mean temperature. Several parameters required to make estimates for the phonon drag driven flows in the materials used in this study are not readily available. Representative calculations can, however, still be made that give an initial estimate for the relative importance of the phonon drag effect. Figure 45 shows the predicted gas-phonon coupling driven flow for various gases and surfaces for the conditions of Lr = 2.5 nm and T = 300K. The models predict that N2 on carbon has the largest phonon drag driven flow due to the deepest interaction potential well depth, 2790K, compared to potential well depths of 225K for He on Si02 and 945K for N2 on Si02. f A \ 4 p 1 (76) 86 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1.E+08 1.E+07 - | 1.E+06 ■ N2 on S i0 2 • He on S i0 2 ▲ N2 on C 1.E+05 1.E+04 4 Figure 45. Gas-Phonon Coupling Driven Flow for Assumed X p h Figure 46 shows the predicted gas-phonon coupling driven flow for N2 on Si02 for a range of temperatures and assumed \ , h- 1.E+09 ■ Iph = .1 • Iph = 1 a Iph = 10 1.E+08 - ? 1.E+07 - } 1.E+06 1.E+05 - 1.E+04 600 800 1000 200 400 Figure 46. Gas-Phonon Coupling Driven Flow Verses Temperature The models predict that the phonon drag effect will become much more pronounced at temperatures below roughly 300K for the given conditions. Figure 47 shows the TMPD that would occur for: the case of neglecting the thermal transpiration effect, the case of neglecting the phonon drag effect, and the total TMPD for C 02 on C with a Lr of 2nm. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 3.5 2.5 0.5 -1 - - 1.5 - 600 500 300 + TMPD TMPD th TMPD ph - 2.5 - 3.5 Temperature (K) Figure 47. Gas-Phonon Coupling Driven Flow for C02 on C The TMPD asymptotes to a value near 0.5 at high temperatures. As the temperature decreases both the transpiration and gas-phonon coupling TMPDs increase in magnitude. The total TMPD is the difference between the two functions that are both approximate making the net uncertain. It does appear, however, that there is a TMPD maximum around 400K and the crossover to negative TMPD at about 225K. It is difficult to make any definitive conclusions based on this rough analysis for the phonon drag effect. It is important to note that phonon drag effects may become important at low temperatures and at pore sizes below 5nm. 5.5 Quantum Effects in Nanocapillary Gas Flows The small physical dimensions associated with gas flows in nanoporous materials hints that quantum effects may play a role. Quantum effects should become important in nanotube flows when the mean radial deBroglie wavelength ( k r = h / r r i ) of the molecules in the capillary becomes on the order of the unoccupied radial dimension in the capillary as given by6 1 2 L. - d >0[l] (77) * This ratio is shown in Figure 48 for N2 at various temperatures. 88 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.5 T = 50K T = 100K X T = 200K o T = 300K 3.5 - 8.0E-10 8.2E-10 8.4E-10 8.6E-10 8.8E-10 9.0E-10 9.2E-10 9.4E-10 9.6E-10 9.8E-10 1.0E-09 Pore Diameter (m) Figure 48 Quantum Ratio for N2 It is apparent that pore diameters of lnm or less will be required at common temperatures to observe quantum effects in the gas flows of gases like N2. Models for the predicted nanoporous flow quantum effects assume the same circular, square well potential as was used in modeling the pressure gradient and temperature gradient driven gas flows in nanoporous materials.6 1 The energy levels of the circular square well potential were obtained from this model and are given by 2 y > \ , <*» (2 i r -<*,) m The first two energy levels for N2 in a Lr=2.5nm channel are E0 =26.1K and Ei=66.3K, while for H2 they are E0 = 101K and E]=258K. Where ^ are the zeroes of the Bessel Function. The nanoporous flow models predict two new flow phenomena due to quantum effects. The first new phenomena occurs when the ground state energy level is greater than the potential well depth in the nanopore as quantified by the ratio — > 1 (79) V 89 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. When this condition is satisfied the zero point energy is greater than the molecule-surface interaction potential, producing an energy barrier. The particle number density in the tube will be reduced by a Boltzmann factor given by v ~ k bT (80) This will tend to decrease both the flow driven by thermal transpiration and the pressure driven return flow due to the decrease in the number density of the molecules in the tube. Another quantum effect that occurs in general whenever particles are trapped in potential wells occurs when the first excited state is at a much higher energy than the ground state as shown by Ex —E0 kkT (81) When this occurs in systems with low energy very few of the molecules are in the excited state so the gas is effectively still a ID gas. Figure 49 shows a comparison of the ID gas effect term listed in Equation 81 for a variety of gases at a temperature of 300K. — N2 + 02 0 02 0.001 0.0001 5.0E-10 7.0E-10 9.0E-10 1.1E-09 1.3E-09 1.5E-09 1.7E-09 1.9E-09 Diameter (m) Figure 49 Quantum ID Gas Effect Strength, T = 300K The ID gas effect is most prominent with low molecular weight gases in pores with diameters of lnm or below, the same as with the gas screening effect. 90 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5.6 Nanopore Condensation Effects It is well known that at small capillary radii increased gas adsorption can occur on the capillary surfaces verses a flat plate.6 5 This effect can lead to capillary blockage through gas condensation. The increased adsorption in the capillaries is due to the decreased vapor pressure from the high curvature of the small capillaries and is related to the increased gas surface potential well depths that were described in Section 5.2. The quantitative effect can be estimated by the Kelvin equation solved for the adjusted vapor pressure ratio given by6 5 m r ’V m o 1 1 (82) = exp< Pm [ kJ R- where R,„ is the mean radius of curvature (negative for concave surfaces) and Vm o i is the molar volume. The surface tension also varies with the radius of curvature and the temperature as shown by d ' / \ n T \ C / v R. (83) Where d is a measure of the thickness of the interfacial region. For small capillary radii this effect can cause certain molecule/surface combinations to accumulate the liquid phase of the gas in a capillary, potentially blocking it. Figure 50 shows the predicted reduction in vapor pressure and the effect on the surface tension for CO2 at a temperature of 200K. 1 .E + 0 0 — g am m a + p/po 0.1 1.E -02 0 .E + 0 0 2 .E + 0 0 4 .E + 0 0 6 .E + 0 0 8 .E + 0 0 1.E +01 P ore D iam eter (nm) Figure 50. Pore Condensation Effect of C 0 2 in Cylindrical Pores, T=200K 91 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. A significant reduction in the vapor pressure occurs for pore diameters less than 4nm. Unlike the gas- phonon coupling effect, pore condensation effects are readily observable and are relatively well understood. Porous Vycor® glass samples, with mean effective pore diameters of 4.1nm have been used in some initial investigations into the TMPD in nanoporous materials carried out by others at USC. Figure 51 shows a porous Vycor® sample at four different times during the membrane heating portion of the sample preparation process. The total elapsed time in the process is several hours. The photo at the initial time (on the upper left) shows the porous Vycor sample full of condensed water. The water vapor that is condensed in the pores is slowly released with heat. The picture on the upper right shows the sample after some initial heating when the water from the outside part of the porous glass has been driven out. The next picture on the bottom left shows the porous glass sample at roughly half of the way through the process. The final picture on the bottom right shows the porous glass sample after all of the water has been driven out. By measuring the weight of the porous glass sample before and after this preparation step it was determined that the entire available pore volume was filled with condensed water. Figure 51. Porous Glass With Condensed Water Vapor Pore condensation effects will occur most strongly with large molecules in nanoporous materials with pore diameters of roughly 5nm and below. This effect can not be neglected when designing Knudsen Compressors that operate at pressures above roughly 10 atm that would require pore diameters under 92 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 5nm to operate efficiently. Pore condensate frequently can be driven out by heating the sample or may be avoided by maintaining high temperatures in the sample. 5.7 Basic Design Considerations and Representative Example Figure 52 shows a side view for an individual stage of the high pressure Knudsen Compressor designed to operate at pressures from 1 atm to as high as 10 atm. No major design changes are anticipated for high-pressure Knudsen Compressors that operate at pressures to roughly 10 atm, although experimental investigations are required to validate the current models for these pressures. Stage optimization, such as aerogel density and carbon dope fraction variation, will be required when the high-pressure Knudsen Compressor models have been experimentally validated. Next Stage Previous Cold Thermal Guard Connector Section Hot Thermal Guard Figure 52. High Pressure Knudsen Compressor Concept A high pressure Knudsen Compressor, based on this schematic, was sized using a carbon doped silicon aerogel, Lr = 2.5 nm, as the transpiration membrane material. Performance calculations were made using the Knudsen Compressor Performance Model and assuming that the validated models for gas pressures under latm were still valid in the pressure range from 1 to 10 atm. A high-pressure Knudsen Compressor cascade was sized to operate from a pressure of 1 atm to 10 atm. For simplicity the stage sizes were held constant along the cascade with Lr = 2.5nm, Lx = 250pm, LR = 1mm, Lx = 93 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4mm. The temperature difference was also held constant at AT = 100 K. The cascade characteristics are shown in Table V. Number of Stages 27 Pressure Ratio 10. Flow Rate 5xlOlb mol/s Volume 40 mm3 Energy Consumption 0.25 W Power Efficiency 5xl0'1 8 W/(#/s) Table V. Large Pressure Ratio Cascade Properties As discussed throughout Chapter 1 a power efficiency of 5xl0'1 8 J/molecule is sufficient for micro/meso-scale pump and compressor applications. The volume of 40mm3 also seems reasonable indicating that it appears viable to base micro-scale gas compressors on Knudsen Compressors. The pressure variation and the pressure ratio across each individual stage along the high-pressure Knudsen Compressor are shown in Figure 53. 1.105 1.2EH06 1.0E-C6 - 1.095 8.0E-G5 - 1.09 1.085 - 1.06 4.0E-G5 Pavg Prat -- 1.075 20EH05 - 1.07 O .O E H O O 1.065 0 5 1 0 15 Stage 20 25 30 Figure 53. High Pressure Knudsen Cascade Pressures The stages are ordered from the lowest pressure to the highest pressure. There are two competing effects that produce the shape of the pressure ratio curve. Initially the pressure ratio across each stage increases along the cascade because a smaller fraction of the maximum throughput is realized, the maximum throughput for each subsequent stage increases due to the mean pressure increasing while the realized throughput is constant due to continuity, yielding a relatively higher realized fraction of the maximum pressure difference. At about the 15th stage, Pa v g =3.3 atm, the flow in the capillary 94 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. section enters the transitional flow regime, Kn = 7.6, where there is a decrease in the maximum pressure ratio and throughput lowering the stage pressure ratio. These results indicate that at 10 atm deleterious effects, due to limited available materials, are detectable in the operation of the Knudsen Compressor. Higher pressures are attainable, but at an ever increasing cost in both pump volume and power per unit of upflow. A similar cascade was sized to operate between 1 atm and 2 atm, representing a case when a smaller differential pressure is acceptable. This cascade is essentially the first 9 stages of the higher pressure difference cascade. The characteristics of the Knudsen Compressor cascade designed for this purpose are summarized in Table VI. Number of Stages 9 Pressure Ratio 2. Flow Rate 5xl01 6 mol/s Volume 13 mm3 Energy Consumption 77 mW Power Efficiency 1.5xl0'1 8 W/(#/s) Table VI. Small Pressure Ratio Cascade Properties This Knudsen Compressor cascade also seems viable as a micro-scale gas compressor under both energy and volume considerations. For operation in a distributed micromechanical context, it would be advantageous to have fast response, normally-off gas compressors. Basically, a satisfactorily instantaneous on-demand pneumatic source, permitting the minimum average power usage. In order to investigate the use of normally-off, high pressure Knudsen Compressors their response time to achieve full operation from the off position must be estimated. There are two internal physical processes that determine the time response of the Knudsen Compressor. The first is the time that is required to set up the thermal gradient across the transpiration membranes. The problem is initially addressed by assuming an infinite plane, ID thermal problem. The thickness of the membrane is given by Lx. Initially the entire section will be at the cold temperature Tc. The power source is turned on and is assumed to deliver a constant and uniform heat flux, Pm /A, to the hot side. It is also assumed that the input power is 95 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. delivered into a certain thickness of the membrane given by Lx,he a t- At the same time the thermal gradient will drive a power loss through the transpiration membrane material. Outward cooling mechanisms are neglected for this initial estimate. The temperature of the hot side of the membrane as a function of time is obtained by solving the transient differential heat flow equation. A characteristic response time resulting from the analysis is r v1 _[ k , ° ~ c p L (l -L j \ p o r r p o r J r . w \ x x,heat/J The steady state temperature difference is given by (84) For an initial estimate the values from the sizing section discussed earlier can be used to estimate a characteristic time for the establishment of a temperature gradient in the membrane. The density and heat capacity for carbon doped aerogel for this case are pp o r = 100 kg/m3, C p o r = 1000 J/(kgK).3 2 For this analysis it is clear that the maximum temperature change and the characteristic time depend on the depth that the heat is applied to, L x ,h eat- For this analysis LX ] h e a t = 0.1*1^. The maximum temperature change is estimated to be 90 K and the characteristic time, to, is 0.03s. The other process relating to the time response for full operation of the Knudsen Compressor is the length of time that it takes for gas molecules to travel through the high aspect ratio capillary membrane in one stage. Clausing6 6 has indicated that for high Lx /Lr ratio tubes and molecular flow, the average travel time can be obtained through the use of a diffusion coefficient given by £» = | v 0(2Zr ) (86) The average travel time becomes For the current problem the average travel time can be estimated as lx l0 '2 s. These approximate models indicate that both characteristic times are on the order of 10 ms. The current Knudsen 96 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Compressor design has been at least partially optimized with throughput, energy consumption, and volume considerations as constraints; primarily for pump and compressor applications. Different optimizations will be required to minimize time response, resulting in Knudsen Compressors with significantly shorter response times, but higher energy use due to altered configurations. It should also be noted that the full time response to achieve a desire pressure ratio also depends on the chamber volumes connected to both sides of the Knudsen Compressor. These volumes, however, are part of the device employing the Knudsen Compressor and not part of the Knudsen Compressor itself and are not considered here. 5.8 M embrane M aterials for Operating Knudsen Compressors at P> lOatm Without experimental validation of the nanoporous membrane effects predicted by the models detailed in this chapter it is inappropriate to estimate the performance of Knudsen Compressors at pressures greater than roughly 10 atm. It is, however, possible to identify candidate nanoporous membrane materials for both experimental validation tests for the predicted nanoporous flow effects and for use as transpiration membrane materials in high-pressure Knudsen Compressors. At pressures above 10 atm. materials with ever decreasing capillary radii must be used in the transpiration membrane. An absolute physical limit can be placed on the upper pressure at which a Knudsen Compressor can operate since the capillary diameter must surely be larger than the diameter of the molecule that is being pumped. For N2 this establishes an absolute pressure limit of 145 atm. There are obvious practical considerations that would arise when operating with such high gas pressures in a micro-scale device, but the goal of the current section is only to determine whether materials exist with the correct pore sizes to operate at these pressures. For pressures between 10 atm and 145 atm membrane materials with capillary radii on the order of several nanometers to 0.1 nm are required. There are many commercially available porous materials with mean pore diameters in this range. However, several additional requirements must be met for porous materials to be considered practical candidate materials for transpiration membranes in Knudsen Compressors operating at pressures above 10 atm. The materials should have minimal thermal conductivities, approaching that of 97 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. aerogel, to minimize the required power and must also have high porosities to maximize the gas throughput. A representative sample of the range of possible nanoporous membrane materials, along with their nominal properties, is listed in Table VII along with the nominal properties for aerogel. From the table it is clear that there are no available nanoporous materials that have a thermal conductivity close to that of aerogel indicating that Knudsen Compressors operating at high pressures will have a lower energy efficiency. The materials do exist, however, if power is not limited, to produce Knudsen Compressors that operate much higher than 10 atm. Material Lr (nm) p (g/cm3 ) kt (W/mK) (300K) Carbon Nanotubes6,6li 0.5 - Several -1.5 3000. Zeolites6 5 ' ~1 -1.5 -1. Porous Glass/u,/1 (Vycor) -2-200 1.5 0.9 Xerogel'" -2-15 -1 -0.2 Aerogel""-'3 -10. Down to 3.6 0.003- 0.35 .0042 Table VII. Nanopore Materials Compared to a Typical Aerogel 98 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 6 Single Stage Experiments: Transpiration Membrane Temperature Difference and TMPD Measurements The Knudsen Compressor Performance Model detailed throughout Chapter 3 begins each stage calculation by calculating the temperature difference maintained across the transpiration membrane by considering: the intensity of the incident radiation, distributed absorption of the incident radiation throughout the transpiration membrane; energy transport through the transpiration membrane due to, solid conduction, gas conduction, and radiation transport; and energy release from the hot side of the transpiration membrane through outward gas conduction and radiation transport. Once the temperature difference has been calculated then the pressure difference and gas throughput can be calculated from the transpiration analysis and the gas conduction analysis. An analogous experimental process was conducted to determine the performance of the Knudsen Compressor. First the temperature across the transpiration membrane was measured for various operating conditions to validate the thermal model component of the Knudsen Compressor Performance Model. Then the steady-state pressure difference and resulting TMPD were measured and compared to the predicted values from the Knudsen Compressor Performance Model. This step validates the transpiration portion of the Knudsen Compressor Performance Model. Both of these experimental measurements and their comparison to the predicted values are described in detail in this chapter. The final step of the experimental process was measuring the complete pumpdown properties for cascades of different numbers of stages. This step was used to validate the transpiration membrane flow models, and is detailed in Chapter 7. 6.1 Conventionally Machined Knudsen Compressor Stage Description Macro/meso-scale Knudsen Compressors (with characteristic length scales >lcm) can be manufactured using conventional manufacturing techniques. Micro-scale Knudsen Compressors (with characteristic length scales < 1cm) will require at least some micro-electro-mechanical systems 99 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (MEMS) manufacturing techniques to achieve the required tolerances. Meso-scale conventionally machined Rnudsen Compressors were used for all of the experimental investigations conducted in this work. Although the required MEMS manufacturing processes for a meso-scale Knudsen Compressor of the same design detailed in this section have been identified, conventional machining of the Knudsen Compressors was roughly one order of magnitude cheaper. Conventional manufacturing also allowed the incorporation of o-ring seals, allowing individual stages to be replaced to fix broken stages or to experiment with different types of stages. Conventional machining also allowed standard fittings to be employed in the design. For all of these reasons conventional machining was chosen for this work. The conventionally machined single stage radiantly driven Knudsen Compressor is shown disassembled in Figure 54. The transpiration membrane was made from carbon doped silicon aerogel. lumtnum Thermal Guar 1 Figure 54. Single Stage Radiantly Driven Knudsen Compressor The carbon doped silicon aerogel was provided in large sheets with a near constant thickness. The aerogel coupon for each stage is first cut out of the aerogel sheet using a razor blade. The aerogel coupon is then attached to the aluminum thermal guard, over an array of l/2mm diameter conventionally drilled holes, using Torr Seal® epoxy, which also seals the outside edge of the aerogel transpiration membrane from gas flow. The Plexiglas cover is placed on the aluminum thermal guard and sealed using an o-ring. The aluminum thermal guard and Plexiglas cover are then placed on the 100 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. aluminum base and sealed with more o-rings. The aluminum thermal guard is in intimate thermal contact with the pump body. This provides efficient transfer of the thermal energy absorbed in the aerogel transpiration membrane through the thermal guard and into the pump body. The entire setup is held together with clamps. Several different types (I: 80 mg/cc, 8% carbon, II: 120 mg/cc 8% carbon) of carbon doped silicon aerogel were used as the transpiration membrane in the single stage conventionally machined Knudsen Compressor. The different types of aerogel were investigated to begin to validate the optimization of the aerogel transpiration membranes predicted by analytical performance models. Repeatability issues with the current manufacturing process for bonding and sealing the aerogel transpiration membrane made larger scale comparisons impractical. The conventionally machined radiantly driven Knudsen Compressor stage was driven by illuminating the free side of an aerogel transpiration membrane through the Plexiglas cover. Different light sources, with different radiant fluxes, including a halogen lamp and small-scale Xenon lamps were used as the driving light sources for these measurements. 6.2 Transpiration Membrane Temperature Difference Measurements The temperature difference maintained across the transpiration membrane was measured for various illumination fluxes, gas species, and gas pressures to understand the effectiveness of radiant heating and to validate the aerogel thermal and optical model portion of the Knudsen Compressor Performance Model. Photos of both the inside and outside of the experimental setup that was used to measure the temperature difference across the transpiration membrane are shown in Figure 55. A single Knudsen Compressor stage was placed inside a 25cm diameter vacuum chamber. The chamber was first evacuated to a pressure below 50 mTorr and then refilled with a pure gas. A halogen lamp was placed on top of the vacuum chamber with optical access through a viewport for driving the single stage Knudsen Compressor. The halogen lamp had a measured radiant flux (using a 101 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. wavelength integrated photodetector) of 65mw/cm2 at the location of the transpiration membrane. One side of the stage (the side exposed to the higher temperature of the transpiration membrane) was left open to the vacuum chamber (which had a much larger volume and therefore maintained a constant pressure during the run). The other side of the cascade was connected to a differential pressure sensor. The Plexiglas® cover was removed for the membrane temperature measurements to allow a thin film thermocouple to be placed in thermal contact with the hot side of the aerogel transpiration membrane. Another thin film thermocouple was placed in contact with the aluminum base. Halogen Lamp Thermocouple tensor ,ine fo Vacuum Piimn Figure 55. Experimental Setup Used to Measure AT The temperature of the aluminum base (which is in direct thermal contact with the cold side of the aerogel) did not rise more than 4K above the ambient temperature during all of the temperature difference experiments. The temperature rise of the aluminum base is heavily dependent on the experimental setup indicating that this measurement doesn’t provide much Knudsen Compressor specific information, but it does indicate that Knudsen Compressors can be designed that experience a minimal rise in the temperature of the pump body. 102 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Many of the applications for the Knudsen Compressor require operation in air making N2 an appropriate initial choice for a working gas. Transpiration membrane temperature difference measurements were made for Nitrogen pressures ranging from atmospheric to the base pressure of the pumping system, 20 mTorr. The same measurements were made with Helium as the operating gas. Helium has a significantly higher thermal conductivity than Nitrogen, which should produce measurably smaller temperature difference for the same radiant flux. Figure 56 shows the comparison of the experimentally measured temperature difference with the temperature difference predicted by the Knudsen Compressor Performance Model. The stage used in this investigation used Type I aerogel and was illuminated with a radiant flux of 65mw/cm2. The measured aerogel cold side temperature was used as an input in the model when calculating the expected hot side temperature of the aerogel. £ H < 60 50 40 30 20 10 ♦ He-Exp ■ N2-Exp o He-Model □ N2-Model □ o * □ 0.0001 0.001 0.01 B □ .............................3 OO, ’ O O O o 0.1 1 10 100 1000 P (Torr) Figure 56. Comparison of Predicted and Observed Transpiration Membrane Temperature Difference There is a general agreement in functional form between the model predicted temperature difference and the experimentally measured temperature difference for both Nitrogen and Helium. The general downward trend for gas pressures between 100 Torr and 1000 Torr is due to the onset of gas conduction through the transpiration membrane. At high gas pressures the thermal model from the Knudsen Compressor Performance Model predicts a gas temperature that is lower than the measured 103 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. value for both Nitrogen and Helium. The onset of outward free convection cooling which, for this configuration, is predicted to become active at gas pressures of several hundred Torr would increase the outward gas cooling above the conduction values causing a reduction in the experimentally achieved pressure difference. The onset of convection is difficult to predict, making further refinement of the thermal model not practical at this time. As the pressure is decreased from atmospheric the temperature difference for both gases increases due to decreased gas conduction through the transpiration membrane because of rarefaction effects. As this effect has become negligible compared to the other cooling mechanisms, at about 100 Torr, reducing the pressure further has very little effect on the temperature difference. At a pressure near 1 Torr the temperature difference begins to increase again due to a reduction in the outward gas conduction flux. This occurs experimentally, for both Nitrogen and Helium, at a higher pressure than predicted from the Knudsen Compressor Performance Model. The pressure range over which this transition occurs is also smaller for the experimental values as gas conduction outward cooling is completely negligible by a pressure of 20 mTorr, while the model requires about an order of magnitude lower pressure. Both of these transitional phases occur at slightly higher pressure for Helium because it has a smaller molecular diameter and hence a larger Knudsen Number for the same gas conditions. The exact location of the transition phases is not accurately defined, but the maximum temperature difference (for negligible gas conduction through the membrane and outward) and temperature difference that occurs with no gas conduction through the membrane are both predicted to within 8% for both Nitrogen and Helium. The experimental error is difficult to access because of uncertainties in accurately measuring aerogel temperatures. The thermocouples were shown to have an uncertainty of ±1K as compared to a mercury thermometer over the temperatures that occurred during the investigation, but it is hard to determine how accurately they mimic the aerogel temperature, even with direct thermal contact, due to the unique thermal properties of aerogel. 104 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6.3 Single Stage Steady-State AP Measurements Once the thermal model portion of the Knudsen Compressor Performance Model was validated the next step was to validate the thermal transpiration component by measuring the steady-state pressure differences maintained across the transpiration membrane by the radiant flux. The steady state pressure differences were measured using the same single stage Knudsen Compressor setup as for the temperature difference measurements. As in the temperature measurements the vacuum chamber was first evacuated and then refilled with a pure gas. The stage was then illuminated and a steady-state pressure difference was allowed to build up across the stage (typically requiring roughly 200s). The vacuum chamber had a much higher volume than the volume evacuated by the Knudsen Compressor so the pressure difference was entirely due to a reduction in the pressure of the evacuated volume. The pressure difference was measured with a differential baratron pressure transducer. Figure 57 shows the steady-state pressure difference produced at different vacuum chamber pressures of Helium and N2 (with and without the Plexiglas® cover) for type I aerogel compared to the analytically predicted values. 100 > N2 Covered Helium Model - - N 2 Model N 2 Covered Mode 10 0.01 0.001 0.1 100 1000 Ph (Torr) Figure 57. Steady State Pressure Difference for Different Configurations The dominant trend of the pressure difference produced by the single stage conventionally machined Knudsen Compressor is a linear variation with the mean pressure of the stage, as anticipated by Equation 43. Several additional minor effects produce a deviation from a linear dependence. As the 105 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. mean pressure is reduced the cooling effects of the gas conduction outward and the gas conduction through the membrane are reduced, causing the temperature difference produced by a given radiant flux to increase. As the pressure is reduced the Knudsen number of the gas in the pores in the membrane is increased which increases the relative importance of the temperature driven flow compared to the pressure driven return flow. Both of these effects cause the pressure difference to increase slightly less than linearly with increasing pressure. The decreased pressure difference of the covered version operating on N2 corresponds to a reduction (roughly 15%) in the radiant flux striking the aerogel transpiration membrane due to the Plexiglas® cover. The pressure difference produced when operating on Helium is relatively smaller compared to N2 because of the decreased temperature difference due to the increased gas conduction through the membrane and outward. For the same temperature difference and mean operating pressure Helium would produce a higher pressure difference (for finite Knudsen Numbers) because of its higher Knudsen number, but this effect is overwhelmed by the smaller temperature difference with Helium as compared to N2. The agreement between the experimentally measured steady-state pressure differences and the values predicted by the Knudsen Compressor Performance Model is within the accuracy of the differential pressure sensor (50 mTorr) at low pressures as shown by the error bars included on the lowest pressure points in Figure 57 and is within 20% (roughly the discrepancy between the model predicted temperatures and the experimentally measured temperatures) over the intermediate pressures (up to several hundred Torr). At pressures above several hundred Torr the discrepancy grows because the discrepancy in the temperature difference grows. Figure 58 shows the variation in the pressure difference produced by the single stage with incident radiant flux for an atmospheric pressure of air. Two different light sources were used to provide the range of fluxes, a small xenon lamp for the fluxes from 0 to 25 mw/cm2 and a halogen lamp for fluxes ranging from 25 mw/cm2 to 175 mw/cm2. The xenon lamp provides a higher pressure difference for the same flux (as measured by the integrated photodetector). The different lamps have different 106 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. spectrum and different angular flux distributions with the halogen lamp providing a broader distribution and the xenon lamp providing a distribution more similar to a point source. The integrated photodetector collects light from 1 cm2 and is wavelength dependent indicating that it may not accurately measure the flux from the different light sources. It also may be possible that the different fluxes and angular distributions are absorbed differently in the aerogel providing different temperature differences. At high temperature differences the model predicted and experimentally measured steady-state pressure difference deviate further. This is likely due to the free convection cooling, which is currently neglected in the model, becoming relatively more important at higher incident radiant fluxes. The model does predict a steady-state pressure difference that is between the experimentally measured value for the two different lamps and is adequate to radiant fluxes of roughly 100 mw/cm2. Further validation is required for fluxes of 150 mw/cm2 and above, likely due to the onset of convection at the higher fluxes. O Halogen Lamp □ Xenon Lamp Model 150 200 Figure 58. Steady-State AP Dependence on Incident Flux 107 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 7 Multi-Stage Measurements: Pumping Curve Measurements and Cascading Effects Investigations The single stage transpiration membrane temperature difference and steady state pressure difference measurements discussed in Chapter 6 provided an understanding of the optical properties of the aerogel transpiration membrane, the thermal properties of the transpiration membrane and its surroundings, and the thermal transpiration properties of the aerogel transpiration membrane. The measurements were used to validate both the membrane’s thermal portion and thermal transpiration portion of the Knudsen Compressor Performance Model for a single stage. The measurements did not, however, provide any information about the flow conductance of the transpiration membrane or the gas throughput produced by the thermal transpiration membrane. Multistage measurements, for various gases and cascades of up to 15 stages, discussed in this section are used to understand the flow conductance properties of the aerogel transpiration membrane and to validate predictions of the throughput produced by the thermal transpiration effect. Validation of the throughput portion of the Knudsen Compressor Performance Model completes the validation of the entire model for the conditions of this investigation. The measurements were also used to demonstrate the cascading performance for the Knudsen Compressor for various numbers of stages and to identify any issues that may arise when operating Knudsen Compressor cascades. 7,1 One to Five Stage Cascade Description The detailed description of an individual stage of the conventionally machined Knudsen Compressor is given in Section 6.1. The same conventionally machined Knudsen Compressor stages are used in the experimental investigations described in this chapter for the cascades of up to 5 stages. The 15 stage cascade had a similar design that is detailed in Section 7.4. Knudsen Compressor cascades of up to 5 stages were assembled by connecting individual Knudsen Compressor stages together in series. The cascades were driven by illuminating each stage individually using Xenon discharge lamps. The 108 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. light sources were all connected in parallel to the same power supply providing a nominally constant incident radiant flux for all of the stages in the cascade. The variation in radiant flux between 2 sample xenon lamps operating at the nominal conditions used in this study (20.9mw/cm2 at the transpiration membrane location) was measured using an integrated photodetector and determined to be less than 5%. Additional incident flux variations due to misalignment of the xenon lamps and variation in the optical properties of the Plexiglas cover for the different stages could not accurately be determined, but would also lead to additional stage-to-stage performance variations. Special care was taken during the manufacturing process in an attempt to produce physically identical stages, but measurable differences between the stages were unavoidable. One obvious physical variation between the different individual Knudsen Compressor stages was the aerogel transpiration membrane’s cross-sectional area. The aerogel for each transpiration membrane was cut using a razor blade yielding pieces with irregular cross-sections. The cross-sectional area of each stage was estimated by multiplying the average of the width and height (both measured at 3 locations: top, middle, bottom). A survey of transpiration membranes used for the 15 stage Knudsen Compressor cascade described in Section 7.4 measured an average cross-sectional area of 0.89cm2 with a standard deviation of 4.87xl0'2. The Type I aerogel density, 80 mg/cc, predominantly used in this study was chosen from initial energy efficiency optimizations. It was not optimized from an ease of manufacturing perspective. At low aerogel densities (40mg/cc for example) silicon aerogel has a “sponge-like” behavior while at high aerogel densities (120mg/cc for example) silicon aerogel has a “glass-like” behavior. This transition in behavior seems to occur at roughly 70mg/cc.3 4 Repeatably cutting the aerogel to the required size and shape proved difficult at this intermediate density because the aerogel has some flexibility like a sponge, but can also shatter like glass. The transpiration membrane thickness also varied between the different stages. The transpiration membranes for the various stages were all cut from a single sheet of aerogel. The thickness changed across the sheet with the thickest part of the aerogel at the sheet edges and the thinnest part in the middle. The aerogel transpiration membrane thickness changed by up to ±20% from the nominal value of 2mm for the 109 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. different stages constructed for this study. The variation in the aerogel transpiration membrane cross- sectional area would produce a corresponding variation in the transpiration membrane flow conductance and the net flowrate produced by the stage. The variation in aerogel transpiration membrane thickness would affect the temperature difference produced across the membrane with a thinner membrane having a lower temperature difference, which would decrease the strength of the thermal transpiration effect and the steady-state pressure difference. The variation in membrane thickness would also, however, vary the stage gas flow conductance, with a thinner membrane having a higher flow conductance, which would tend to increase the flowrate produced by the stage and counteract the reduction in flowrate from the lower temperature difference. New stage production techniques are required to provide more repeatable manufacturing to allow more thorough investigations to be made in the future. 7.2 Pumping Curve Experimental Process The experimental setup, detailed in Chapter 6, that was used to measure the transpiration membrane temperature difference and steady state pressure difference did not allow the throughput of the stage to be measured at any point in the pumpdown curve. The experimental process used to determine the throughput of the Knudsen Compressor chosen for this study was to measure pressure difference across the Knudsen Compressor as a function of time during a pumpdown process while the pump is operating between two known volumes. This simple technique allows the determination of the pump throughput for the entire pressure range during a pumpdown. The experimental apparatus used to determine the complete pumping performance of cascades of 1, 2, and 5 stages investigation is shown in Figure 59. 110 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Separation Valve Differential Pressure Sensor To Evacuation and Gas FiU Line Absolute Pressure Sensor Figure 59. Five Stage Knudsen Compressor Experimental Setup Figure 59 shows the 5-stage cascade assembled by connecting 5 individual stages in series, but the same setup was used to investigate individual stages and cascades of 2 stages. Xenon lamps are placed above each of the stages to illuminate them each individually. The two sides of the cascade can be separated by closing a separation toggle valve. The absolute pressure was measured on the low-pressure side of the pump by a baratron pressure sensor. The differential pressure across the pump was also measured using another baratron pressure sensor. The high-pressure side of the pump was also connected to a mechanical pump and gas bottle system that allowed the Knudsen Compressor and the experimental setup to be evacuated and then refilled with a pure gas. The volume connected to both sides of the Knudsen Compressor consisted of the tubing and the dead volume of the baratron pressure sensors. The entire experimental apparatus was surrounded by air at atmospheric pressure. Gas leaks into the system and the sensitivity of both the differential baratron and the absolute baratron limited the experiments to tests with an operating average pressure of above 250 mTorr. The first step of the experimental process was to evacuate the Knudsen Compressor and setup volumes to a pressure lower than 50 mTorr using a mechanical pump and then refill the volumes with a pure gas to the required mean pressure. The gas valve to the gas fill system was then closed, isolating the system. The xenon lamps were then turned on, illuminating the stages and establishing 111 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the temperature differences across the transpiration membranes in all of the stages. For all of the results described in this chapter the stages were individually illuminated with xenon lamps providing a nominal radiant flux of 20.9 mW/cm2 at the top surface of the aerogel transpiration membrane. The separation valve was initially left in the open position to avoid any pressure difference from being built up by the Knudsen Compressor while the temperature difference across the transpiration membrane was established. The temperature difference across the transpiration membrane is established rather quickly (on the order of seconds), but it takes more time (usually several minutes) for the temperature of the body of the stages to reach a steady state. The separation valve was then closed, isolating the two volumes, allowing the cascade to build up a pressure difference between the volumes on the two sides of the Knudsen Compressor. There is no pressure difference across the cascade immediately following the closure of the separating valve, but the rate of change of the pressure difference is maximized because the cascade is operating at the maximum flow rate condition. The pressure difference continuously builds until the steady-state condition is reached with a constant pressure difference, which is the maximum pressure difference that the stage is capable of producing for the operational conditions. Once the steady state pressure difference was established the xenon lamps were shut off, removing the temperature gradient, leaving only the pressure gradient return flow in the transpiration membrane. The temperature difference across the membrane dropped became negligible within several seconds. The pressure difference across the pump then decreased due to the pressure gradient driven return flow. The pressures were measured at 1 or 2 second intervals during the entire process using a computer with a data acquisition card and Labview software. A representative pressure trace for the entire experimental process is shown in Figure 60 for a single stage with type II (120 mg/cc 8% carbon) aerogel operating on air with a radiant flux of 20.9 mw/cm2. 112 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 766 765 764 — 763 | 762 ^ 761 760 759 758 tim e (s) Figure 60. Representative 1 Stage Cascade Pressure Trace For the first 100 seconds the xenon lamp was off and the separation valve was open. After 100 seconds the lamp was turned on while keeping the separation valve closed. During this time a slight pressure increase is due to the gas in the isolated system being heated by the radiant flux. After another 200 seconds the separation valve was closed allowing the pressure difference to be established. The large jump in pressure difference seen at this time is an artifact due to the separation valve closure. At an elapsed time of 800 seconds the xenon lamp was turned off and the pressure difference across the cascade dropped due to the pressure return flow. By an elapsed time of 1200 seconds the pressure difference had become negligibly small and the Xenon lamp was turned back on. The second pumpdown was not an exact repeat of the first because the separation valve was already closed when the lamp was turned on. This demonstrated the relative importance of the valve closure and the finite time it takes to establish the temperature gradient across the aerogel transpiration membrane. At an elapsed time of 1700 seconds the Xenon lamp was turned off. The pressure difference, AP, and the pressure of the cold side of the pump, Pc were measured while Ph is calculated by adding the measured pressure difference to the cold side pressure. The throughput produced by the Knudsen Compressor during the powered portion of the pumping curve was calculated from 113 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. N = • 5(AP) dt { / k + (88) Where Vc and Vh are the volume on the low pressure side and high pressure of the Knudsen Compressor, respectively. The pressure difference as a function of time for the pumpdown curve trace for pumps with a well-defined pumping speed can be represented by AP = AP (89) Where the time constant for a Knudsen Compressor cascade with small pressure differences can be given by = (90) Where Q o ta i is the total gas conductance for the Knudsen Compressor. The pressure difference traces for both the steady-state heating case (sh) and the transient startup heating case (th) (where the separation valve is already closed when the Xenon lamps are turned on) are shown in Figure 61. A DPsh X DPth ^sh “ 35 0s xth = 3 3 .0 s Csh = 4.63E -7 n f/s C,h = 4.91 E-7 itP/s 100 time (s) 150 200 Figure 61. Pressure Difference Traces for a Single Type II Stage on Air Figure 61 also shows the time constant and corresponding membrane flow conductance for the two cases. The time constant was calculated by fitting the exponential form shown in Equation 89 to the 114 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. experimental curve such that it would provide the correct time to reach 63.2% of its maximum value. For this specific case the time constants measured by the transient heating and steady heating cases agree to within 6%. The pressures were measured at 1 second intervals in this case. The uncertainty in the assignment of a starting point for the pumpdown can lead to uncertainties of this magnitude. The time response of the baratron pressure sensors is published as 1 second leading to additional uncertainty when comparing the experimental pumpdown curves with the curves from the Knudsen Compressor Performance Model. Figure 62 shows the relationship between throughput and pressure difference for the powered portion of the traces. Both the measured maximum pressure difference and maximum flowrate agree to within 4% for the transient startup and steady heating cases for this particular run. This repeatability is well within the uncertainties associated with the method. The gas conductance of the transpiration membrane can be determined from the nonpowered portion of the pressure trace by using the relationship Figure 63 shows the comparison of the normalized throughput to the normalized pressure difference relationships for the venting portions of the traces. The slope of the line is the gas conductance for the cascade. b c r i u . . . . Linear fS te a H v H e atin n t ♦ Steady Heatini Steady Heating L ilw m tii 7 E + 1 6 vT 6 E + 1 6 * 5 E + 1 6 J 4 E + 1 6 3 E + 1 6 2 E + 1 6 1E + 1 6 0 1 2 3 4 5 6 AP (Torr) Figure 62. Performance Curves for a Type II Single Stage on Air (91) 115 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 4.0E-09 3.5E-09 3.0E-09 J {2 2.5E-09 f 2.0E-09 J 1.5E-09 1.0E-09 5.0E-10 O.OE+OO 0 0.002 0.004 0.006 0.008 A P/Payg Figure 63. Venting Traces for a Single Type II Stage on Air The gas conductance calculated from both traces for this run agrees to within 1%. The gas conductance calculated from the steady-state pumpdown curve also agrees to within 1%. This same experimental process was used for all of the following results. 7.3 Summary of Pumping Trace Results Pumping curve experiments were conducted with a radiantly driven single stage Knudsen Compressor using type II aerogel, illuminated by a xenon lamp with a flux of 20.9 mw/cm2, and operating on air. The steady-state maximum pressure difference produced by the stage for various pressures is compared to the model predicted values and shown in Figure 64. 7 ♦ Experiment Model 6 5 S 4 H CL 3 < 2 1 0 0 200 400 600 800 Pc (Torr) F ig u re 64. Maximum Pressure Difference verses Pressure for a Single Type II Aerogel Stage 116 ♦ Steady Heating ■ Transient Heating — — Linear (Steady Heating) . . . . Linear (Transient Heating) C = 4.65E-7 trP/s Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The agreement between the model predictions and the experimentally measured values is within 20% over the entire pressure range. At the lowest pressure, 100 Torr, the model overpredicts the steady- state pressure difference while at atmospheric pressure the model underpredicts the steady-state pressure difference. This trend is in agreement with the trend for the discrepancy between the model predicted and experimentally measured temperature difference for type I stages in Nitrogen. A similar discrepancy in membrane temperature difference is expected for type II aerogel stages. Figure 65 shows the maximum flowrate produced by the single stage for various pressures. 1.E+17 - 9.E+16 - 8.E+16 - 7.E+16 - ^ 6.E+16 - * 5.E+16 - z S 4.E+16 - 3.E+16 - 2.E+16 - 1.E+16 - O.E+OO - 0 200 400 600 800 Pc (Torr) ■ Experiment Model Figure 65. Maximum Flowrate verses Pressure for a Single Type II Aerogel Stage The model predicted values seem to agree well with the experimentally measured throughput values at low pressures, but a discrepancy appears at higher pressures. The discrepancy between the model and the experiment is explained by the combining the discrepancy for the steady-state pressure difference, shown in Figure 64, and the gas conductance, shown in Figure 66. The Knudsen Compressor Performance Model overpredicts the steady-state pressure difference at low pressures and underpredicts it at high pressures, while the model underpredicts the gas conductance for the entire pressure range, which, when combined, produce the discrepancy shown in Figure 65. Figure 66 compares the gas flow conductance calculated from the pump down and vent up curves with the value predicted from the Knudsen Compressor Performance Model. 117 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 6.0E-07 5.0E-07 - 4.0E-07 E 3.0E-07 X Rjmp Dow n X Vent up + Model 2.0E-07 - 1.0E-07 600 800 200 Figure 66. Comparison of Experimentally Measured and Predicted Gas Flow Conductances for Type II Aerogel All of the gas flow conductance values agree to within 10% except for at the 100 Torr case where they agree to within 20%. This is well within the experimental uncertainty and the uncertainty of the inputs for the Knudsen Compressor Performance Model. The pumping curve investigation process detailed in Section 7.2 was also used to investigate different Knudsen Compressor cascades composed of 1,2 and 5 stages with type I aerogel transpiration membranes. Figure 67 shows the steady-state pressure differences for cascades with 1, 2, and 5 stages (with type I aerogel) for various pressures of N2. 45 T 40 - 35 30 5 25 t- r 2o- < 15 - 10 - 5 - 0 - 0 100 200 300 400 500 600 700 800 _____________________________________ Pc (Torr)_______________________________ Figure 67. Steady-State Pressure Difference for Various Numbers of Stages 118 ♦ 1 Stage Exp ■ 2 Stage Exp ▲ 5 Stage Exp 1 Stage Model 2 Stage Model ■ “ “ 5 Stage Model Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The stages were individually illuminated by xenon lamps with a flux of 20.9 mw/cm2 at the hot side of the aerogel transpiration membrane. Figure 67 also shows the steady-state pressure differences predicted by the Knudsen Compressor Performance Model for the same conditions. The agreement between the predicted values and the measured values is within 8% over the entire pressure range. Each Type I stage produced a steady state pressure difference of roughly 8 Torr at atmospheric pressure. This is higher than the type II aerogel stages due to the increased temperature difference across the membrane for type I aerogel membranes. The type II aerogel membranes are thinner and have a higher thermal conductivity. Both of these factors tend to lead to a smaller temperature difference across the membrane. The maximum pressure difference scales like the number of stages. This is the expected trend for cascades with small numbers of stages. Figure 68 compares the experimentally measured maximum flowrate to the values predicted by the Knudsen Compressor Performance Model for the same conditions. 1.E+17 9.E+16 8.E+16 7.E+16 •76.E+16 S-5.E+16 J 4.E+I6 3.E+16 2.E+16 1.E+16 0.E+00 X 1 Stage Exp X X 2 Stage Exp X + 5 Stage Exp X + --------- 1 Stage Model X + --------- 2 Stage Model — — 5 Stage Model X + * ..... .......... " ' 1 ' 1 “ T .................... 200 400 M T orr) 600 800 Figure 68. Maximum Flowrate for Various Numbers of Stages The Knudsen Compressor Performance Model predicts the same flowrate for the different numbers of stages because of the low temperature difference obtained across the transpiration membranes in each of the stages. The difference between the experimentally measured values for different numbers of stages is likely due to stage-to-stage variations due to manufacturing. The Knudsen Compressor Performance Model again underpredicts the throughput, similar to the case for the Type II aerogel stage shown in Figure 65. The throughput for the type II membrane, 8.8E16 #/s, is much closer to the 119 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. throughput for the type I aerogel stages because while the temperature difference across the membrane is lower for the type II stage, the gas conductance is higher. Stage variations due to manufacturing have a larger effect on the throughput than on the pressure difference. Stage variations affect both the temperature difference and the gas conductance of the transpiration membrane. The stage pressure difference depends only on the temperature difference, while the stage throughput depends on both the temperature difference and the stage conductance. Figure 69 shows the measured and predicted total gas conductance for the different cascades. 4.0E-07 3.5E-07 3.0E-07 -| ? Z5E'° 7 £ 2.0E-07 J 1.5E-07 1.0E-07 5.0E-08 0.0E+00 200 400 600 Pc (Torr) ♦ 1 Stage Exp • 2 Stage Exp A 5 Stage Exp 1 Stage Mod 2 Stage Mod 5 Stage Mod 800 1000 Figure 69. Cascade Gas Flow Conductance for Various Numbers of Stages The Knudsen Compressor Performance Model tends to consistently underpredict, by roughly 30%, the total gas conductance (for cascades of 1 and 2 stages), which is the dominant factor in producing the discrepancy for the cascade throughput shown in Figure 68. The 5 stage cascade shows good agreement between the experimentally measured and model predicted gas conductance. This variation for the various numbers of stages is likely due to the limited manufacturing repeatability. The possible factors leading to the throughput discrepancy are an underestimate of the pore diameter, an underestimate of the porosity, a thinner membrane than nominally measured, or a larger membrane area than nominally measured. The range of possible pore radii for p=80mg/cc aerogel, predicted in Section 3.3, is 11.1 to 27.9 nm with the nominal value being 20. lnm. If the real mean effective pore radius was at the upper end of the range, 27.9nm, the conductance would be 39% higher, which is 120 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. sufficient to explain the discrepancy. The estimated porosity for the Type I aerogel is 0.969, while the maximum is 1, indicating that an underestimate of the porosity is not likely the cause of the discrepancy. The maximum variation in the stage cross-sectional area was roughly 7% while the maximum variation in stage thickness was roughly 20%. Additional work with more reliably manufactured stages is required to determine the relative importance of the listed candidates for the throughput discrepancy. Figure 70 shows the maximum pressure difference maintained by the 5 stage Knudsen Compressor for Nitrogen and Argon verses mean pressure. The variation in the maximum pressure difference for different gases is due primarily to the different temperature difference produced across the transpiration membrane because of the variation in the gas thermal conductivity. The results agree to within 5% over the entire pressure range, which is typical for APm a x . N2 Model — — A r Model 50 - 40 - 30 - 20 - 10 - 100 200 300 400 Pc (Torr) 500 600 700 800 Figure 70. Maximum Pressure Difference for 5 Stage Knudsen Compressor Figure 71 shows the maximum throughput produced by the 5 stage cascade for the same conditions. 121 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 9.0E+16 8.0E+16 N2 Model A r Model 7.0E+16 6.0E+16 | 5.0E+16 J z 4.0E+16 3.0E+16 2.0E+16 1.0E+16 O.OE+OO 500 600 700 800 200 300 400 0 100 Figure 71. Maximum Throughput for 5 Stage Knudsen Compressor Again, the Knudsen Compressor Performance Model consistently underpredicts the gas throughput for both Argon and Nitrogen. More repeatable manufacturing procedures are required to make more accurate performance measurements for various stage conditions to determine which portion of the Knudsen Compressor Performance Model is producing the discrepancy for the Knudsen Compressor throughput. 7.4 IS Stage Conventionally Machined Knudsen Compressor A 15 stage cascade was also constructed to demonstrate the operation of a Knudsen Compressor composed of a large numbers of stages. The 15 stage cascade was a self-contained unit built to limit the gas leaks from the gas connections between each stage. It also allows the identification of issues associated with a cascade of stages all contained in one unit. Each of the stages is sized the same as the single Knudsen Compressor stages detailed in Section 6.1. Each stage of the cascade was illuminated individually by the same Xenon lamps used in the experiments detailed in section 7.3. The assembled 15 stage cascade is shown in Figure 72. 122 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Figure 72. Fifteen Stage Knudsen Compressor Cascade Figure 73 shows the pumpdown trace obtained with the 15 stage cascade operating at a mean pressure of 1 atm of air and illuminated by individual Xenon lamps with a flux of 20.9 mw/cm2 at the location of the aerogel transpiration membrane (type I). The 15 stage cascade produces a maximum pressure difference of 120 Torr or 8 Torr per stage. The 1,2 and 5 stage cascades also produced about 8 Torr per stage for the same conditions. The 15 stage cascade also produced a maximum gas throughput of 5xl01 6 #/s, which is lower than the 7.5xl01 6 #/s for the 5 stage cascade. Again this can be attributed primarily to manufacturing differences between the stages. The difference between the two experimental curves is a fundamental difference between transient heating startups and steady-state heating startups. The nonlinear trend of both experimental curves for low pressure differences is likely due to transient pressure gradients within the Knudsen Compressor immediately after startup. 6E+16 □ Steady Heating o Transient Heating Model 5E+16 4E+16 3E+16 2E+16 1E+16 100 120 AP (Torr) Figure 73. 15 Stage Cascade Pumpdown Curves 123 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 8 Proposed Future Knudsen Compressor Designs Conventionally machined radiantly driven Knudsen Compressor cascades of up to 15 stages were experimentally demonstrated with Nitrogen, Air, Helium, and Argon with mean pressures ranging from 200 mTorr to 1 atm and with radiant fluxes up to 150 mw/cm2. The various components of the Knudsen Compressor Performance Model were individually validated over this range of operating conditions. The knowledge gained during the experimental process and while developing the analytical performance model can be used to generate several candidate Knudsen Compressor designs for various applications in order to: (1) compare predicted Knudsen Compressor performances to performance requirements that can be estimated for the applications identified in Chapter 1; (2) demonstrate the potential range of applicability of Knudsen Compressor technology; and identify potential manufacturing concerns that may arise. The Knudsen Compressor Performance Model was first used to perform an optimization analysis to gain general design insight for the wide range of potential Knudsen Compressor applications without regard to specific manufacturing limitations. The design optimization is carried out for three cases to bound the problem based on the parameter k ; k = 0 for pure flow production, k = l A for both maintaining a pressure ratio and producing a flow, and k = 1 for simply maintaining a pure pressure difference. Candidate Knudsen Compressor designs are detailed for three different applications; a radiantly heated meso-scale gas roughing pump sized to back Creare’s ultraminiaturized turbomolecular pump, a resistively heated meso-scale low pressure ratio gas pump, and a general description of waste heat driven Knudsen Compressors. 8.1 Single Point Knudsen Compressor Optimization The variety of potential Knudsen Compressor applications outlined in Chapter 1 leads to a corresponding range in potential Knudsen Compressor designs. Some applications, the chemiresistor 124 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. based gas detector for example, require only a net gas flow rate while others such as meso-scale gas roughing pumps or gas compressors require both significant pressure ratios and gas flowrates. Still other applications can be envisioned, such as a micro-scale solid-state pressure regulator that would maintain a steady pressure difference with only a minimal net flow. It is clearly not possible to define a globally optimized design for the entire range of potential applications, but it is possible to bound the optimization problem by considering several representative single point optimization cases. Three separate single pumping curve optimizations were conducted and are discussed in this section: moderate k representing applications requiring both a net gas flows and significant pressure differences, k = 0 representing applications that require only throughput, and k = 1 representing applications that require only a pressure difference. 8.1. a Knudsen Compressor Optimization - Moderate k Knudsen Compressors employed as meso-scale gas roughing pumps will operate through many pumpdown cycles, requiring efficient operation over the entire range of k . At other times they will operate at a steady-state condition with a significant pressure difference and gas flow. The simplest optimization case that can represent this type of operation is to minimize the power required to operate at some intermediate pressure difference-throughput point in the pumping curve, k = Vi for example. The representative moderate k optimization procedure was completed in two steps: first performing a single stage moderate k optimization study, then demonstrating the performance of several representative Knudsen Compressor cascades, each implementing a different level of optimization, operating as the backing pump for the Creare miniaturized turbomolecular pump, detailed in Section 1.7. An individual stage of the Knudsen Compressor can be optimized for moderate k operation, under power consumption considerations, by minimizing the energy per unit throughput and normalized pressure difference as given by 125 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. By substituting the analytical expressions for the throughput and pressure difference for a single stage of a Knudsen Compressor from Equation 43 and rearranging terms the energy efficiency can be written as The first bracketed term approximately represents how efficiently an incident flux, Q , can maintain a temperature difference across a transpiration membrane with a thickness, Lx. The first term is plotted in Figure 74 for 1 atm of N2 with membrane parameters, pp O r=80 mg/cc, f car b o n = 8 % , for a variety of Initial energy optimization of the aerogel membrane density and carbon dope fraction was completed in Section 3.10 for radiantly driven Knudsen Compressors, these optimized values, p = 80 mg/cc and fcarb o n = 8%, were held constant for the optimization analysis as it is assumed that they are relatively independent of the bracketed terms in Equation 93. The area of each stage was adjusted so that they would all produce the same throughput of 6.05xl01 7 #/s at k = 1/2. (93) radiant fluxes verses membrane thickness. Figure 75 shows the same information for 1 Torr of N2. 100000 —• — f = 50rrw /cm 2 —■— f = 100rrw /cm2 —* — f = 200rrw /cm2 f = 500nrw /cm2 f = 1000mw/cm2 b- 10000 100 0 2 3 4 5 L (mm) Figure 74. Minimization of First Bracketed Term for P = 1 atm of Air 126 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 100000 —«— f = 50mw/cm2 —■— f = 100rrw/cm2 —A— f = 200rrw/cm2 —* — f = 500rrw l e n d — •— f = 1000rrw /cm2 10000 1000 100 L (mm) Figure 75. Minimization of First Bracketed Term for P = 1 Torr of Air The minimum of the first bracketed term, corresponding to the minimum required energy, occurs at a membrane thickness of 0.5mm and an incident radiant flux of 1000 mw/cm2 for both the high- pressure and low-pressure case. The optimization of the first bracketed term appears to be negligibly affected by the gas pressure indicating that the same optimization can be used for all of the stages in a Knudsen Compressor cascade. It does appear that a decrease in the required energy of several orders of magnitude is possible by using thinner transpiration membranes (0.5mm instead of 2mm) and higher fluxes (1000 mw/cm2 instead of 100 mw/cm2 ) compared to the current Knudsen Compressor design used in the experiments detailed in Chapters 6 and 7. Future experimental investigations at these conditions will be required, however, since the Knudsen Compressor Performance Code has not been validated for these conditions. The second bracketed term represents the optimal scaling of the transpiration membrane pore size with Knudsen Number (or gas pressure). Figure 76 shows the second term, normalized by its minimum value for a given gas pressure, for various pressures of N2. 127 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1.E+06 S' 1.&-05 4) N | 1.EMJ4 1.Ef03 1.E+02 £ 4) I- ■ o o ■ g 1.&01 r a o 5 ? 1.E+00 CM 1.E-01 9 1.E-03 1.E-01 1.Ef01 1.E+03 Kn o 10 m Torr □ 100 mTorr * 1 Torr 1.E+05 1.Ef07 Figure 76. Minimization of Second Bracketed Term The minimum of the second term occurs at a Knudsen Number of roughly 1.2 for all of the gas pressures, which agrees with the findings from previous work.3 1 This indicates that the pores in the transpiration membrane of each stage should be individually sized to provide a Knudsen Number of 1.2 for the design conditions. The Knudsen Compressor design employed in the present work has a transpiration membrane Knudsen Number of 2.5x10s at a pressure of 10 mTorr providing and energy consumption of more than four orders of magnitude greater than the optimized stage for 10 mTorr. The third bracketed term represents the optimal location on the pumping curve to operate each stage and is shown in Figure 77 for completeness. The third term is minimized for a k of 0.5, the location on the pumping curve corresponding to the Knudsen Compressor stage operating at half of the maximum pressure difference and half of the maximum throughput. The optimization of the third bracketed term is forced by the definition of the energy efficiency, given in Equation 92, where both the throughput and normalized pressure difference are treated equally. This optimization technique can be incorporated into Knudsen Compressor designs by varying the cross-sectional area of each transpiration membrane such that the throughput through each of them produces and k = Vi condition for the stage. Even with the stage k of 0.2 or 0.8 the energy consumption is only increased by 50% indicating that this is the least important optimization factor to consider. The fourth bracketed term 128 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. represents the conditions of the working gas and although it will affect the overall power consumption, it is not involved in the optimization process. 10 0.8 0.2 0.4 0.6 Figure 77. Minimization of Third Bracketed Term From this analysis it is evident that the most critical term to optimize is the second bracketed term, accomplished by choosing stages with the right pore size for the mean operating pressure of each stage. The second most important term to optimize is the first term, which is accomplished by using high radiant fluxes (500 to 1000 mw/cm2 ) and thin transpiration membranes (500 p.m). The third bracketed term is the least important term to optimize and at this stage in the development of the Knudsen Compressor it is satisfactory to neglect its effects. It is apparent from this optimization analysis that orders of magnitude decreases in power consumption can be achieved from the experimental design employed in this investigation by properly sizing the transpiration membrane pores and by using an increased incident flux and decreased transpiration membrane thickness. It is useful to demonstrate the effect of optimizing individual Knudsen Compressor stages on the performance of an entire Knudsen Compressor cascade. This was accomplished by using the Knudsen Compressor Performance Code to estimate the performance of Knudsen Compressor cascades, under various levels of optimization, as a backing pump for Creare’s miniaturized 129 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. turbomolecular pump. Table VIII lists a summary of the properties of Creare’s pump that were used to develop appropriate performance targets for the Knudsen Compressor cascade. Volume V = 165cmJ Power 1 W Flow Rate 5 1/s @ lxlO"5 Torr or 1.7xl01 5 #/s Backing Pressure 1 Torr Lifetime 1 Year Continuous Operation Table VHL Properties of Creare’s Miniaturized Turbomolecular Pump The performance targets for a Knudsen Compressor operating as the backing pump for the Creare pump at a steady flowrate condition are listed in Table IX. The performance requirements for the device’s volume and power were obtained by assuming that the volume and power of the Knudsen Compressor should be similar to that of the turbopump. Volume < 165 cc Power < 1 W Flow lJ x lO 1 5 #/s Pressure Range 1 Torr - 760 Torr Table IX. Required Properties for the Meso-Scale Gas Roughing Pump The characteristics of six different Knudsen Compressor cascades, each at different levels of optimization, were determined using the Knudsen Compressor Performance Model to demonstrate, for entire cascades, the significance of each of the terms in Equation 93. Cascade #1 was based on the current experimental Knudsen Compressor detailed in Chapters 6 and 7. Cascade #2 was modified by employing the optimum radiant flux, 1000 mw/cm2, and membrane thickness, 'A mm, (optimizing the 1s t bracketed term in Equation 93) for each stage of the cascade. Cascade #3 adds perforated aerogel transpiration membrane technology, with the holes sized to provide a Knudsen Number of 1.2 for each stage in the cascade, thus minimizing the second bracketed term in Equation 93. Cascade #4 includes the optimization of the 3rd bracketed term by adjusting each stage area to optimize the pumpdown location for each stage in the cascade. Cascade #5 was sized to incorporate the same stage optimizations in cascade #4, but under the currently practical limitation that the smallest available hole diameter possible in perforated aerogel is about 5 p.m. Unetched aerogel was used for stages that would require holes smaller than 5pm under the Kn = 1.2 optimization regimen. All of the cascades 130 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. were designed to operate between 1 Torr and 760 Torr with a throughput of 1.7xl01 5 particles per second. Table X details the characteristics of the different cascades. Cascade #1 Cascade #2 Cascade #3 Cascade #4 Cascade #5 Case Base Optimal < t> ,L x K n= 1.2 © I I * Practical Stages 314 57 448 312 127 Pmin(W) 435 151 .600 .489 .946 Volume (cc) 208000 1120 .159 .137 .592 Table X Cascade Optimization Effects It is clear that some level of optimization is required because Cascade #1, a default cascade based on the laboratory Knudsen Compressor design used in this work, would require 435W of power and have a volume of 0.2m3 which are both clearly inconsistent with meso-scale pumping requirements. By optimizing the incident radiant flux and transpiration membrane thickness the pump volume is reduced by several orders of magnitude and the pump power is reduced by roughly a factor of 3. Optimizing the transpiration membrane pore diameters for each individual stage reduces the pump power by several orders of magnitude and the pump volume by almost 4 orders of magnitude. Optimizing the transpiration membrane area to locate each stage at the optimal location on the pumpdown curve provides only modest reductions in both power consumed and volume required. Adding practical aerogel drilling constraints only causes modest increases in both the required power and volume for the cascade. It should be noted here that the listed volume and power are minimum values. The required power is only the radiant power striking the aerogel transpiration membranes and the volume represents only the interior volume (accessible to the working gas) of the Knudsen Compressor. It appears, however, that the practical Knudsen Compressor design can operate efficiently enough at the moderate k conditions for application as the backing pump for the miniaturized turbomolecular pump from Creare. 8. l.b Knudsen Compressor Cascade Optimization -M oderate k Knudsen Compressor applications requiring repeated pumpdowns will require efficient operation over the entire pumpdown curve indicating that future optimization work is required to determine the effect of optimizing the Knudsen Compressor for a single k on the entire pumpdown process. The current 131 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. form of the Knudsen Compressor Performance Code is incapable of making accurate pumpdown predictions for cascades made from a large number of stages with different properties, making it impossible to directly compare the different cascades listed in Table X for the entire pumpdown process. An initial understanding of this effect can be gained by comparing the energy efficiency of single stages of perforated aerogels over the entire operating pressure range. Optimally perforating the aerogel transpiration membranes is stage specific and has the largest effect on the overall power consumption indicating that it is the most critical optimization step consider. Figure 78 shows the energy efficiency for a single stage Knudsen Compressor (p = 80mg/cc, fc a rb o n = 0.08, A=lcm2 ) illuminated by < ) > = 1000mw/cm2 operating on N2 for 4 different stages: no perforation, Lr = 6xl0'6 m (optimized for lOTorr), Lr = 6xl0‘5 m (optimized for ITorr), Lr = 6xl0'4 m (optimized for lOOmTorr). 1E-11 — - Nominal Aerogel Optimized fo r F^IO Torr — — Optimized fo r P=1 Torr Optimized fo r P=100 1E-12 1E-13 1E-14 1E-15 1E-16 0.1 100 1000 0.01 P (Torr) Figure 78. Nonoptimal Operation of Perforated Aerogel Stages Figure 78 again illustrates the requirement for using perforated aerogel technology (or other technologies such as glass microsphere beds) at low pressures; the energy efficiency is 4 orders of magnitude worse for nominal aerogel at lOOmTorr than at atmospheric pressure. It is also apparent that it is reasonable to use a limited number of pore diameters (roughly 1 per order of magnitude of pressure) with only minimal increases in the required energy. The effect of optimally perforating the aerogel transpiration membranes on the pumpdown performance of a Knudsen Compressor cascade can be qualitatively understood by comparing the practically optimized Knudsen Compressor cascade 132 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. (Cascade #5) to a similar cascade without any perforations. The stages in Cascade #5 can be divided into two types: perforated and unperforated. When both cascades are initially turned on all of the stages will be at atmospheric pressure. It is evident from Figure 78 that none of the perforated stages will contribute significantly to the net pumping at atmospheric pressure. Their gas flow conductance is, however, several orders of magnitude higher than the gas flow conductance of the unperforated aerogel stages so they will not contribute significantly to restricting the flow either. The throughput for both cascades will then be roughly the same at startup. The cascades will both begin to build up a pressure difference, which will be predominantly across the unperforated aerogel stages for Cascade #5 because of their orders of magnitude lower gas conductance. At the same pressure difference Cascade #5 will be achieving a higher fraction of its maximum pressure difference (k) since it has less stages pumping which correspond to a lower throughput than for the unperforated cascade. The practically optimized Knudsen Compressor cascade would then have a slightly lower energy efficiency at pressures just below atmospheric. Although this could be counteracted by selectively illuminating only those stages that would be actively pumping at any point on the pumpdown curve. At some pressure, around 100 Torr according to Figure 78, the perforated aerogel stages will begin significant pumping which will increase the throughput compared to the Knudsen Compressor made from completely nominal aerogel stages. As more of the perforated aerogel stages begin pumping the energy efficiency of the optimized cascade will increase relative to the unperforated cascade. By the time that the low-pressure side of the optimized Knudsen Compressor cascade has reached ITorr (the design parameter used in the single stage k = Vi optimization procedure) it will have an energy efficiency of roughly two orders of magnitude better than the imperforated cascade. It appears from this analysis that the optimized Knudsen Compressor cascade is likely to have an increased pumpdown performance (by decreasing the energy and time required to evacuate a chamber), although it could perform worse during the portion of the time between startup and when the low- pressure side is at a pressure of 100s of Torr for the current design unless the stages that aren’t pumping in this regime are shut off. 133 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 8 . 1 . C Knudsen Compressor Optimization - k = 0 Some micro/meso-scale Knudsen Compressor applications, chemiresistor based gas detectors for example, operate at ambient gas conditions and require only a net gas flowrate, the k = 0 condition on the pumping relationship. Resistive heating is required for Knudsen Compressors producing only a net gas flowrate because they require transpiration membrane thicknesses of several micrometers, which is insufficient for radiant absorption. These applications require a different Knudsen Compressor optimization that minimizes the energy required to produce a given throughput as shown The first bracketed term is similar to that for the moderate k condition and again represents the efficiency of the incident radiant flux in producing a given temperature difference. The second term is also similar to the second term in the moderate k optimization and represents the proper choice of transpiration membrane pore diameter. The 2n d bracketed term for the k = 0 case has no pressure gradient flow coefficient dependence, however. The optimization process used for a meso-scale Knudsen Compressor as a zero pressure difference flow producer was to vary different variables in Equation 94 over a practical range while maintaining the other variables at their nominal value. Once the optimum was determined for that variable then the next was varied and so forth. The k = 0 optimization process started with nominal stage conditions of: A = 1cm2, oriented vertically, Tc = 300K, p = 80mg/cc, fc a rb0 n = 0.08, Lx = 0.5mm, < j > = 500mw/cm2. Figure 79 shows the effect of varying the aerogel density on the k = 0 energy efficiency of the Knudsen Compressor compared to the energy efficiency of the Honeywell Dual Diaphragm Pump detailed in Section 1.5. by (94) 134 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 1 0 0 0 ~ 100 o X X X X X X X X 5 E, o 10 X Q d o l/N d o t-K n u d s e n -— Q d o t/N do t- H oneyw ell 0.1 50 100 p (mg/cc) 150 200 Figure 79. Aerogel Density Effect on Energy Efficiency The energy efficiency is increased by decreasing the aerogel density over the entire range from 200 mg/cc to 10 mg/cc. Practical limitations due to the strength of the aerogel material will, however, limit the density that can be used. A nominal aerogel density of 20 mg/cc was chosen for the next stage of the optimization process. Figure 80 demonstrates the effect of changing the aerogel transpiration membrane carbon dope fraction on the energy efficiency through its effect on the thermal conductivity of the membrane. 100 X X X X I 10 8 s E X Q d o t/N d o t-K n u d s e n Q dot/N dot - H oneyw ell 0.1 0.05 0.1 0.15 carbon fraction 0.2 Figure 80. Carbon Dope Fraction Effect on Energy Efficiency 135 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The optimal carbon dope fraction is roughly 8-12%, the same as the k = 0.5 case since it affects primarily the temperature difference produced across the transpiration membrane for a given powering flux. An optimized carbon dope fraction of 12% was chosen. Figure 81 shows the effect of then varying the transpiration membrane thickness on the energy efficiency. 1000 ~ 100 0 8 1 10 x X X X X X X X X Q d o t/N d o t-K n u d s e n Q dot/N dot - H oneyw ell 0.1 0.5 1 L x (m m ) 1.5 Figure 81. Aerogel Transpiration Membrane Thickness Effect on Energy Efficiency The required energy decreases with decreasing thickness over the entire thickness range studied. A nominal thickness of 5pm was chosen for the final optimization step. Figure 82 shows the effect of changing the powering flux on the predicted energy efficiency. 100 i 10 8 i E, 4 _ | O ? 1 -6- 0.1 i -----------------1 -----------------1 -----------------1 -----------------1 ----------------- 0 200 400 600 800 1000 p (m g /c c ) Figure 82. Powering Flux Effect on the Energy Efficiency 136 flOK X X X X Q d o t/N d o t-K n u d s e n —— Q dot/N dot - H oneyw ell Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. The energy efficiency is relatively constant with flux because the transpiration membrane is so thin, 5pm, that the dominant fraction of the delivered energy goes through the transpiration membrane making the temperature difference, and correspondingly the gas flowrate, linear with the incident radiation flux. The approximately optimized power consumption (17.7 mw/sccm) occurs for very thin aerogel membranes (Lx = 5 pm, p=20mg/cc, fc a rb 0 n = 12%C) and is independent of flux and area because the power transferred through the membrane far exceeds the outward cooling mechanisms for thin aerogel transpiration membranes. The Honeywell DDP has a reported energy efficiency of 0.26 mw/sccm (8mw/30sccm) or roughly 2 orders of magnitude better indicating that the Knudsen Compressor is not competitive under only energy considerations at the centimeter scale.2 3 Further comparison is made in Section 8.3 when the design of a resistively heated Knudsen Compressor for flow production is detailed. S.l.d Knudsen Compressor Optimization - k = 1 To complete the single k optimization analysis the energy efficiency for a k = 1 cascade was investigated. The k = 1 optimization represents applications such as micro-scale pressure regulators. The energy efficiency, or energy per normalized pressure difference, for a low throughput pressure regulator is given by «(!) = ' 0 ' j 0 Qp fAPm J f \ AT Q, p \ m g T \ O V * (95) The single stage k = 1 optimization procedure was conducted by first performing an energy efficiency calculation with nominal parameters, p = 80 mg/cc, fc a rb o n = 0.08, Lx = 2mm, and < t > = 100 mw/cm2, and then varying the parameters individually in sequence. First the optimal aerogel density and carbon dope fraction were determined to be 150 mg/cc and 6%, respectively. The optimal aerogel density is higher than for the k = 0 optimization because the smaller aerogel pore size that occurs at higher densities provides a higher ratio of the flow coefficients Qt/QP. At higher aerogel densities, 137 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. however, the thermal conductivity increases, decreasing the temperature difference for a given incident radiant flux, which is what establishes the optimum. Figure 83 shows the completion of the optimization procedure, the variation of the k = 1 energy efficiency with Lx and ( |> for 6% carbon doped 150 mg/cc aerogel with A=lcm2. 10 100mw/cmA 2 500mw/cmA 2 1000mw/cmA 2 1 0.1 5 2 3 4 1 0 Lx (mm) Figure 83. k = 1 Energy Efficiency Optimization As expected increasing the aerogel membrane thickness increases the energy efficiency. The majority of the gain in efficiency is experienced by a membrane thickness of 2mm, however. Increasing the membrane thickness increases the temperature difference produced by a given thermal flux through the membrane, but it also reduces the thermal flux through the membrane because of its increased thermal resistance compared to the outward cooling mechanisms. 8.1.e Summary The Knudsen Compressor optimizations carried out in this section produced orders of magnitude reductions in both required power and volume for the single point optimization cases of k = 0, 'A, and 1 as compared to the Knudsen Compressor used in the experimental investigations detailed in Chapter 6 and Chapter 7. They also provided insights on the variation in design required for different 138 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Knudsen Compressor applications and placed bounds on the Knudsen Compressor characteristics such as the membrane thickness and density for such designs. 8.2 M anufacturing Techniques for Meso-Scale Radiantly Heated Knudsen Compressors as a Gas Roughing Pump A proposed design for a radiantly driven Knudsen Compressor that operates as a gas roughing pump sized to work with Creare’s miniaturized turbopump is detailed in this section. The design corresponds to Cascade #5 detailed in Section 8.1.a. Early sizing calculations have indicated that a typical Knudsen Compressor cascade designed for application as a gas roughing pump will require several hundred stages.1 0 In order to efficiently and repeatably manufacture a large number of meso- scale Knudsen Compressor stages MEMS manufacturing processes must be employed because of its parallel fabrication capabilities. The aligned transpiration membrane cascade layout used in the conventionally machined Radiantly Driven Knudsen Compressor is naturally applicable to MEMS parallel processing indicating that minimal changes are required to the overall layout for MEMS based Knudsen Compressors from the layout employed in this work. The Knudsen Compressor design detailed in this section, however, was made under the constraints of MEMS fabrication processes and materials. A single stage of the MEMS fabricated radiantly driven Knudsen Compressor cascade is shown going through the manufacturing processes in Figure 84. The cross-sectional area of each stage varies along the cascade, but the stages all have transpiration membrane cross-sectional areas around 1mm2. The first manufacturing step in the construction of the radiantly driven Knudsen Compressor is to etch the thermal guard from a 250 pm thick silicon wafer using the deep reactive ion etch (DRIE) process. The pattern of holes etched underneath the aerogel bonding site is the same pattern that is required in the aergoel transpiration membrane, the thermal guard will be used as the mask during the aerogel etching process. The next manufacturing step is to attach the bulk aerogel transpiration membrane to 139 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. the silicon thermal guard. The manufacturing process employed in the present work; growing the aerogel in thin sheets, cutting the aerogel to size, and then attaching it to the thermal guard using Torr Seal epoxy, is not consistent with MEMS fabrication processes indicating that a new technique is required. One promising technique that avoids the difficulties associated with cutting and attaching aerogel is to grow the aerogel in place on the thermal guard. This technique is also consistent with the parallel stage manufacturing aspect of MEMS manufacturing. The aerogel is grown in place by using the silicon thermal guard as one side of the mold when forming the aerogel. The other sides of the mold are specially treated to release from the aerogel leaving it only attached to the silicon thermal guard. Step #7: Anodically Bond Parts Step #2: Grow Aerogel in Place Step #1: DRIE Thermal Guard Pattern Step #4: Deposit Thin- Film Sealing Ring Step #5: Waterjet Machine Pyrex Pieces Figure 84. Manufacturing Process for an Multi-Stage Radiantly Heated Knudsen Compressor After the bulk aerogel is attached to the silicon thermal guard optimally sized holes, which vary throughout the cascade, must be etched in the aerogel membranes. Conventional drilling techniques can produce capillaries with diameters as low as 250pm, which is not sufficient for the pressure range requirements of a Knudsen Compressor based gas roughing pump. Research done at the University of 140 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Virginia has demonstrated laser machining of aerogel using a high intensity femtosecond laser.5 0 Their results indicate that it is possible to laser machine aerogel structures with a feature size of 20pm. Using their setup it would take two pulses to produce one hole through a 500pm thick aerogel transpiration membrane. Research done at UCLA has validated different MEMS processes for application on aerogel including dry etching with XeFl and Deep Reactive Ion Etching (DRIE) with similar capabilities.5 1 Both processes were shown on thin film aerogel samples (~5pm), but it is believed that the processes can be easily scaled to work on bulk aerogel. Both of the candidate aerogel drilling techniques have been proven and the choice of the optimal hole drilling process will depend on the design employed in the particular Knudsen Compressor. The DRIE process was chosen for the current design because of its parallel manufacturing abilities and its compatibility with the thermal guard manufacturing process. There are two potential techniques for sealing the sides of the aerogel transpiration membrane to limit gas leakage from the sides. The first technique would be to not seal the sides of the aerogel transpiration membrane at all. This would allow gas leakage from the sides of the membrane, which would decrease the maximum pressure difference that the stage can produce, but if the area of the membrane sides is small compared to the cross-sectional area of the membrane the leakage may be acceptable. The other possible technique, which is selected for the current design, is to deposit a thin film of material around the edge of the aerogel. The seal may not be required to be structural depending on the strength of the aerogel bond with the thermal guard. The thickness of the seal is not as critical for the radiantly driven Knudsen Compressor designs where the thermal energy is absorbed inside the aerogel transpiration membrane. Figure 84 shows a gold thin film sealing ring, but experiments must be conducted to determine which material works the best as the transpiration membrane sealing ring. The next step is the fabrication of the connector sections of the Knudsen Compressor. Only two materials are consistent with the anodic bonding process: kovar and pyrex. The top cavity walls will 141 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. be waterjet machined out of pyrex because of its optical transparency. A pyrex top plate will be glass frit bonded to the pyrex walls. The bottom cavity will be conventionally machined out of kovar because its higher thermal conductivity will remove waste heat more efficiently than pyrex. After the connector sections have been manufactured the cascade will be bonded together using the anodic bonding technique. Anodic bonding is an electrostatic bond used to bond two dissimilar materials under elevated temperatures and with an applied voltage. The temperatures required for anodic bonding are roughly 350-450C. Anodic bonding requires a surface roughness of tens of nanometers. Anodic bonding can only be used to join glass, such as pyrex, to silicon and glass to the metal kovar. Further experimentation is required to determine the proper bonding order for the different parts. This design for the radiantly driven Knudsen Compressor requires a radiant flux of 1000 mw/cm2 at the location of the aerogel transpiration membrane. For this version this is achieved by using a Plexiglas lens system to collect enough solar energy and direct it only to the different transpiration membrane. A nominal incident solar flux of 80 mw/cm2 and a collection efficiency of 80% is assumed in calculating the required lens collecting area. The characteristics of the solar powered MEMS fabricated Knudsen Compressor are given in Table XI. Number of Stages 127 Volume (cm ) 1.7 Area (cm2 ) 3.2 Light Collection Area (cm2 ) 19.1 Flux at Aerogel Surface (mw/cm2 ) 1000 Mass (g) < 100 mg AP, N at operating condition 760 to 1 Torr, 1.7xl01 5 #/s Table XI. MEMS Fabricated Radiantly Driven Knudsen Compressor Characteristics It appears that a meso-scale radiantly driven Knudsen Compressor is a viable option for a roughing pump based on the predictions made using the Knudsen Compressor Performance Model and the available manufacturing processes and materials. Additional design work is required for the gas feedthroughs, packaging, and integrated sensors. 142 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 8.3 Meso-Scale Resistively Driven Knudsen Compressor as a Low Pressure Ratio Pump The optimization procedure completed in Section 8.1.c concluded that Knudsen Compressors designed to produce primarily a net gas flow will require only a single stage Knudsen Compressor that has a thin transpiration membrane (on the order of 5pm). Radiantly driving is therefore not an option for this application because the transpiration membrane is too thin to effectively absorb the incident radiation. The best candidate heating technique for this application appears to be resistive heating due to the thin film transpiration membrane. Depositing a thin film resistive pattern directly on the aerogel surface allows the possibility that the sides of the aerogel transpiration membrane don’t have to be sealed. A single stage Knudsen Compressor designed as a flow producer is shown in false color in Figure 85. A gold thin film resistive pattern is deposited directly on the aerogel top surface. The aerogel is grown directly on the substrate using thin film aerogel manufacturing procedures. Base Material (perforated under am Gold thin film pattern pm thick) Aerogel transpiration membrane (lcmxlcmx2.5pm) Figure 85. False Color View of Single Stage Knudsen Compressor Flow Producer The properties of the optimum design using the analysis from 8.1.c are listed in Table XII for a 1cm2 inductively driven flow producer. Also shown is the throughput produced by the pump as a function of the operating power. It appears that the Knudsen Compressor is not competitive as a meso-scale flow producer when compared to the energy efficiency of the Honeywell Dual Diaphragm Pump detailed in Section 1.5. It may become competitive as the size scale is reduced, however. The 143 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Knudsen Compressor also has other attractive features such as: it is solid-state, has a simple design, requires no oil or other supplementary fluids, is easily scaled to different sizes, has a steady flow, is easily integrated with other micro-scale devices, and is easily throttled through orders of magnitude in flowrate. Membrane Area 1cm2 Aerogel Density 30 mg/cc Carbon Dope Fraction 12% Device Area 1.08cm2 E Device Thickness 3.5pm C O Nominal Device Power 500mW 3 Nominal Device Voltage 5V Ol Nominal Device Current 100mA s Nominal Temperature 1.6K f: Difference Nominal Gas 1.3xl0i!,#/s Throughput (28SCCM) y = 0 .0 5 3 4 X + 0 .0 9 8 7 1 SCCM - 17m W 30SCCM - 560m w 600 8 0 0 1000 200 400 0 P (m W ) Table XII. Resistively Driven Low Pressure Ratio Knudsen Compressor Characteristics 8.4 Meso-Scale W aste Heat Driven Knudsen Compressors Some potential Knudsen Compressor applications have sufficient internal temperature differences and waste heat available to power the Knudsen Compressor by driving the waste heat through it. It is useful at this point to determine the possible design differences between powered and waste heat driven Knudsen Compressors. The designs for the radiantly driven gas roughing pump and the inductively driven flow producer were carefully done to minimize the power consumption. Waste heat driven Knudsen Compressors may not require such optimization depending on the relative amounts of temperature difference and waste heat available. Aerogel was chosen as a transpiration membrane material for the other designs partially because of its extremely low thermal conductivity. In some applications with high amounts of waste heat and only moderate temperature differences available it may be possible to employ different transpiration membrane materials because the minimum power requirement may be removed. Other devices, such as those used to maintain sections of a device at a temperature different than ambient, would require limited heat flow between the maintained temperature differences and would probably still use aerogel as the transpiration 144 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. membrane material. It is useful at this point to identify the general considerations for a waste heat driven Knudsen Compressors without regard to a specific application. Three system parameters define the thermal environment available to a waste heat driven Knudsen Compressor: Th (the hot temperature), Tc (the cold side and ambient temperature), and Q (the available thermal flux at for these temperatures). Waste heat driven Knudsen Compressors will require thermal guards on both sides of the transpiration membrane. Waste heat driven Knudsen Compressors must also have a controlled thermal path to both thermal guards and through the Knudsen Compressor. An expanded false color view of a single stage of a general waste heat driven Knudsen Compressor is given in Figure 86. The most critical component in the design of a waste heat driven Knudsen Compressor is the section including the two thermal guards and the transpiration membrane/sealing ring section. Care must be taken in their design to produce a pump with the required thermal flux under the constraint that a large fraction of the total temperature difference across the Knudsen Compressor should occur across the transpiration membrane. A waste heat driven Knudsen Compressor can be similar in overall layout to the meso-scale gas roughing pump Knudsen Compressor. Different materials, wall thicknesses (cross-sectional areas), and stage thicknesses can be used to provide the desired thermal flux between the hot and cold side. The thermal resistance through the transpiration membrane/sealing ring section must be much higher than the thermal resistance of the thermal guards and the pump body to make sure that the dominant fraction of the temperature difference occurs across the aerogel transpiration membrane. The individual stages in a waste heat driven Knudsen Compressor can be arranged in two basic configurations: top-bottom and side-by-side. The two configurations along with their effect on the characteristics of the waste heat driven Knudsen Compressor are detailed in Figure 87. 145 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Top Cavity Top Thermal Guard Aerogel 'Aerogel Sealing Layer Bottom Thermal Guard Bottom Cavity Figure 86. Waste Heat Driven Knudsen Compressor Schematic Top-Bottom Configuration AT per stage ~ 1/N ~ 1/N N ~ 1/N AP per stage ~ 1/N -> AP total ~ 1 Side-by-Side Configuration AT per stage ~ 1 Q to ta l ~ N N ~ 1 AP per stage ~ 1 AP total ~ N Figure 87. Approximate Scaling of Candidate Waste Heat Driven Stage Configurations By arranging the different stages in different configurations different performances can be achieved. An additional interesting possibility for configurations requiring a minimum thermal flux is to use one 146 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. sheet of aerogel instead of having a sealing ring around each transpiration membrane. If the distance between each stage is large compared to the aerogel transpiration membrane thickness and if the stages are arranged in a linear side-by-side configuration the leak between each stage through the aerogel can be minimized and may even be offset by an increase in temperature difference due to the higher thermal resistance. 8.5 Summary Knudsen Compressors have a wide variety of potential applications making a general design and optimization procedure difficult. Single point optimizations for the cases of k = 0 , moderate k , and k = 1 have identified the different potential capabilities for these cases. The design for the meso-scale gas roughing pump concludes that it is efficient enough to be viable. The meso-scale low-pressure difference pump was shown to be several orders of magnitude less efficient than the Honeywell Dual Diaphragm Pump at the meso-scale, but additional considerations like size scalability and orders of magnitude of throughput control increase the attractiveness of the inductively driven flow production Knudsen Compressor. General design considerations for a waste heat driven gas compressor have also been identified. 147 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chapter 9 Conclusions Micro/meso-scale gas roughing pumps and micro/meso-scale gas compressors are an enabling infrastructure technology for envisioned gas sensor networks and other micro/meso-scale applications. The recent availability of low thermal conductivity, high porosity materials with the required pore sizes, such as aerogel and beds of microspheres, enables the construction of a particular version of a thermal transpiration based pump/compressor, the Knudsen Compressor, for these applications. It is predicted, based on currently available materials and manufacturing processes, that the Knudsen Compressor can efficiently operate at pressures ranging from 10 mTorr to 10 atm The Knudsen Compressor Performance Model was constructed to predict the performance of various Knudsen Compressor configurations and to perform optimization studies used for future Knudsen Compressor designs. The analytical performance model was shown to predict transpiration membrane temperatures, stage pressures, and stage throughput, typically within 20%. The Knudsen Compressor Performance Model can predict the stage performance for a variety of incident energy fluxes, gas species, pressures, carbon doped aerogel transpiration membrane properties, and glass microsphere transpiration membranes. Knudsen Compressor pumpdown experiments were conducted to validate the performance model and to demonstrate operation of the Knudsen Compressor over the variety of conditions likely to be encountered in applications. Transpiration membrane temperature measurements were taken for Nitrogen and Helium as a function of gas pressure. The results agreed with the Knudsen Compressor Performance Model predictions except for gas pressures around 100 mTorr, where the gas conduction outward cooling mechanism was transitioning to rarefied behavior. Further experiments with more accurately prescribed boundary conditions are required to investigate this pressure region. Single stages of the Knudsen Compressor operated from mean pressures of 500 mTorr to 1 atm of Air, Nitrogen, Helium, and Argon. Knudsen Compressor cascades of up to 15 stages were also proven. 148 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Thermomolecular pressure differences were measured for a bed of glass microspheres, with 1mm diameters, for gas pressures of 100 mTorr to 10 Torr of Helium. The Knudsen Compressor Performance Model consistently underpredicts the TMPD for the glass microspheres and future experiments are required to settle this discrepancy. An optimization analysis concluded that the energy efficiency of the current 15 stage conventionally machined Knudsen Compressor could be improved by roughly three orders of magnitude. The most important design improvement was to etch optimally sized holes through the aerogel substrate to maintain stage Knudsen numbers of roughly 1.2. A design was given for the radiantly driven Knudsen Compressor as a gas roughing pump sized to work with an existing meso-scale turbomolecular pump. The design appears feasible from both a performance and manufacturing perspective. A design for a very low pressure ratio pump was also given. The design consumes more power than typical state-of-the-art meso-scale pumps, but may be the only option for a low pressure ratio micro-scale pump. Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Bibliography 65. Adamson, Physical Chemistry of Surfaces, John Wiley & Sons, Inc, New York, 1990. 19. Arkin, R., Aircraft Based Volcanic Emissions Mass Spectrometer (AVEMS), Presented at the 4th Harsh-Environment Mass Spectrometry Workshop, St. Petersburg Beach, FL, October 7-10, 2003. 60. Beenakker, J.,J., Borman, V.,D., Yu., S., Krylov, “Molecular Transport in the Nanometer Regime”, Phys. Rev. Lett., 72, 4, 514-517, (1994). 61. Beenakker, J.,J., Borman, V.,D., Yu., S., Krylov, “Molecular transport in subnanometer pores: zero-point energy, reduced dimensionality and quantum sieving”, Chem Phys Lett, 232, 379-382, 1995. 3. Blomberg, M., Rusanen, O., Keranen, K., Lehto, A., in The 9th International Conference on Solid-State Sensors and Actuators - Transducers ’97 1257-1258 (IEEE, Chicago, IL, 1997). 62. Borman, V.,D., Yu., S., Krylov, A.,V., Prosyanov, A.,M., Kharitonov, “Theory of transport processes in a nonequilibrium gas-solid system”, Sov. Phys. JETP, 63(1), 43-56, 1986. 12. Butefisch, S., Seidemann, V., Buttgenbach, S., Novel micro-pneumatic actuator for MEMS, Sensors and Actuators A, 97-98, 638-645, 2002. 17. Personal communication with John Callas at the Jet Propulsion Laboratory. 23. Cabuz, C., Herb, W.R., Cabuz, E.I., Son Thai Lu, The Dual Diaphragm Pump, Presented at the 14th IEEE International Conference on Micro Electro Mechanical Systems, Interlaken, Switzerland January 21-25, 2001. 67. Che, J., Cagin, T., Goddard III, W.,A., “Thermal Conductivity of Carbon Nanotubes”, Submitted for publication in Nanotechnology. 66. Clausing, P., Ann. Phys. (Leipzig) [5], 12, 961, 1932.; J. Vac. Sci. Technol., 8, 636-646, 1971. 72. D ’Angelo, G.,D., Tripodo, G., Bartlotta, A., Carini, G., Fontana, A., Montagna, M., Rossi, F., Ferrari, M., Terki, F., “Low-Temperature specific heats of porous silica xerogels of low densities”, J. of Non-Crystalline Solids, 280, 222-227, 2001. 63. Derycke, I., Vigneron, J.P., Lambin, Ph., Lucas, A.A., Derouane, E.G., Physisorption in Confined Geometry, J. Chem. Phys, 94,6, 4620-4627, 1991. 71. Drake, J.,M., Klafter, J., “Dynamics of Confined Systems”, Physics Today, 46-55, May 1990. 55. Dullien, F.A.L., “Porous Media: Fluid Transport and Pore Structure”, Academic Press, New York, (1979). 28. Epstien, A., Millimeter Scale, MEMS Gas Turbine Engines, Proceedings of ASME Turbo Expo 2003, GT-2003-38866, Atlanta, GA, June 16-19, 2003. 150 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 15. Eyre, B., Myung, M., Wiberg, D., LiGA Fabricated Quadrupole Mass Filter and Scroll Pump for Meso-scale Mass Spectrometer, Presented at the 4th Harsh-Environment Mass Spectrometry Workshop, St. Petersburg Beach, FL, October 7-10, 2003. 51. Fan, S.-K., Paik, J.-A., Patterson, P.,R., Wu, M.,C., Dunn, B., Kim, C.-J., "MEMS with Thin-Film Aerogel", IEEEConf. Micro Electro Mechanical Systems (MEMS ’01), Interlaken, Switzerland, Jan. 2001, pp. 122-125. 2. Ferran, R. J., Boumsellek, S., High-Pressure Effects in Miniature Arrays of Quadrupole Analysers for Residual Gas Analysis from 10"9 to 10'2 Torr. Journal of Vacuum Science and Technology A 14, 1258-1265 (1996). 64. Fletcher, R., Tsaousidou, M., Coleridge, P.T., Feng, Y., Wasilewski, Z.W., Electron-Phonon Coupling and Phonon Drag Thermopower of a Very Low Mobility 2DEG, Physica, E, 12, no. 1-4, 478-81, Jan. 2002. 33. Husing, N., Schubert, U., Aerogels - Airy Materials: Chemistry, Structure, and Properties, Angew. Chem. Int. Ed., 37, 22-45, 1998. 18. http://www.nineplanets.org/ 20. http://cyranosciences.com/ 22. http://www.knf.com/usa.htm 24. http://www.airsquared.com/prod.html 26. http://www.edwards.boc.com/ 27. http://www.varianinc.com/ 32. http://eande.lbl.gov/ECS/Aerogels/satoc.htm 35. http://cpl.usc.edu/knudsen/ 36. http://www.lumileds.com/ 53. http://www.dukescientific.com/ 68. http://www.pa.msu.edu/cmp/csc/nanotube.html 70. http://www.coming.com/lightingmaterials/products/wcor.html 73. http://www.airglass.se/ 34. Personal Communication With Steven Jones at the Jet Propulsion Laboratory. 52. Kaganer, M.G., “Thermal Insulation in Cryogenic Engineering”, IPST Press, Jerusalem, (1969). 16. Kenton, M., Kline-Schoder, R., Innovative Vacuum Pumps to Support Mass Spectrometry in Harsh Environments, Presented at the 4th Harsh-Environment Mass Spectrometry Workshop, St. Petersburg Beach, FL, October 7-10, 2003. 151 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 54. Klein, J.D., Symposium on thermal radiation of solids, NASA SP-55 (1965) 73. 6. Knudsen, M, “Eine Revision der Gleichgewichtsbedingung der Gase. Thermische Molekularstromung”, Ann. Phys., 31, 205, (1910). 45. Lafferty, J.M., “Foundations of Vacuum Science and Technology”, Wiley, New York, 1998. 41. Lee, D., Stevens, P., Zeng, S., Hunt, A., “Thermal Characterization of Carbon-Opacified Silica Aerogels”, Journal of Non-Crystalline Solids, 186, 285-290, (1995). 50. Liu, X., Du, D., Mourou, G., Laser Ablation and Micromachining with Ultrashort Laser Pulses, IEEE Journal of Quantum Electronics, Vol. 33, No. 10, 1706-1716. 43. Lu, X, Arduini-Schuster, M.,C., Kuhn, J., Nilsson, O., Fricke, J., Pekala, R.,W., “Thermal Conductivity of Monolithic Organic Aerogels”, Science, Vol. 258, 971-972, (1992). 58. Mach, P., Wiltzius, P., Megens, M., Weitz, D.A., Lin, Keng-hui, Lubensky, T.C., Yodh, A.G., “Electro-optic Response and Switchable Bragg Diffraction for Liquid Crystals in Colloid- Templated Materials”, Physical Review E, Vol 65, 031720, (1983). 25. Moore, E., Muntz, E.P., Eyre, F., Myung, N., Orient, O., Shcheglov, K., Wiberg, D., Performance Analysis for Meso-Scale Scroll Pumps, Presented at the 2nd NASA/JPL Miniature Pumps Workshop, Pasadena, CA, March 28 2002. 5. Muntz, E.P., Vargo, S.E., “Microscale Vacuum Pumps”, The Mems Handbook, CRC Press, 2000. 31. Muntz, E.P., Sone., Y., Aoki, K., Vargo, S., Young, M., “Performance Analysis and Optimization Considerations for a Knudsen Compressor in Transitional Flow”, J. Vac. Sci. Technol., A, 20(1), 214-224, 2002. 69. Murashov, V., “Thermal conductivity of model zeolites: molecular dynamics simulation study”, J. Phys. Condens. Matter, 11, 1261-1271, 1999. 47. Ohwada, T., Sone, Y., Aoki, K., “Numerical Analysis of the Poiseuille and Thermal Transpiration Flow Between Two Parallel Plates on the Basis of the Boltzmann Equation for Hard Sphere Molecules”, Physics of Fluids A, vol.l, no. 12, p. 2042-2049, (1989). 14. Orient, O., J., Chutjian, A., Garkanian, V., “Miniature, High-Resolution, Quadropole Mass- Spectrometer Array”, Review of Scientific Instruments, 68, 1393-1397, (1997). 57. Park, S.H., Xia, Y., “Assembly of Mesoscale Particles over Large Areas and Its Application in Fabricating Tunable Optical Filters”, Langmuir, 15, 266-273, (1999). 29. Pham-Van-Diep, G., Keeley, P., Muntz, E.,P., Weaver, D.,P., “A Micromechanical Knudsen Compressor” in Rarefied Gas Dyanmics, eds. J. Harvey, G. Lord, Oxford University Press, Oxford, 715-721, 1995. 13. Phelan, P., Chiriac, V., Lee, T.Y., Current and Future Miniature Refrigeration Cooling Technologies for High Power Microelectronics, IEEE Transactions on Components and Packaging Technologies, Vol. 25, No. 3, 356-365, September 2002. 152 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 59. Pieranski, P., Strzelecki, L., Pansu, B., “Thin Colloidal Crystals”, Phys Rev Let, 50(12), 900-903, (1983). 39. Rettelbach, Th, Sauberlich, J., Korder, S., Fricke, J., “Thermal Conductivity of Silica Aerogel Powders at Temperatures from 10 to 275K”, Journal of Non-Ciystalline Solids, 186, 278-284, (1995). 30. Reynolds, O., “Experimental Researches on Thermal Transpiration of Gases Through Porous Plates and on the Laws of Transpiration and Impulsion, Including an Experimental Proof That Gas is Not a Continuous Plenum”, Philosophical Transactions of the Royal Society of London, B170, 727-772, 1879. 44. Rolle, “Heat and Mass Transfer”, Prentice Hall, New Jersey, 2000. 1. Shepherd, D., Networked Microsensors and the End of the World as We Know IT, IEEE Technology and Society Magazine, 22, no. 1, 16-22, (2003). 37. Smith, D.M., Scherer, G.W., Anderson, J.M., Shrinkage During Drying of Silica Aerogel, Journal of Non-Crystalline Solids, 188, 191-206, 1995. 46. Sone, Y., Ohwada, T., Aoki, K., “Temperature Jump Knudsen Layer in a Rarefied Gas Over a Plane Wall: Numerical Analysis of the Linearized Boltzmann Equation for Hard Sphere Molecules”, Phys Fluids, A l, 363-370, (1989). 48. Sone, Y., Itakura, E., “Analysis of Poiseuille and Thermal Transpiration Flow for arbitrary Knudsen Numbers by a Modified Knudsen Number Expansion Method and their Database”, J. Vac. Soc. Japan, 33, 3, 92-94, (1990). 49. Sone, Y., Kataoka, T., Ohwada, T., Sugimoto, H., Aoki, K., “Numerical Examinations of the Applicability of the Linearized Boltzmann Equation”, Eur. J. Mech. B/Fluids, 13, 573, (1994). 21. Personal communication with Steven Sunshine at Cyrano Science. 4. Terry, S. C., Jerman, J. H., Angell, J. B., A Gas Chromatographic Air Analyzer Fabricated on a Silicon Wafer. IEEE Transactions on Electron Devices ED-26, 1880-1886, (1979). 7. Vargo, S.,E., Muntz, E.,P., “An Evaluation of a Multiple Stage Micromechanical Knudsen Compressor and Vacuum Pump”, Rarefied Gas Dynamics, ed. Ching Shen, Peking University Press, Beijing, 995-1000, (1997). 8. Vargo, S.,E., Muntz, E.,P., Shiflett, G.,R., Tang, W.,C., “The Knudsen Compressor as a Micro and Macro Scale Vacuum Pump without Moving Parts or Fluids”, J. Vac. Sci. Technol, A 17,2308-2313, (1999). 9. Vargo, S.,E., “The Development of the MEMS Knudsen Compressor as a Low Power Vacuum Pump for Portable and In Situ Instruments”, Ph.D. Thesis, University of Southern California, Los Angeles, 2000. 56. Wijnhoven, J.E.G.J., Vos, W.L., “Preparation of Photonic Crystals Made of Air Spheres in Titania”, Science, Vol. 281, 802-804, (1998). 153 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. 10. Young, M., Vargo, S.,E., Shiflett, G ., Muntz, E.P., Green, A., “The Knudsen Compressor as an Energy Efficient Micro-Scale Vacuum Pump”, the 2001 ASME International Mechanical Engineering Congress and Exposition (IMECE2001), November 11-16, 2001, New York, NY. 11. Young, M., Vargo, S.,E., Shiflett, G ., Muntz, E.P., Green, A., “Thermal Transpiration as a Co-Located Micro-Scale Source of High Pressure Gas for MEMS Devices”, the 2001 ASME International Mechanical Engineering Congress and Exposition (IMECE2001), November 11-16, 2001, New York, NY. 38. Zeng, S.Q., Hunt, A., Greif, R., Geometric Structure and Thermal Conductivity of Porous Medium Silica Aerogel, Journal of Heat Transfer, Vol. 117, 1055-1058, 1995. 40. Zeng, S.,Q., Hunt, A., Greif, R., “Theoretical Modeling of Carbon Content to Minimize Heat Transfer in Silica Aerogel”, Journal of Non-Crystalline Solids, 186, 271-277, (1995), 42. Zeng, S.Q., Hunt, A., Greif, R., “Mean Free Path and Apparent Thermal Conductivity of a Gas in a Porous Medium”, Journal of Heat Transfer, 117, 758-761, (1995). Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

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Creator Young, Marcus Paul (author)

Core Title Investigation of several important phenomena associated with the development of Knudsen compressors

Contributor Digitized by ProQuest (provenance)

School School of Engineering

Degree Doctor of Philosophy

Degree Program Aerospace and Mechanical Engineering

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag engineering, aerospace,engineering, mechanical,OAI-PMH Harvest

Language English

Advisor Muntz, E. Phillip (committee chair), Kim, Eun Sok (committee member), Ronney, Paul D. (committee member), Shemansky, D.E. (committee member), Shiflett, Geoffrey (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c16-562540

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