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A rheological study of an alkyl aryl sulfonate slurry

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A rheological study of an alkyl aryl sulfonate slurry

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Content A · oLOGICAL STUDY O F A 0 AT!!, SLURRY A Thesis Presented to KY ARYL tha Faculty cf tha School of Engineering The University of Southern California In Partial ulfillment of the Requirements for the Degree M aster of Science in Chemical ~ngineering by Russell G. M c enzie January, 1958 This thesiJ, written by ........ Russell .. G •.. McKenzie ............................ .......... _ .... .. . under the guidance ofhie Faculty Committe e and approved by all its menibers, has been presented to and accepted by tlze School of Engineering in partial fulfillment of the re quirements for the degree of _. _ .............. _ .... ~~~~~ .. Qf .. ~ ienc.e .. in. _ _____ ... ____ _ _ .... _ ._ ._._ ._. Date .... J. an.uar_J" .. 19.S 8 .................. . F aculty Conunittee STATEME~IT O F THE PROBLEM A company with headquarters in South Gate, Cal i fornia was engaged in the manufacture of connneroial and household synthetic detergents. The basic surface active ingredient of the detergents was an alkyl aryl sulfonate made by sulfonating a polypropylene alkyllate of benzene with 25% olewn and neutraliz i ng with sodium hydroxide. The resultant slurry was fortified with various builders, spray-dried and packaged. Many problems were encountered in handling large quantities of the aulfonate, especially in pumping and agitating. The physical properties of the material were variable and did not neoessarily have any relation to the chemical analysis. The flow behavior deviated considerably from that of a N ewtonian fluid and it seemed to depend to some extent on the past thermal and physical history. Past practice of the company had been to determine an apparent viscosity on each batch of sulfonate slurry in addition to the regular chemical analyses. This viscosity was determi ned by a Brookfield Synchroeleotric Viscometer operating at one speed or one rate of shear. The apparent viscosity of each batch was compared to that of other batches and used as one phase of quality contro l . The same viscosity waa used to predict pumping time and t o size any new pipe lines. The physical properties of the surface-active agent had a very pronounced effect on the spray dr.ring operation, and past use of t he apparent viscosity gave no correlation with results achieved in plant iii operations. It proved to be highly unreliable when used as a design factor for new installations. The use of the one-speed viscometer and the apparent viscosity concept was finally abandoned, and more reliance put on subjective type tests by experienced plant personnel. In an effort to minimize subjective testing and devise a more reliable method of fluid consistency testing, the Research Department proposed a program of investigation with the following objectives: l. To select or develop an instrument suitable for determining the consistency of the alkyl aryl sulfonate in question. 2. To perfect a procedure for using the instrument. 3. To determine the consistency curves or viscosities of the sulfonate at plant concentrations and temperatures. 4. To examine the effects of temperature from 110 to 160 degrees Fahrenheit (°F.) on the consistency curves or vis e os ities. 5. To correlate the resultant data. The investigation was intended to be a preliminary part of a long range attempt to correlate the behavior of the fluid in spray drying with its original physical properties~ and find a reliable method for batch to batch consistency control. TABlli OF CO 'lli TS CH.APTER PAGE 1 1 I. INT ROD UC TION • • • • • • • • • • • • • • • • • • • • • • • Related Literature and Prior Art • • • • • • • • • • • • • Fluid 'lypas • • • • • • • • • • • • • • • • • • • • • • 3 Newtonian. • • • • • • • • • • • • • • • • • • • • • • Non-Newtonian. • • • • • • • • • • • • • • • • • • • • Dilata.nt Fluid • • • • • • • • • • • • • • • • • • • • 3 3 4 Psaudopla.stic Fluid • • • • • • • • • • • • • • • • • • 4 Bingham Plastic : F 1 luid • • • • • • • • • • • • • • • • • 4 Rhaopactic Fluid • • • • • • • • • • • • • • • • • • • Thixotropy • • • • • • • • • • • • • • • • • • • • • • II• VISCOhlliThR ShUC TIO • • • • • • • • • • • • • • • • • • • 5 5 7 Capillary Viscometers • • • • • • • • • • • • • • • • • • • 7 Viscometers for Absolute Poiseuilles' Viscometer eas uremants • • • • • • • • • • • • • • • • • • • • • • • 7 7 Thorpe and Rodgers' Viscometer. • • • • • • • • • • 7 Coas' Viscometer . • • • • • • • • • • • • • • • • • Visoometers for Relative easurements • • • • • • • • • Ostwald iscomater • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • Redwood Viscometer . ·ngler iscomater • • • • • • • • • • • • • • • • • Rotational iscometars • • • • • • • • • • • • • • • • Stormer Viscometer • • • • • • • • • • • • • • • • • Couatte iscometer • • • • • • • • • • • • • • • • • 8 8 8 12 12 12 12 12 CHAPTER Brookfield Viscometer • • • • • • • • • • • • • • • • Haroules Hi-Shear Viscometer • • • • • • • • • • • • • MacMichael Viscometer • • • • • • • • • • • • • • • • Preoision Interchemioal ~iscometer Discussion of Viscometer Selection •• • • • • • • • • • • • • • • • • • • • • III• PROCEDURE • • • • • • • • • • • • • • • • • • • • • • • • Calibration of the Viscometer • • • • • • • • • • • • Auxiliary ~quipment • • • • • • • • • • • • • • • • • Consistency Curves M ethod • • • • • • • • • • • • • • Curve Interpretation • • • • • • • • • • • • • • • • IV. CONSISTENCY CU RVES-VARYI NG TIME -AT-TEI ERATURE • • • • • Cons is tanoy Curves at 110 °F' . • • • • • • • • • • • • Basic Shear Diagram • • • • • • • • • • • • • • • • • Consistency Curves at 120 0F. • • • • • • • • • • • • Cons is ta ncy Curves at 130 OF. • • • • • • • • • • • • Consistency Curves at 140 O F . • • • • • • • • • • • • Consistency Curves at 150 O F . • • • • • • • • • • • • Consistanoy Curvas at 160 O F . • • • • • • • • • • • • v. SUMMARY O F RESUL 1S • • • • • • • • • • • • • • • • • • • • VI. CON CLUSIONS " • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • BIBLIOGRAPHY APPEIDIX •• • • • • • • • • • • • • • • • • • • • • • • • • • • PAGE 14 14 16 15 15 22 22 23 25 29 33 33 37 41 42 54 64 59 72 79 81 83 V TABLE I. II. III. IV. LIST OF T ABLES Torsion W ire Cons tan ts • • • • • • • • • Time-Temperature Curves at 110 °F •••• Fluid Behavior Varying Time-at-Temperat ure Basio Data at 110 °F. • •••••••• • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • PAGE 24 35 36 38 V. Time-Tempera tu.re Curves at 120 °F. • • • • • • • • • • • 44 VI. VII. VIII. IX. Fluid Behavior Varying Time-at-Temperat ure Basic Data at 120 °F. • ••••••••• • • • • • • • • • • • • • • Time-Temperature Tes ts at 130 OF. • • • • • • • • • • • Fluid Behavior Varying Time-r..t-Temperat ure ••••••• x. Basic Data at 130 OF. • • • • • • • • • • • • • • • • • XI. Time-Temperature Tests at 140 °F. • • • • • • • • • • • XII. Basic Data at 140 OF. • • • • • • • • • • • • • • • • • XIII. XIV• xv. XVI. XVII. XVIII. Time-Temperature Tests at 160 °F'. • • Basic Data at 150 °F. • ••••••• • • • • • • • • • • • • • • • • • • Fluid Behavior Varying Time-at-Tem perature Time-Temperature Tests at 160 °F. • • • • Fluid Behavior Varying Time-at-Tem perature Basia Data at 160 OF. • ••••••••• • • • • • • • • • • • • • • • • • • • • • • • • • • • • 46 46 60 51 52 56 57 62 63 64 68 69 70 CHAPTER I IN'IRODUCT ION The fluid in question appeared to exhibit a radical departure from ideal Newtonian behavior, on the basis of plant experience. From results obtained with a single point viscometer, tha consistency curve appeared non-linear and subject to peaks at certain tempera tures. At high temperatures a jell-like condition existed where the water in the solution appeared to be bound tightly. Since no record of previous rheological work on the subject fluid could be found, and in view· of past failures with the single point viscometer and seeming complexity of the fluid, it was necessary to review the literature for information or suggestions on the follow ing main points, 1. The selection of, or construction of a viscometer suitable for evaluating the alkyl aryl sulfonate slurry. 2. Development of a technique for determining the consistency curves at temperatures from 110 to 160 degrees Fahrenheit I. Related Literature and Prior Art The basis of the study of viscomatry still rests upon the works of Newton, Poiseuilla and Wiedeman . Before any absolute measurement of viscosity could be determined, some hypothesis was necessary ooncerning the magnitude of the force required to overcome viscous resistance. 2 Such an hypothesis was proposed by Newton (1) who oonsidered two parallel planes in a liquid each of area (A), separated by a distance (X), and moving at velocities (V1) and (V2) in the direction of either of the planes. The force (F) required to maintain the differ ence of velocity i proportional to the gradient of velocity, but as tho velocity in the liquid is changing continuously the equation may be written, F o( Adv _ NAdv dt - dx The coefficient (N) is the coefficient of viscosity of the liquid. ~xpari.mants have shown (N) to be a characteristic constant for aach Newtonian fluid at a given temperature. Poiseuilles' basic work (1) on determining a law of flow t hrough cylindrical tubes made possible the deduction of absolute values for the viscosity of a simple fluid. Poiseuille discovered the following relationship, using water in five glass tubes: Q = K~PD 4 L Where Q = quantity discharged in unit time ~p = pressure difference between ends of capillary D • tube diam.a-tar L = tube length K = constant, charaoteristi o of liquid It should be noted, that, had Poisauille used blood, in which ha was interested, instead of water he might never have arrived at his conclusions, since blood is not a simple fluid. Fluid 1'ypas Liquids and suspensions fall into two general types, (2, 3) 3. Newtonian and non-Newtonian, with the latter type bein divided into several classes. Newtonian. A Newtonian fluid is characterized by a constant viscosity at constant temperature independent of the rate of shear; or in other words, the rate of shear in t he liquid is directly propor tional to the shearing stress. The curve of a Newtonian fluid on a shear diagram is a straight line beginning at the origin. Water is a typical Newtonian - or simple fluid. Non-Newtonian. For non-Newtonian fluids or suspensions, the viscosity is a variable, varying as the rate of shear, the time of shear or as some function of the past history of handling of the fluid. Non-Newtonian fluids are generally classified by the type of consistency curve they exhibit, and are considered to fall into four general classes: (1) Dilatant, (2) Pseudoplastic, (3) Bingham Plastic, and (4) Rheopectio. Fluids which evidence thixotropic properties are not considered a separate class in t his study because of t he fact that any of the mentioned four classes oa.n evidence thixotropy. Dilatant Fluid. The consist ency curve, or a plot of shearing rate versus torque of a dilatant fluid is not a straight line, but concave toward the force axis. The curve usually appears to start from the ori in. A typical example is beach sand, in which the water to sand ratio is such that there is just enough water to fill the voids when the latter are at their minimum value. Any applied shear will radually dilate the voids, induoin a state of partial dryness, 4 and the resistance to shearing stress increases more rapidly than it would otherwise. Thus the consistency curve is concave to the force axis. Pseudoplaatic Fluid. The consistency curve of a material of this type is not a straight line, but convex to the force axis. The ourve starts at the graph origin and the viscosity decreases with increasing rates of shear. The rate of shear is not directly propor tional to the shearing stress. Pseudoplastic fluids are generally considered to be composed of long chain molecules which do not align in the direction of flow at low rates of shear. As shear rate increases, molecular alignment increases, and frictional resistance between adjacent layers decrea ses. The result is a greater rate of shear for a given stress. Bingham Plastic Fluid. The consistency curve of the so-called ideal Bingham Plastic (4) is a straight line, originating at some point along the force axis, the rate of shear being directly propor tional to the shearing stress in excess of the yield value. The intercept of the curve on the force axis is called the yield value. Actually, the curve is very seldom a perfectly straight line, especially with fluids which exhibit thixotropio behavior as well. Some typical examples of this type of fluid are margarine, cup grease and mayonnaise. Rheopectic Fluid . The apparent viscosity of a material of this type increases with time at any constant rate of shear. he consis tency curve shows that in most rheopectio systems, thixotropy exists 6 also. Some examples are vanadium pentoxide and gypsum in wat er. Thixotropy. The consistency curve of a thixotropio material is convex toward the force axis and originates at some point along the force axis. If an upcurve and downcurve are run using a rotational viscometer. the two curves will not coincide but will form a loop. Generally the following phenomena are observed in testing a thixo tropio material: 1. The breakdown of the structure increases as a function of increased shear rates. 2. The structure rebuilds upon rest. 3. Breakdown increases continuously with constant shear rates. Figure I was plotted to illustrate the shear diagrams of the various types of fluids. T he diagram as plot ted illustrated the synonyms used in describing the ordinate and a bscissa of a shear diagram. 6 Newtonian Psel)doplast,c D,lot:ont ~ ~ ~ ~ ..... V ~ u ..... ~ ~ ~ ~ ~ ~ a.. & ' ~ ' ~ - ~ ~ ~ --(. ~ Cl) ~ C ~ ~ 0 Tor-'11.«, A x1.1 0 Fo,c.e Ax,s 0 Slteo r Stress 8,n'}hom Plasf,c Tl-i, xotto pie f?J,eopett,c 0 Force Ax1.s FJGUR[ 1 FLUID TYPES C PIBR II VISCO ' 'IER ~L CTION Sinoa the time of Poisauilla, Tnal'\Y types of viscometers have been perfected and used, both for the study of ewtonian and non .1·awtonian Fluids . A few of the viscometers (1, 8) which have been of most basic importance are discussed briefly hare. I. CAPILLARY VISCOMETERS These can be divided into two classes: 1. Those for measuring absolute viscosity direotly. 2. Those for measuring relative viscosity by reference to standard liquids. Viscometers for Absolute easuromants Poisauilles' isoometar, Figure 2, page 9. The bulb (A) and capillary are filled with, and immersed in the liquid under test. Tha liquid in (A) is foroad out throu h the capillary and tha time for t he level to fall from (B) to (B 1 ) is noted. 1be instrument is precision made with aocurate measurements being taken. Thor,E_a and odgers '. Viscometer , Figure 3, page 10. The visoo filater is filled and pressure is applied at (H2) until the level stands at (K2), and excess flows into (T1) . The liquid is then forced through the capillary by air pressure and the time noted for the meniscus to pass from ( m1) to (In2) • A duplicate reading can be obtained by reversing t.~e recess . ha instrument is made of fine glass with ground joints. and with maintenance of very small toler- anoes. Coes' Viscometer, Figura 4, page 11. This is supposedly the most accurate absolute viscometer known for teats on water. 8 Liquid flows from (C) through (D) to (E), the pressure differ anoe being obtained by a differential mercury manomatar (G) in which levels are indicated by electrical contacts. A known rate of flow is produoed by injecting mercury into the upstream reservoir from a cylinder (B) having a piston (A) driven by a geared synchronous motor. The rate of volume displacement is accurate to ± 0 .01%. Viscometers for Relative Measurements. A greater precision is usually obtainable with viscometers designed specifically for relative measurements. This is due partly to simplification in desi gn and partly to elimination of errors in dimension measurements. Relative viscometers use either an externally applied pressure or rely on the hydrostatic head of liquid in the viscometer itself to induce flow. Ostwald Visoomater, Figure 5, page 13. This unit is charged with a constant volume, and liquid is drawn up into the left limb above (A), then allowed to level at (A) . The time of flow from (A) to (B) is then measured. Calibration with a known simple fluid is necessary. Redwood Viscometer. This unit consists of a standard cup with an agate jet mounted in the bottom. The time of flow by gravity or t--+-~ B A ......,__......,. a' FIGURE Z POISEUILLE VISCOMETER 10 H, H 6 T, Ta L R K, FIGURE 3 THORPE AND RODGERS I VISCOMETER • I 11 A C, ~c c FIGURE 4 COE '5 VIS COMET£ R a measured voluma of fluid through the jet is used as an arbitrary measure or kinematic viscosity. 12 Engler Viscometer.. This instrument is very similar to the Redwood. The resultant viscosity is measured in ~nglar degrees which is the time ratio of oil flow to water flow under the same conditions. Rotational Viscometers Stormer Viscometer. In this instrument (12) a cylindrical cup holds the fluid and tha shearing stress is supplied by a rotating bob or paddle suspended in the liquid by a steel rod supported by a pre cision bearing. A non-stretch cord is wrapped aroWld the upper end of the supporting rod, and the latter is rotated by the simple means of hanging standard weights on the cord. The force of gravity acting on the weights rotates the rod and simultaneously the bob in the fluid. Thus a shearing stress is exerted on the fluid commensurate with the weight suspended on the cord. Couette Viscometer. This unit was one of the earliest of the rotational types. Most of the modern rotational viscometers are modi fications or improvements of the original Couette unit. The instrwnant consists of two concentric cylinders, ona inside the other. with the outer cylinder having an open top and the inner cylinder baing solid. The inner cylinder is supported by a torsion wire fixed at the upper end. T he outer cylinde r is rotat ed at a certain speed, and the torque transmitted to the i nner cylinder by the fluid in between is measured by the deflection of the tors i on wire. FIGURE 5 OSTWALD VISCOMETER 14 Brookfield Viscometer. The Brookfield (9) is one of the most popular instruments in industry today because of its simplicity of use. It was originally a one-speed unit reading an apparent viscosi• ty but recent models furnish eight different speeds. Basically the unit consists of a constant speed motor driving a round, bearing-supported shaft on tha end of which is fixed a bob. paddle or disc. The bob is immersed in the fluid to be tested and then the motor energized. The resistance or drag which the fluid exerts on the bob is measured by a spiral spring of beryllium-copper. The latter is calibrated to read directly in cantipoisas. Any con venient beaker serves as the sample cupo Hercules Hi-Shear Viscometer. This instrument (11) is compara tively new to the industrial scene. The unit operates somewhat on the principle of the Brookfield but is much more elaborate. The resis tance which the fluid exerts on a bob immersed in the fluid is measured and recorded automatically at all rotor speeds. MacMiohael Viscometer. Figura 6, page 16. This instrument (10) consists of a bob or plunger suspended from a phosphor-bronze torsion wire with the bob being immersed in the fluid to be tasted. The fluid is contained in a sample cup which is eared to a variable speed back-geared motor. The speed range is from ten to forty revolutions par minute. The drag or resista ca of the fluid exerted on the bob is measured by the deflection or twist of the torsion wire . T.he speed oan be ohanged by turning a conveniently mounted control. Precision lnterchemioal Viscometer . This is probably the most 15 expensive and elaborate viscometer (2) available. It consists of a rotating cup containing the material to ba measured and a stationary bob inmersed in the material. The bob is suspended by a torsion spring and laterally supported at its lower end. Yhen the cup is rotated a viscous drag is exerted on the bob and the force is measur ed by the deflection of a dial scale. Th.a principle is identical with that of the MaoMichael Viscometer, but the construction is much better and the list of accessories greater. II. DISCUSSION OF VISCOMETER ElliCTION Past plant experience with the alkyl aryl sulfonate fluid had led to the belief that it was not a ewtonian fluid, inasmuch as the one-point method of measuring viscosity has unpredictable results and the flow was not necessarily in proportion to the applied force in many pumping operations. Furthermore, the fluid appeared to pass through a jell phase at elevated temperatures. Tests with the capi llary type viscometers were unsuccessful. ' · he sulfonata fluid would not flow at a constant rate, and even though the complete unit was kept at constant temperature, the water in the sulfonate settled and flowed through the apparatus leaving a more concentrated sulfonate behind. The capillary type viscometer appeared to have addi ional shortcomings in measuring a non- Jawtonian fl uid in t ha t the sam ple could not be remeasured in a short period of time. I n measuring non Newtonian fluids, it is of great importance to instantaneously measure the effect of past handling or shearing and plot a consistency curve of shearing rate versus shear s t ress. This is not practical with the • • FIGURE 6 MACMICHAEL VISCOMETER 16 17 capillary viscometer. The laminar flow of a non-Newtonian fluid in a tube is of'ten aocompanied by plug flow. In the oase of a Bingham Plastic. there exists a solid plug of material near th capillary axis regardless of the flow velocity. It is necessary to have a finite length of tube to get a measurable shear stress. However, if the fluid shows a time dependency, as in the case of a thixotropic material, it would be necessary to build a tube viscometer with a finite length and a different ial time element. This is not possible. In the rotational viscometer, the confining walls of the instru ment move relative to a fixed batch of fluid, whereas in the tube viscometer the fluid flows relative to the confining walls. Because of the shortcomings of the capillary and orifice type viscometers, it was decided to concentrate on selecting a rotational viscometer for the investigation. A survey of the literature showed that in almost all cases, the consistency curves of non-Newtonian fluids were determined by rota tional viscometers of basically t}e same type. This was done primar ily because the consistency curve of a non-Newtonian was not linear when done with a capillary viscometer, but it was linear when done with a rotational viscometer. In the latter viscometer the conditions were such that all of the fluid was in laminar flow once the applied torque exceeded the yield value of the fluid. Also, with the rota tional viscometer, the rate of shear applied to the same sample could be varied within the limits of the speed range of the instrument with very small time lags. Hence, fluid breakdown, build-up or yield 1 value oould be easily detected. 1his was possible only by indireot im1ans with other types of viscometers. On a shear diagram plotted from results obtained by use of a rotational viscometer, the apparent viscosity was determined by the inverse slope of a line drawn from the origin to a point on the con sistency curve, multiplied by the instrumental constants . The development of the flow equation for the rotational visco mater of the ~ acMichael type was furthered primarily by Reine r and Riwlin, (2) and applied where the torque to which a fluid was subjeot ed, was sufficiently large such that all material in the sample cup was in laminar flow. T he equation was as follows: where W = angular velocity when all material was in lB.minar flow. JJ.: mobility or reciprocal of plastic viscosi-mJ. T ::. torque applied. h = depth of innnersion of the bob in tha sample. R = radius of the bob. R = radius of the sample cup. f :. yield va 1 ue of the f 1 ui d • 1 1 - Rb2 Rc2 4n- h letting =Sand - C - then f: CT2(T2 - intercept of linear curve section). Plastic viscosity U = {torque)(S)(K); where · • o. T2 == o. (RPM) K = constant of torsion wira supporting tha bob. The Brookfield Viscometer had bean used to some extent in plant • tests on the subject fluid. Both the single-speed and multispeed models gave very erratio results. 19 The use of the Brookfield entailed changing the bob to one of another size while retaining the same torsion wire for each range of viscosity. It was extremely difficult to keep the bob assembly from wobbling after the first ft!IW runs. After a specific bob had been handled on several runs a wobble would develop. This undoubtedly contributed to inaccuracies. The Brookfield Viscometer was specifically designed to read apparent viscosities. Its calibration inherently gave a viscosity which a non-Newtonian fluid would have if it were a Newtonian fluid. Thus, the fact that the torsion spring was accurately calibrated in eentipoises, was of no value in the study of non-Newtonian fluids. On the bas is of" the above, the Brookfield Viscometer was ruled out of consideration. A model of the Stormer Viscosimeter was examined critically and though it appeared to be a precis ion instrument, there were several unsatisfactory features. The fact that a new weight had to be attached to the instrument for every change in the rate of hear made the operation too slow for studying non-Newtonian fluids. In addi- tion, the time of descent of the weight had to be timed with a stop watch. Even though a stroboscopic revolution counter was available as an accessory, the timing was still necessary. It was decided that one operator oould not possibly record all the data and still 20 maintain a minimum time lag between changed rates of shear. The Precision-Interchemical Viscometer was examined oarefully and was deemed ideal for the study. All shear or viscosity ranges could be studied without changing either the bob or the sample cup, and a speed range of 10 to 400 revolutions per minute was available by changing the variable speed control. without stopping the instru ment. Forty changes in speed could be made in three minutes. .Accu rate temperature control of the sample cup was an added feature. This viscometer was not used for the investigation solely because of high cost. Very little information was available on the Hercules Hi-Shear Viscometer. This viscometer appeared to be satisfactory except for a peculiar spring-loading feature. The price of this instrument was also beyond the investigative budget. A model of the acM iohael Viscometer was obtained and examined critically. The basic operation of this instrument was identical with that of the Precision-Interchemical iscometer although not as elaborate. The unit had a speed control of from 10 to 40 revolutions per minute and a sample cup with built-in heater. he bob was sus pended from a torsion wire of phosphor bronze and the deflection of the wire was measured by a dial scale and pointer. The instrument had all the necessary features for the study of a non-Lawtonian fluid, (5, 6) such as a wide range by merely changing torsion wires, a variable speed w hereby shear rates could be changed rapidly, and sample temperature control. It was decided to use this instrument in view of the test performance, the adaptability, and the cost. 21 CHAPTER III PROCEDURE Calibration of the Viscometer In order to measure the fluid properties in absolute units it was necessary to calibrate each torsion wire and the instrument itself. The constant of each wire was determined by actual measure ment. The viscometer was assembled in operating position with no sample in the sample cup. The damping dashpot was filled with 600 W oil and the clearance between the circumference of the assembly and the walls of the dashpot was decreased to about 0.002 inches by means of a soft brass collar, in orcer to eliminate wobbling. An instrument constant (Z) was calculated to compare results from the viscometer to published results on a standard fluid. This was the only emperieal constant used, and was determined in the following manner: A solution of glycerol in water was prepared, and its exact composition determined by the standard pycnometer and specific gravity methods. The composition was determined to be 94.674% glycerol. This corresponded to a viscosity of 419 centipoises ( cp.) at 73 degrees F 1 ahrenheit (°F.). This solution was t hen run on the MacM ichael viscometer and a curve was plotted. The curve indicated a viscosity of 692 centipoises (cp.). Thus the correction factor (Z) for the viscometer became 419/692 • 0.59. This factor had no effect on the basic character or type of the curves. 23 A non-stretch cord was wound around the circumference of the indicating dial and run out horizontally parallel to the face of the dial. The cord was then passed over a precision bearing and then vertically downward in apace. Standard ram-weights were then hung on the cord and the deflection of the dial scale and torsion wire noted. This was done for each size of torsion wire used and gave a direct comparision among the wire constants. The latterwere desig nated by the letter (K). K: (Wt. in grama)(980)(radius of dial in cm.): (dial deflection OM) - Cm. • centimeters The dial of the viscometer was circular and graduated in degrees MacMichael or ( 0 M) from Oto 300 around the circumference. Table I shows the results obtained by this calibration. Auxiliary Equipment In order to keep the main supply of sulfonate fluid at a constant temperature and to bring individual samples to test tempera ture, a double water bath with temperature control had to be fabrica ted. This was accomplished by remodelling an old Launderometer which was available. The latter consisted of a double water bath, a rotating sample agitator and a constant temperature control. The center shaft was removed, new piping was added and the temperat re controls checked, with the result being a. constant temperature bath of fifteen gallon capacity with a temperature control range of ambient water to 212 degrees ahrenheit (°F.). The controls held a Wire No. 26 22 18 TAB LE I TO RSION W I RE CONSTAi TS W t. Grams Deflection °M 2 100 10 75 30 35 24 K ~e-C m -OM 101 674 4334 25 constant temperature of plus or minus one degree Fahrenheit. This bath was used throughout the investigation. both for bringing samples up to teat temperature, and for storing the main supply of sulfonate slurry. Further work was necessary in maintaining constant temperature oontrol of the individual sample once it had been removed from the bath and transferred to the viscometer sample cup for testing. The viscometer cup had an electric heater wire in the walls with a slip ping contactor to supply power. The slipping contactor was necessary beoause of the rotation of the cup. There were no provisions for varying the power input. Thus, it was necessary to disassemble the unit and rewire the input circuit. The power circuit was modified to incorporate two power supplies, one to the variable speed motor and one to the heating elem ent of the sample cup. A Powerstat or vari able voltage regular was incorporated in the latter circuit so that the cup heater output could be varied as desired. Consistency _Gurve_s Method The MacMichael Viscometer was set up, levelled carefully and fixed in place. The speed range of the viscometer was divided into regular intervals or Revolutions Per M inute (RPM) values and marked on a dial attaohed to the speed control knob. In running the actual consistency curve, the sample was measured into the viscometer cup, the bob was inserted and the viscometer started at its lowest speed. After seven seconds at the initial spee~ the viscometer was set to the next speed interval and the torque 26 reading from the first speed recorded. After five seconds at tha second speed the torque value was recorded and a third speed interval begun. The upcurva, or period of increasing speed, was continued, with the total time at eaoh speed bein five seconds. When the highest viscometer speed was att ained, the downcurva, or period of decreasing speed, was begun, as a cont inuation of the upcurve with exactly the same time and speed intervals. 1he total time for running any consistency curve was 87 saoonds. ha time interval between any two torque val~es was five seconds, with the exception of tha first torque value which was read at seven seconds. A downourva was run throughout the investigation in an attempt to determine the extant of breakdown or build-up of fluid resistance due to applied rates of shear. An upcurve by itself would classify tha fluid but would not determine thixotropy or the degree of build up. Careful attention was given to t he time element in all tests because of its extrema importance (7) in dealing with thixotropic materials. hen the slurry was subjected to a constant shearing rate for a period of t i me, cons i derable breakd own was evidenced. Further breakdown was found during peri ods of increasing shear rates at small time intervals. The effec t of t he two methods of breakdown of a t hixotropio material was ill·ustrated by plotti g Fi 0 ura 7, page 28. A consis tancy curve run on the material would approach the line (TB) if no breakdown occ urred. I f tha te at were run i n zero time, breakdown• 27 due strictly to 'tune at shear rate', would be eliminated, but break down would oocur due to the increasing rate of shear. Thus, the consistency ourve would approach (TB 0 ). Since, in any test, a finite time interval would be involved, the real curve of a thixotropic material would fall to the left of (TB 0 ), and would approximate (TB1). If the shear rate were kept at one level over a period of time, the resulting curve would be represented by. (Bo Bi B 8 ). The downcurves shown were run in the same manner as the upcurves with no time delay at the point of maximum speed. If e. time lag had occurred at the (B) level speed, the downourves would begin at some point to the le.rt or their plotted positions. It was apparent therefore. that any consistency curve of a thixotropio material would inherently evidence breakdown due both to 'time as shear rate' and 'increasing shear rate'. Sinoe it was desired to compare the consistency curves of the sulfonate slurry at various temperatures and thermal histories, it was necessary to run curve points in an identical manner with respect to time, from test to test. In the main phase of the investigation, samples were tested in sets of six, with each set of six having a different temperature. Each sample within a set had a different time at temperature. Slurry in the main tank was agitated and a sufficient number of samples bottled for the test. The heatin bath was brought up to teat temperature and all samples were put in the bath at t he same time. As soon as the samples had reached the bath temperature, one I I Be 8, Bo 8 FIGURE 7 THIX0TROPIC BREAKDOWN 28 29 sample was arbitrarily sel cted and a consistency test run. The time was noted also. ha balance of the six samples ware run one at a time at 30 minute intervals. Thus, the last se.mpla had a tima-e.t tamperature equal to the elapsed time of all tha runs, whereas tha first sample had a t·ma-at-t9mparature of very close to zero. Thi procedure was duplioatad at temperature intervals of 10 degrees Fah ranhait (°F.) from 110 to 160 degrees Fahrenheit ( 0 .) inclusive. Curve Interpretation As a means of achieving a truer representation of the fluid than that afforded by the apparent viscosity conoapt, the concept of plastic viscosity as developed by Green and , altmann (2) was used for interpreting the curves. This method was based exactly on the Rainer and Riwlin equation mentioned previously. According to raan and eltmann, the upcurva of a thixotropic plastic had an infinite number of downcurves, all of them straight and all intercepting the torque axis at some yie ld value. 'lhua, using a rotational vi cometer, their procedure was to run two down curves and calculate two plasti c viscosities. Two yield points were oaloulated from the downcurva intercepts on tha torque axis. From these four values a coefficient of thixotropic breakdown was calcula ted which was tha s ama for both curves. ha basis of comparison of two different ourvas was tha breakdown coefficient, and the viscosi- tias, as well as the ent ire consistency curve. illustrated by i ure 8 , page 32. ha prooedura was In igure 7 tha pcurva was designated (OC) with the top 30 viscometer speed occurring at (C). The tw downourves were shown as (CT), and (BT2)• The second downourve could equally well have been run from point (F) or point (E), as long as the first downcurve was run from the maximum speed point of the test. Green and Weltman found that, with an increase in speed from point (B) to point (C), there occurred a small increase in yield value intercept of the cor responding downcurve. This was shown by points (T1) and (T2)• This increase in interc~pt was quite small even though an increase in speed of 200 revolutions per minute (RPM) was used by Green and Weltman. In the present report, where the maximum viscom eter speed was 42 revolutions per minute (RPM ), no increase in yield value intercept could be detected and all downcurves intercepted the torque axis at the same value. Thus, since the upcurve of a thixotropie plastic material had an infinite number of downcurves all intercep ting the torque axis at the same point, it was necessary to plot only the downcurve from the point of maximum shear of the instrument. The coefficient of thixotropic breakdown was calculated as follows: M • 2(Ul - U2) ln (w 2 2 ) w 2 l M was the loss in shearing force per unit area per unit increase in rate of shear. The above procedure was specifically intended to cover thixo tropic breakdown, where t he downcurve was a straight lie falling to the left of the upcurve. In this investigation the concept of thixotropy was extended to cover build-up as wel as breakdown. Another coefficient ( b), was introduced as the coefficient of 31 thixotropio build-up. (Mb) was defined as the gain in shearing foroe per unit area, per unit increase in rate of shear, and was calculated in the same manner. 32 C // I / D 0 T, T, TORQU[ 0 M FIGURE 8 CURVE ANALYSIS METHOD CHAPTER IV CONSISTE CY C URVES-VA YIN G TIM E-AT-TE:N ERA URE Consistency Curves at 110 D eErees Fahrenheit (°F) Six samples were run at this temperature with Figure 9 being presented here, and the remaining five being listed in the appendix. In Table II, page 35, the subscript (A) means that the figure is listed in the appendix. The curve of Figure 9 with a time-at-temperature factor of approximately zero closely approached Newtonian behavior. The up curve indicated very slight dilatanoy while the downcurve indicated an almost negligible build-up in shear induced resistance. The intercept of the downcurve was to the left of the origin, indicating no yield value. Calculations for Fi gure 9 were made as follows: f : TCZK = (0)(2.1)(10- 2 )(0.59)(674) • 0 dynes/cm2 u 1 = (22 4)(9.55)(13.56)(10-3)(0.59)(674) • 47.8 poises 28 u 2 = (35 4)(9.55)(13.56)(10- 3 )(0.59)(674) • 47.8 poises 4 Mb= (2)(47.8-47.8) • 0 dynes/cm2 ln (422)- (28~) In general, the 'time-at-temperature' factor appeared to make little difference in the fluid behavior at t his temperature. The plastic viscosities showed little change, as did t he torque :in:t:ercepts. It did appear, however, that t he longer time-at-temperature prior to viscometer measurements made t he fluid less free-flowi ng in appear ance and slightly more sticky. The build-up coefficient also tended 34 4Z • 40 38 ~ 34 3a 30 28 ~ a~ 22 ~ zo /8 Q_ ~ /l:, /4 /Z /0 8 0 4- 2 TORO//£ 0 M - WIRE Z2 FIGURE t:t CONSISTENC y CURVE JJO °F Figure Number 9 29 30 31 32 33 TABI.E II T IME- TE)fi'ERATURE CURVES AT 110 ° F . Torque Intercept OM -4.0 -s.o -3.0 -7.0 -5.0 -2.0 U1 Poises 47.8 49.6 43.8 49.6 53.5 42.4 U2 Poises 47.8 52.6 ---- 55.0 _..,._.., 45.5 0 -7.4 -.. ~- -13.6 ---- -7.7 Time at Temp. M inutes 0 20 50 80 110 140 35 Fluid Behavior Pattern Slightly Dilatant Plastic Thixotropic Build-up Thixotropic Breakdown Yield Value Transition Stage Sticky Pourable Jelled Loose Fluid Stringy Approaches Newtonian Sli~htlI Tac~ TABLE III FLU ID BEHAVIOR VARYIN G TI]IIB;-AT-T~MPERATURE Time at 110 °F. - 'inutes 0 20 50 80 110 X X :xx XXX X X X xx X X X X X X X X X X X X X X X X X X 36 - - 140 X xx X X X X - 37 to increase with time. A summary of the properties at this tempera ture was listed in Tablas III and IV. Basic Shear Diagr~ For the MaoMiohael or rotational viscometer, the shear stress varied with radius, that is, it varied with the distance from the center of the sample cup toward the inner wall of the oup. Shear stress was generally calculated at the wall of the bob for presenting basic shear diagrams. The basic shear diagram for Figure 9 was shown as Figure 10 and plotted as du/dy versus Tb where: du/dy - rate of shear in radians/second at bob wall du/dy: 2nrb (revolutions/second): radians/second ro - rb Tb sr shear stress in dynes/c~. at bob wall where T • OMacMichael All symbols are the same as listed previously. Since du/dy = rate of shear, then (du dt = Total displacement in direction of flow )dy for time interval (dt.). Figure 11 was plotted showing the displacement versus the time function. The latter was actually the time at shear rate, and all intervals were five seconds as mentioned previously. A measure of comparison between the curves at various time-a.t temperature intervals, should be the work input required to run the test. Thus, at the b ob all, the foroa would be approximately equal to 38 TABLE IV BASIC DATA AT 110 °F. Displace- ment Torque Ns Tb Time rad. oy Rev./Seo. _ du/d7 dynes./em 2 • t.sec. du/d_x_ dt 10 0.20 1.38 252 7 9.66 13 0.234 1.62 328 12 8.10 15 .317 2.20 378 17 11.00 19 .400 2.77 479 22 13.85 22 .466 3.23 555 27 16.15 25 .534 3.70 630 32 18.50 29 .600 4.15 730 37 20.75 32 .666 4.62 806 42 23.10 35 .700 4.85 882 47 24.25 34 .666 4.62 856 52 23.10 29 .600 4.15 730 57 20.75 27 .534 3.70 680 62 18.50 22 .466 3.23 555 67 16.15 18 .400 2.77 454 72 13.85 13 .317 2.20 328 77 11. 00 9 .234 1.62 227 82 8.10 7 .200 1.38 176 87 6. 10 39 4-8 ◄., 4.4 Q 4.2 <: 4.o B ~ 5.8 ~ .3., V") ~ J,,'f <C ,.2 ........ a 3.0 <: 2-8 ex: I z., >- 211 a 2.2 ............ ::::, z.o a /.8 /,,I, /.4, ,.z L 0 /()0 zoo '"° 400 500 1()() 800 '"° Ti,- DYNES/CM~ FIGURE 10 BASIC SHEAR DIAGRAM 110°F. 40 330 _...,_ l4J 300 :::::a. -- t-- q: ~7() -.J ::::, ~ 1.4'J ~ '-> '- ZIO V) ~ ~ /80 -- ~ ~ ~ ISO \ ~ C 1ro >- a 'lo ~ ~ ,o 30 0 10 10 ~o 50 eO 70 80 '10 IIJ" . FIGURE 11 DISPLACEMENT VERSUS TIM£ 11o•F 41 (2 rbh)(Tb)• The displaceme t would be ( 8 )(t·me)(2 io), where the time was the number or seconds or rotation at a given speed and torque. The work would be the product of force and displacement, with the total, or avera _ e work per test being the sum of all the work done at the various intervals. Since the speed and time inter vals in all tests were i dentical, and the torque varied with the fluid condition, the work input per test should also vary directly as the fluid condition. ~onsistency Curves at 120 D egrees Fahrenheit (°F.) Six consistency curves were run at 120 degrees Fahrenheit (°F.). As before, each test was run on a different sample having a different tL~e-at-temperature. Sinoe the results were similar in all cases, only one consistency curve, Fi gure 12, page 43, was shown, with the balance being appended. The viscosities and ooeffieients were listed in Table V. The upcurve of Figure 12 indicated some dilatancy and a consi derable build-up. Both items were higher than found at 110 degrees Fahrenheit (°F.). The rate of decrease of torque shown by the down curve was also greater than that at 110 degrees ahrenheit (°F.). N o yield value was indicated. The balance of t he curves at 120 degrees Fahrenheit (°F.) followed a similar pattern, and there appeared to be no established trend. The viscosities vari ed somewhat but were not greatly changed from those at 110 de rees Fahrenheit (° F.). A basic shear dia ram for Fi ure 12 was constructed, showing torque at the bob wall versus shear rate.. his was shown as 'i ure 13, page 47, with the necessary data listed in Table VII , pa e 46. Consistency Curves at 130 Degrees Fahrenheit (°F.) Six consistency curves were run at 130 de rees Fahrenheit (°F.) each with different time-at-temperature. Two of t he curves, i gure 14 and 15, pages 48 and 49, were shown, with the rest bein appended. The viscosities and coefficient were listed in Table VIII, page 50. Figures 14 and 15 showed two sta~es called transition sta es, that appeared to exist at 130 degrees Fahrenheit (°F.). The stage of the transition appeared to be independent of the time factor. All curves at this temperature showed a pronounced yield value. In the transition stage the ourve showed both build-up and breakdown to increasing rates of shear, depending on the shear range examined. Viscosities were lower than at lower temperatures, tending to increase with time. A basic shear diagram was constructed f or F'igure 14 and tabulated as Figure 16, page 53. In addition the work input was calculated. Consistency Curves at 140 Degrees Fahrenheit (°F.) Six samples were run at 140 degrees Fahrenheit (°F.) in the same manner as before. All curves were appended except for F'i gure 17. Behavior at 140 degrees Fahrenheit (°F.) closely approached the ideal curve of a thixotropic Bingham Plast·c as postulated by Bingham in his ori i al works. In most cases the rate of increase of flow was directly proportional to the rate of increase of ap lied force, once the yield value of the fluid was exceeded. At 140 degrees 43 42 40 38 " '4 32 30 ~8 a, ~4 22 ~o [ /8 Cc /I, /4 IZ /0 8 ' 4 ~ TORQIIE o/1 - WIR£ 22 FIGURE 1Z. CONSISTENCY CURVE 120°F. Figure Number 12 34 35 36 37 38 ■ TABLE V TIME-TEMPERATURE CURVES AT 120 °F. Torque Intercept U1 U2 OM Poises Poises -3 47.8 49.0 -3 51.5 54.0 -3 ------ 67.0 -2 49.6 54.0 -5 67.0 55.0 p - 41.0 50.0 Mb 2 Dynes/cm. -3. 9 -6.2 --- --- -== -10.9 t:.s -24.4 • fs - - - Time at Temp. Minutes 0 40 70 100 130 160 44 Fluid Behavior Pattern Dilatant Ple.st ic Build-up Breakdown Yield Value Transition Stage Sticky Pourable Jelled Loose Fluid - Stringy Ta.cky TABLE VI FLUID BEHAVIOR VARYI G TIM E AT TE , ' 1 RATURE 45 Time at 120 °F. before testing - M inutes 0 40 70 100 130 160 X X X X X X X X X X X X • - - X X X X X X - X X X X X X X X X X ■ • . X xx . - .. -- Torque Ns OM Rev.7Sec. 12 .20 14 .234 16 .317 20 .400 23 .466 25 .634 27 .600 32 .666 37 .700 36 .666 33 .600 30 .534 26 .466 20 .400 16 .317 11 .234 9 .20 T A BLE VII B ASIC D ATA A T 120 OF. du/dy Tb Time rad./ dynes/ t sec. cm2. sec. 1.38 302 7 1.62 353 12 2.20 402 17 2.77 504 22 3.23 580 27 3.70 630 32 4.15 680 37 4.62 805 42 4.86 932 47 4.62 906 52 4.15 830 57 3.70 755 62 3.23 655 67 2.77 504 72 2.20 402 77 1.62 277 82 1.38 227 87 46 Ive. Viork xl0- 3 2 du/dy- dt re.d. dynes-cm. 9.66 70.9 8.10 69.2 11.00 107.0 13.85 169.0 16.15 226.0 18.50 282.0 20.75 342.0 23.10 450.0 24.26 547.0 23.10 506.0 20.75 465.0 18.50 380.0 16.15 293.0 13.85 197.0 11.00 135.0 8.10 74.0 6.90 44.6 Total W ork 4357.6 47 Q 4.9 ~ <::) 4.4 ~ LL.a ~ 4.0 Vl ~ ~ ,., --- Q ~ 3.2 Q:: ' >- 2.8 ~ ~ C t.~ 1.0 ,., u ------------------ 0 100 zoo 300 400 500 t,oo 100 80() 'loo l1J1Jo 1; - D Y NE 5 /CM . 2 FIGURE 13 BASIC SH £AR DIAGRAM 120 ·r. 48 42. 40 38 3' 34 32 JO • 21, ff 22 ~ 20 /8 n... tr /6 '" /Z /() 8 ' 4 2 0 S /0 IS zo 25" 30 35 40 J/S- TORQUE 0 M - WIRE 22 FIGUR£ 14 CONSISTENCY C URV£ 130°F 49 4~ 40 38 ~ 34 3% 30 ~8 21, 24 za ~ zo Q_ IS lt: 1, /~ ,~ /" 8 ' 4 2 0 3 '1 '1 12 IS 18 ZI 24 Z1 30 33 -'' 3'1 ilf-2 ~S ~8 51 ~ 57 TORQVE 0 M - 'w'IRE 22 FIGURE 15 CONSISTENCY CURVE 130°F. 60 TAB LE VII I TDlE-TE E RATURE T EST S A T 130 °F. - Inter- Yield Time Figure eept Value U 1 U 2 ~ At Temp. Number o:M Dynes/om 2 • Poises Poises D ynes/cm 2 • M ins. 39 10.5 87.5 ----- ----- --- -- --- 0 40 21 175 21.2 30.6 -23.2 30 41 16 134 31.3 36.8 -13.7 60 14 16 134 ---- 36.0 ----- 96 42 23 192 ------ 33.1 ----- 125 15 15 125 40.5 46.2 -17.2 ·155 Fluid Behavior Pattern Dilatant Plastic Build-up Breakdown Yield Value Transition Stage Stioey Pourable Jelled Loose Fluid Stringy Tacky TAB LE IX FLUID BERA IOR VARYI NG TIME-AT-TE14PE RATURE Time at 130 °F. before testing - Minutes 0 30 60 95 125 156 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X 51 62 TABLE X BAS IC DATA AT 130 ° F. du/dy Tb Time Ave. ork Torque Ns rad./ dynee/ t du/dy x10- 3 014 Rev.7Sec. om 2 • dt rad. 2 sec. sec • dyn s-cm. 26 • 20 1.38 630 7 9.66 148 25 .234 1.62 630 12 8.10 124 26 .317 2.20 655 14 11.00 174 28 .40 2.77 705 22 13.86 227 33 .466 3.23 830 27 16.15 324 41 .634 3.70 1031 32 18.50 462 45 .600 4.15 1135 37 20.75 570 47 .666 4.62 1185 42 23.10 664 47 .700 4.85 1185 47 24.25 696 44 .666 4.62 1110 52 23.10 622 40 .600 4.15 1010 57 20.75 508 38 .534 3.70 957 62 18.50 429 34 .466 3.23 855 67 16.15 333 32 .40 2.77 805 72 13.85 270 29 .317 2.20 730 77 11.00 194 22 .234 1.62 554 82 8.10 109 19 .20 1.38 479 87 6.90 80 Total W ork 5932 63 4.4 a :c: 4.0 C '-1 - 1-lJ 36 ~ V) < 3.i <C ...__ a 2.8 I <t: /0 ~ I '2.4 >- ~ z.o a 16 l'Z ~ 0 4 oo Soo 600 'f lJ() Boo 'llJIJ /IJO() I/(}() l2tJo T;, - DYNES/CM~ FIGURE lb . BASIC SHEAR DIAGRAM l30°F. Fahrenheit (°FJ no general trend with time-at-temperature could be established. A basic shear diagram was plotted, listed as Figure 18, page 58, and the input work of the test oaloulated. Consistency Curves at 150 De~reas Fahrenheit (°F .) Five tests were run as before at 150 degrees Fahrenheit (°F.) with two of the curves, Figures 19 and 20, pages 60 and 61, being included in the main report. 64 The fluid at 150 degrees Fahrenheit (OF .) entered a completely different phase. From a free-flowing fluid at 140 degrees Fahrenheit (°F.) it changed to a stioq, tacky jell of immobile consistency. On cooling, the materi al flowed in long strings or as a plug. As shown by igure 19, the transformation required several minutes at temperature to take place. Figure 20 showed the material to be well into the jell stage after 100 minutes at temperature. Except for Figure 19, it was not possible to determine whether the curves were dilatant or plastic, although the latter appeared to be a more true characterization. The yield values and viscosities were much higher than at previ ous temperatures. A basic shear diagram was cons tructed for Figure 20 and listed as Figure 21. page 65 . In addition, the work input was calculated. Consistency Curves at 160 Degrees Fahrenheit (°F.) Five samples we re run at 160 degrees Fahrenheit (°F.) with two being presented in the report and as Figures 22 and 23, pages 66 and 55 .,, 40 3B 3' ,,, 3t "' ZS Z(, 24 0 I zz to ~ 18 ~ '' ~ ,.,. I~ /0 8 I, 4 2 0 . 5 /0 /~ 20 ~5" 30 3S 45 TORQVE 0 M- WIRE 2Z FIGURE 11 CONS I STE NC Y cu R VE 140 °F. Inter- Figure oept Number O M 17 10 43 16.5 44 11.0 45 15.0 46 15.5 47 17.5 TABLE XI TIME-TEMPE RATURE TESTS AT 140 ° F. Yield V alue Ul u2 M 2 Dynes/cm 2 • Poises Poises Dynes/cm. 84 28.5 25.8 6.7 138 21.2 17.8 8.4 92 27.6 23.3 10.6 125 23.0 19.6 8.7 130 32.2 23.9 20.3 146 32.2 25.2 17.4 56 Tilne At Temp. ins. 0 20 40 60 80 100 57 TABLE XII BASIC DATA AT 140 ° F. du!dy • Tb Time Ave. _Jork Torque NS rad./ dyne~/ t du/dy xlO 2 OM Rev.7Sec. see. cm • sec. dt rad . dynes-cm. 18 .20 1.38 454 7 9.66 106 20 .234 1.62 604 12 8.10 99 22 .317 2.20 565 17 11.00 148 26 .40 2.77 630 22 13.85 212 25 .466 3.23 630 27 16.15 246 27 .534 3.70 680 32 18.50 305 29 .600 4.15 730 37 20.76 368 30 .666 4.62 755 42 23.10 422 31 .700 4.85 781 47 24.25 460 28 .666 4.62 705 52 23.10 395 26 .600 4.15 655 57 20.75 330 26 .534 3.70 630 62 18.50 283 23 .466 3.23 580 67 16.15 226 22 .40 2.77 555 72 13.85 186 20 .317 2.20 504 77 11.00 134 - 17 .234 1.62 429 82 8.10 84 16 .20 1.38 378 87 6.90 63 - Total ork 4067 58 s.o a ,,,.z. "<: <:::) 3-8 u Ll.J V) 3.4- ~ Cf) :z: ·I <t: z.s ........ a < . 24 Cr I >- 2.0 C =5' /. '1 ~ 0 /.2 ~--------- 0 3/JO 400 .st» lxJo 1tJ" 8()() 'f()O /a,tJ I loo FIGURE 18 BASIC SH EA F? DI A GRAM J 4-0 .F. 59 67. The other ourves were appended. As shown by Figure 22 in comparison with Figure 23, a definite time-at-temperature was necessary before the fluid completed the transformation from the plastic state to that at 160 degrees Fahren heit (°F.). At zero time, Figure 22 was still a true Bingham Plastic although partially jelled. At this temperature the fluid was very tacky and was unpour able. A basic shear diagram was constructed for F 1 igure 23 and listed as Figure 24, page 71. The work input was also calculated. 60 4~ 40 31 ,t. 34 31 0 30 . Z8 " 24 J 1 ZI ~ %0 ,11 ~ " H ,, /0 8 ' 4 a ,ORQI.IE 0 1'1 - WI RE tB FIGURE 1'1 CONSISTENCY CURVE. 150 °F. 61 42 40 38 3' 34 32 3" 28 24' 24 tt 20 ~ 19 /I, I 1 ~ /4 ,~ /0 8 " 4- a TOROVE 0 11 - WIRE 18 FIGURE 20 CONS IS TE NC y CUR VE J50°F 62 TABLE XIII TI 1E- TEMPERATURE TESTS AT 150 ° F . Inter- Yield Time Figure cept Value U1 U2 M At Temp. N umber O M Dynes/cm 2 • Poises Poises Dynes/cm 2 • Mins . 19 5 268 38.6 35.6 7.15 0 - -. - - --. - 48 -- ---.. - ---- ---- ..... ._ .. 30 49 25 1340 71.2 71.2 0 60 50 24 1315 65.2 67.2 - 4.9 75 20 21.5 1100 __ .,..., 75.0 0 100 ~ .. :: ca ' g == =: Torque OM NS Rev.7Sec. 25 • 20 26 .234 25 .317 26 .40 27 .466 28 .534 29 .600 30 .666 30 .700 30 .666 28 .600 28 .534 27 .466 26 .400 25 .317 24 .234 23 .20 TAB LE XIV BASIC DATA AT 150 °F. .. =::; E 1 l = = •• - - du/dy Tb Time rad./ dyn~s/ t sec. cm • sec. 1.38 4050 7 1.62 4060 12 2.20 4050 17 2.77 4210 22 3.23 4370 27 - 3.70 4540 32 4.15 4700 37 4.62 4850 42 4.85 4850 47 4.62 4850 52 - 4.16 4540 57 3.70 4540 62 3.23 4370 67 2.77 4210 72 2.20 4050 77 1.62 3980 82 1.38 3720 87 Total 63 du/dy Ave. Wgrk xio- dt rad. dynes-cm. 9.66 950 - ---- 8.10 795 -....-._ .. _ 11.00 1077 13.86 1415 16.15 1710 18.50 2030 -- 20.75 2360 23.10 2720 24.25 2860 23.10 2720 20.75 2280 18.50 2030 16.15 1710 13.85 1415 11.00 1077 8.10 780 6.90 625 ork 28,544 Fluid Behavior Pattern Dile.tant Plastic Build-up Break-down Yield Value Transition Stage Sticky Pourable Jelled loose Fluid Stringy Tac~ TABLE XV FLUID BERA VIOR VARYING TIME-AT-TEMP RATURE Time a.t 150 OF• before testing 0 30 60 75 X X X -- X X X X . X X X X X X X X X X X X X X X X X X X X X X 64 - Minutes 100 X X X X X X 65 4.'f a ~ 4.o C) '-' l,lJ 3./. ~ V) 3-Z < c:c ........ 2.8 a <t: .rr. 2.4 I >- 2.0 ~ 1 ~ Q 1., • I. 0 /.2 L 0 3100 3850 4000 4/SO 4300 4450 4600 4150 4'100 FIGURE ZJ BA5IC SHEAR DIAGRAM 150°F. 66 42 40 0 .38 3, 34 3Z 30 28 z, t4 j 0 0 1 22 ~ zo /8 Q__ Cl: ,, /4 /~ 0 /0 8 ' 4 ~ TORQUE 0 /1 - WI RE 18 FIGURE 22 CONSISTENCY CURVE 160°F 67 4Z 0 4o 3B ¼ 34 3Z Jo 28 2, 1 l 24 n zo ~ 18 ~ 1, ~ 14 12 /0 8 II 4 ~ TORO VE 0 M - w' IR£ 18 FIGURE 23 CONSISTENCY CURVE 160°F 68 TABLE XVI T IME-TE1'1 .Pr~RATURE TESTS AT 160 OF. Inter- Yield Time Figure cept Value U1 U2 M At Temp. Number OM Dynes/cm 2 • Poises Poises Dynes/cm 2 • Mins. 22 15 804 47.5 41.5 14.8 0 51 19 1020 71 . 0 71.0 0 35 52 22 1180 ---- ----- 0 65 23 28 1500 ---- ---- Neg. 100 53 26 1400 ------ ---- Neg. 135 Fluid Behavior Pattern Dilatant Plastic Build-up Breakdown Yield Value Transition Stage Sticky Pourable Jelled Loose Fluid Stringy Tac~ TABLE XVII FLUID BEHAVIOR V ARYI G TIM E-AT-TEM PE:RATURE Time at 160 °F. before testing - 0 35 66 100 X X X X X - X X X X X X X X X X X X X X X X X X X X X X X - 69 inutes 136 X X X X X X X X Torque Na OM Rev ./Sec. 26 • 20 25 .234 25 .317 25 .40 25 .466 26 .534 - 27 .600 29 .666 29 .700 28 .666 28 .600 28 .534 28 .466 28 .400 27 .317 25 .234 25 .20 .......... TAB LE XVIII BASIC DATA AT 160 ° F. du/dy Tb Time rad./ dynes/ t sec. cm 2 • sec . 1.38 4050 7 1.62 4050 12 2.20 4050 17 2.77 4050 22 3.23 4050 27 3.70 4210 32 4.15 4360 37 4.62 4700 42 4.85 4700 47 4.62 4540 52 4.15 4540 57 3.70 4540 62 3.25 4640 67 2.77 4540 72 2.20 4360 77 1.62 4050 82 1.38 4050 87 du/dy dt rad. 9.66 8.10 11.00 13.85 16.15 18.50 20.75 23.10 24.25 23.10 20.75 18.50 16.15 13.85 11.00 8.10 6.90 Total · ork 70 Ave. Wgrk xlO- dynes-cm. 950 794 1079 1360 1580 1890 2200 2630 2762 2540 2280 2030 1775 1620 1160 794 680 28,004 a ~ 0 u ltJ V) ~ V) ~ <t: ~ D ~ ex: ' >- a ~ :::, a 4.4 4.0 3., 32 t.8 2.4 2..0 1., /. 2 / 0 LJ O 3700 3850 40oo · 4150 4300 445tJ 4600 4150 4900 1i, - OYN£S/CM. 2 FIG URE 24 BA SIC SHEAR j:DI AGRAM 1 b0°F . ' ' 71 C HAPrER V s· , Vf ARY O F RESULTS The al~Jl aryl sulfonate slurry was fond to be a non-Newtonian fluid with peculiar characteristics. The fluid simulated Newtonian behavior at 110 degrees ahrenheit (°F.) but varied through a wide range of non-Newtonian characteristics as the temperature was raised. At 120 degrees Fahrenheit (°F.) the fluid showed a build-up in shear resistance and evinced dilatant properties. At 130 degrees Fahren heit (°F.) a transition range was found wherein behavior simulated plastic or dilatant fl ow depending on the shear rate. The transition range ended at approximately 134 degrees Fahrenheit (°F.). From 136 to 148 degrees Fahrenheit (oF.) the fluid showed all the properties of a Bingham Plastic. At 150 degrees Fahrenheit (oF.) and higher, another transition range was found in which the fluid became a thick unpourable jell and thixotropio breakdown disappeared. Several min utes at temperature were necessary for t he material to enter the jell stage. While the fluid viscosity decreased from 110 to 140 degrees Fahrenheit (°F.) it increased at higher temperatures, showing its highest value at the jell sta e. The greatest changes, however, were not in viscosity, but in yield value and work required to induce laminar flow. From 110 to 150 de rees Fahrenheit (°F.) there was a two-fold increase in viscosity a.nd a seven-fold increase in work input per test. Graphs of the variation off notions of temperat re were plotted 73 and tabulated. (Fi ures 26 throu h 28). It would appear that, from a plant-handling standpoint, the plastic viscosity changes were not as important as the changes in yield value and physical behavior. There appeared to be a close relationship between the rather peouliar behavior of the slurry a.nd the water present in the slurry. At the jell stage, at higher temperatures, there appeared to be no physically free water in the material. At this stage the slurry was almost ilimovable. On standing, with no agitation, free water would seep from the mass and coat the walls of a container. Water would also collect in myriad layers within the mass itself. The material would become less imnovable and flow as stringy layers, or as a solid plug lubricated by the free water. Upon further agitation, the free water would disappear and the mass would again become semi Lmmovable. The same action occurred at lower temperatures to a much lesser extent. The alkyl aryl sulfonate molecule was described by previous investigators as being a hydrophile at one end and a hydrophobe at the other. It was possible that these forces varied with both the temperature and the amount of shear to whi h the solution was subjec ted, passing through a maximum or minimum force area. The hydro philic force could have removed enou h free water from solution such as to cause a dilate.nt behavior. At another point the effect of shear and temperature combined could have been such as to make the hydrophobic force dominant, releasin more free water and causing the 74 material to exhibit thixotropio behavior. The above was considered highly postulativa, and was beyond the scope of the investigation; however, behavior of the water in the solution did appear to have a great effect on the behavior or the sulfonate fluid. " I ~ ~ X • V) l: ~ ' Lu ~ >- Q ~ V) kl \-- Cr: LLJ Q_ ~ ~ Q_ ~ ....... ~ cc C) ~ 42 38 31- 30 26 22 18 14 /0 ' 2 75 0 /10 /20 /30 /40 /50 /60 TEMPERATURE 0 ,=: FIGURE 25 TEMPERATURE VERSUS AVERAGE TOTAL WORK 76 '" V) ,3 41 ~ 57 --.... c£ J 51 >-- \-- .__. 45 CJ) a u 3'1 V) ....... :::::- 33 tJ ...... ~ ~1 ' l/') < -J Q. a1 Lu C!l <( JS Ck: ltJ > ' ~ 0 J/0 /2/J /30 /40 /50 /t,O TEMPERATUR[ 0 F. FIGURE 26 TEMPERATURE VERSUS AVERAGE VISCOSITY 77 /650 /SOO l::: /3!10 ~ c.n 1200 llJ <: .:>- /050 C I Lu 'ltJO ~ -J q:: 15'0 ::::::. a ,oo -J l..1J ~ 4S'O ~ C!) 3oO q::_ Cc LL.) /50 ::> ~ 0 //0 IRtJ /30 /40 /Sl) 160 TEMPERATURE °F FIGURE Z7 TEMPERATURE VERSUS YIELD VALUE 78 16 .. . ~ 12. ~ Cl) 8 1.4.J ~ >- 0 4 I L 0 1--- /lo Ito /30 l4o //,() <= -4 LLJ ...... u ...... -8 LL LL LU -12 0 u -16 TEMPERATURE 0 F. FIGURE ZB TEMPERATURE VERSUS COEFFICIENT M. CHAPTER VI C O fCLU S IONS A viscometer believed suitable for testin the al~ J l aryl sul fonate was selected and a technique for evaluating the fluid proper ties was developed. Consistency curves were run on the fluid and analyzed through the temperature range of interest. The peculiar properties of the jell structure were investigated and values plotted. The fact that the sulfonate was a non-Newtonian fluid was established. The process plant manufacturing the sulfonate, at one time relied heavily on the concept of apparent viscosity. The concept eventually proved inadequate and was abandoned. The reasons for this inadequacy were illustrated, with the basic reason being the impossi bility of representing a non-Newtonian consistency curve by one point. For purposes of plant quality control, the investigation illus trated the necessity of each batch of sulfonate being represented by a complete consistency curve; with upcurve, downcurve and yield value if any, being plotted. With each consistency curve, it would be necessary to note the temperature, and any unusual deviations in thermal or handling history. The investiuation pointed out the fact that factors other than viscosity were of at least equal importance. The yield value and the coefficients of t hixotropic buil -up and breakdown would have a great effect in a pumping or mixin operation. 00 The investigation showed that new areas of exploration would be necessary in order to completely answer the 'whys' of the material behavior. Rigorous solubility and chemical study of the forces at work in the solution was indicated. A thorough microscopical study would also be helpful. With further work in this direction, it is quite possible that plant operating conditions could be altered such that at less power input, better mixing and pumping could be achieved. There seems to be no reason why results in the plant could not be correlated with fluid viscometry as an aid in predicting final results. This investigation should, in the future, be extended to deter mine consistency curves of mixtures of builders and sulfonates, using a similar viscometer capable of higher shearing rates. BIBLIOGRAPHY BIBLIOGRAPHICAL ENfRIES A. BOOKS 1. Barr, Guy. A Monograph of Viscometry. 0.xf'ord University Press, 1931. 2. Green, Henry. Industrial Rheology and Rheological Structures. New Yorks John Wiley and Sons, Inc., 1949. Lapple, c. E. Fluid and Particle .Mechanics, First Edition. Newark: University of Delaware Press, 1954. Reiner, Marcus. Jerusalem, Ten Lectures on Theoretical Bheology. Sheckter and Fainberg, 1943. 5. Scott Blair, G. w. Survey of General and Applied Rheolo(5l• Philadelphias Blakeaton's Son and Company, 1938. s. Scott Blair, G. · w. Survey of General and Applied Rheology. New Yorks Pitman Publishing Corporation, 1944. 7. Waltmann, R. N. Breakdown of Thixotropic Structure as a Function of Time. J. Applied Physics, 1943. a. Waltmann, R. N. Industrial Viscometers. Interchemical Review 2, 1943. B. PUBLICATIONS OF THE GOVERNMENT, LEARNED SOCIETIES, AND OTHER ORGANIZATIONS 9. Brookfield Engineering Laboratory. Brookfield Synchrolectrio Viscometer. Stoughton, Mass. 10. Fisher Scientific Company. MacMichael Viscosimster Type 15-347. New York. 11. Smith, J. w ·ilson and Paul D. Applegate. 1'he Hercules Hi-Shear Viscometer. New Yorks Paper Trade Journal, June. 1948. 12. Arthur H. Thomas Co. The Stormer Viscoaimeter. Bulletin D024- 5M. Philadelphias Arthur B. Thomas Company, 1948 . • APPENDIX A CONSISTENCY CUR~ VARY ING T nm-AT-TEMPERATURE 86 IZ 40 • ,, 34 32 90 • 2, . Z4 6R ZtJ i IB ~ 1, /4, /2 /0 8 ' 4 2 TOROVE 0 M - WIRE Zt FIGURE zr CONSISTENCY CURVE Jt0°F 86 4Z 40 !fr . " ~ n so Z8 z, 24 n [ a, /8 Cc /I, /4 /~ /0 . 8 ~ 4 z TORQVF 0 M- WIRE 22 FIGURE 30 CONSISTENCY CURVE JJo•F. ··- 87 4Z 40 38 3' 311 ,~ .50 / ZS 0 ~ 'R4 zz ~ ~o ~ 18 /i, /4 /~ /0 8 ' + z TOROVE 0 M - 'vJIR£ 22 FIGURE 3l CONSJSTENC Y CURVE 1 Jo- •r: 88 42 ~o 38 3' u 3% 30 ZS 21, ~4 n ~ XO 18 ct ~ /I, 14 IZ /0 8 ' 4 ~ FIGURE 32 CONSISTENCY CURVE JJ0°F 89 42 40 lB -" '4 3a 30 28 R' Z4 tR ~o t: 18 /I, Q ct /4 IR /0 8 ~ 4 2 TORQIIE 0 11 - WIRE 22 FIGURE 33 CONSIST£ NC Y CUR V £ 110°F 90 4t 40 38 3' 34 32 30 28 a, 24 ta ao . ~ /8 Q. '' ~ /4 /2 /() 8 ' 4- 2 . 024~8Mn~~m~~NN~~~~~~# TORQUE 0 M - WIRE 22 FIGURE 34 CONS[ STE NC Y CURVE l 20 °F 4-2 4<J .. 38 3' 34 32 30 28 ~, 24- Zt ~o 18 1, /4 IR /0 8 ' 4 2 0 91 0 TORQUE 0 M - WIRE ?2 . PJGURE 35 CONSISTENCY CURVE 0 120 F 92 4Z 40 38 3, 34 32 30 28 ~, 24 ~~ • 20 ~ 18 Cl ~ 1, /4 /2 /0 e " 4 % TORQUE "M - WIRE 22 PIGURE 36 CONSISTENCY CURVE 120°F 93 42 40 38 3' 34 ,i 30 28 261 24 22 • ~() ~ /8 ~ ~ /6, 14 /Z /0 8 ' 4 2 TORQUE o/1 - 'v/1 RE R2 FIGURE 37 CONSISTENCY CURVE 120°F. 94 4t 40 :38 3' 34 31 30 ~8 a, a4 ~z t a, /8 Q__ ~ I~ I-I 12 /IJ 8 " 4 '2 () 5 10 /5" ~o 2S 30 35 TORQUE 0 M - WI RE 22- FIGURE 38 CONSISTENCY CURVE 120°F 96 4Z 40 38 3(, 34 ,a 30 28 ZI, 2~ 22 ~ ~ /8 ~ /I, 14 I~ /0 8 " 4 ~ TORQVE 0 /1 - WIRE 22 FIGURE 39 CONSISTENCY CURVE 130 °F 96 41 40 38 ,, 34 32 30 / as 0 z~ 24 • n [ ~() Q:: 18 '' /4 /2 /() 8 " 4 ~ o s 10 1s 20 ~5' 30 35 ~o ~s 50 TORQI./£ 0 M- WIR£22 FIGURE 40 CONSISTENCY CURVE 130.F 97 41 ~ 31 3' 14 ,. 30 28 ~, Z4 12 . 2/J ~- 18 ~ 1, ct /4, /2 /0 8 ' 4 2 0 TORO//£ 0 M - WI R £ 22 FIGURE 41 CONSISTENCY CURVE 130°r. 98 42 40 0 38 -3' 34 32 3o ts 21, Z4 t2 t ~(J I Q 18 0 Ct: /I, /4 It /0 8 6 4- 2 0 5 10 IS 20 2~ 30 3S- TORG UE 0 M - WI RE: Z2 FIGURE 4Z CONSISTENCY CURVE 130°F. 99 ,fz 40 38 ,, 34 32 I I 30 28 2, Z4 ~2 zo ~ 18 Cl__ ~ 1, 14 ,~ /0 8 " 4 a 0 3S TOROU£ 0 /1 - WIRE 2Z FIGURE 43 CONSISTENCY CURVE 140°F 100 4t 40 ~8 3, 34 32 30 28 I I r, 24 2Z [ zo 18 ~ 1, /4 /2 /0 tJ I, 4 '2 0 5 TORQI/E 0 /1 - WIRE ZZ FIGURE 44 CONSIST£NC Y CURVE 140 °F 101 4a 40 38 3, 34 32 30 I 28 I a, 14 22 ~ 20 ~ 18 ~ ,, 14 ,~ 0 /I) 8 6 4 2 0 S lo IS zo ~s 30 3S ~o ~5 TOROUE 0 /1 - WIRE Z2 FIGURE 4-5 CONSISTENCY CURVE J40°F 102 42 40 38 ¼ 34 32 0 3" ff / 0 ! a, 24 ~a 20 ~ 18 IIJ Cl ~ /4 12 /0 8 " 4- a 0 /0 16 ~o 2S 3S 4S TOROtlE 0 M - W l R £ 22 FIGURE 46 CONSISTENCY CURVE t40°F. 103 /Z 40 38 ~ 34 32 3o lo I 28 1' 24 22 20 ~ 18 Q.. Ct: ,, 14 /2 /0 8 ' ti(. 2 0 S 10 IS 20 2~ 30 40 45 TORQUE 0 M - WIRE zz PIG UR£ 4 7 _ CONSISTENCY CUR V ·E J40°F 104 41. 40 38 3' 34 .32 30 I ~8 21, '24 I Z2 10 ~ 18 ~ '' ~ /4 ,a lo 8 ' 4 ~ TORQUE 0 M - WIRE 18 FIGURE 48 CONSISTENCY CURVE 150°F. 105 '12 ,o 38 " 34 3t 30 38 zt, I %4 n zo ~ 18 ~ /I, ~ /4 IZ /0 8 ' 4 ~ TOROIIF 0 M - WIRE JB FIGUR£ 4'1 CONSISTENCY CURVE 150~ 106 4Z 40 ,, JI- 34 32 ao ZB ~, t4 n to ~ 18 1, <l ~ /,I. IZ 10 8 6, 4 2 o 2 4 ~ 8 10 12 .14 11, 18 zo aa 24 2, 2s 3IJ 3z 31# 31, 38 ,ORQI./£ 0 M - WIRE 18 FIGURE 50 CONSIST[NC Y CURVE t50 °F. 1 7 '" 4(J • 36 3f. Ja Jo ZS ,, I I M u. ~ zo 18 • Cl. ~ ,, ff IZ /0 8 ' 4 2 0 8 12. /6 20 24 28 32 TORQUE 0 M - WIRE 18 FIGURE 51 CONSISTENCY CURVE l60°F. 108 4t 40 38 3' 34- 3Z .30 as ~, Z4 22 20 [ 18 l /I, ct 14 IZ /0 8 ' 4 2 TORQIJE 0 M - WIR£ 18 FIGURE 52 CONSISTENCY CURVE 1b0°F. 109 4'Z 40 38 3' 34 32 30 :28 i, H 12 r j 20 ~ 18 ~ /I, /4 IX /0 8 ' 4 2 TORO I.IE 0 M - 'vv' IRE J 8 FIGURE 53 CONSISTENCY CURVE t60°F APPENDIX B APPENDIX FINAL CALCULATIONS I. INSTRUMENT FUNCTIONS Rb= radius or the bob. R 0 e radius or the cup. h = depth or immersion of the bob. T • torque. Rb~ 1~7/16" • 1.83 cm. 2 Rc = 3.49 om. 1 l 1 2 1 2 s • Rb 2 - Rc 2 - (l.83) - (3.4 9 ) _ (13.56)(10-3 ) /cm3. - 4lTh - \4)(3.l4)(l.27) - c .(13.56)(10-3) = (2.1)(10-2) /om3. -(2.303)log(3.49) (1.83) II. INSTRUMENT CONSTANTS Radius or dial c 2•1/32" • 5.16 om. For Wire No. 18 30 gms • = 36°M. K : (30)(980)(6.16) ~ 4334 Dyne - om. 18 (36) 0)4 For Wire No. 22 10 gms • = 75°1.( K'l 2 = (10) ( 980) (6.16) .: 674 Dyne - om. i:. Oi4 For Wire No. 26 2 gms • = 100°14 K 26 = (2)(980)(5.16) : 101 Dyne - om. {100} OM III. CONSISTENCY CURVE CALCULATIONS Figure 9 f = 0 u 1 • (22 4)(9.55)(13.56)(10- 3 )(0.69)(674) = 47.8 poises 28 o 2 = (36f4)(9.S5)(13.56)(10- 3 )(0.S9)(674) • 47.8 poises - (42) Sinoe (9.56)(13.56)(10-3)(674)(.59) • 51.S then 51.S is used for abbreviation. Mb• 0 Figure 29 f = 0 U1 • (22 5)(51.5) • 49.6 poises 28 o 2 = (38/5)(61.5) = 52.6 poises (42) Mb= (2)(49.S-52.6) = -7.4 dynes /cm 2 • ln(42'2) · (2a 2 ) Figure 30 r = o u 1 = (31 3)(61.5) • 43.8 poises 40 40 RPM. used because of irregular curve. Figure 31 f • 0 U1: (20,'7)(51.5) • 49.6 poises (28) 112 u 2 • (38 7)(51.6) • 55.0 poises 42 Mc,• (2)(49.6-55.0) • -13.6 dynes/om 2 • 1n'(422) (28~) Figure 32 - f • 0 U1 • (2~5)(51.5) • 53.5 poises (28) u 2 = (35/5)(51.5) • 49.0 (42) M = (2)(53.5-49.0) • 11.2 dynes/cm 2 • - ln (422) (2s'2) Figure 33 f • 0 u 1 = (21 2)(51.6) • 42.4 poises 28 U2 = (36/2)(51.5) = 45.4 poises (42) Mb• (2)(42.4-45.5) = -7.65 dynes/cm 2 • ln (42 2 ) (28°2) Figure 12 f : 0 U1 • (23 3)(51.5) = 47.8 poises 28 M • (2)(47.8-49.0) = -3.0 dynes/cm2. ln (42 2 ) (28°2) 113 Figure 34 - f • 0 U1 • (25f3)(51.5) = 51.5 poises (28) U2 = (41 3)(51.5) • 64.0 poises 42 Mb• (2)(51.5-64.0) • -6.2 dynes/cm2. ln (422) (~ Figure 35 Too irregular to calculate reliably. Figure 36 r = o U1 • (25/2)(51.5) = 49.6 poises (28) u 2 • (42/2)(51.6) = 54.0 poises (42) Mb• (2)(49.6-54.0) • -10.9 dynes/cm 2 • ln (422) _ , (282) Figure 37 f • 0 U1 • (26 5)(51.5) • 57.0 poises 8 Mb• (2)(57.0-55.2) • 4.6 dynes/cm 2 • ln (422) (28~) 114 Figure 38 t : (3)(2.l)(lo-2)(0.59)(674) a 25 dynes/om2. Since (2.1)(10-2)(0.69)(674) • 8.34 then r • ( 3) ( a. 34) == 2 5 U1 • (26~)(51.5) = 40.5 poises (28) Uz = (44-3)(61.5) • 50.3 poises (42) ~ c. (2)(40.6-S0.3) ;; -24.4 d:ynes/om2. ln {422) <2a 2 ) Figure 14 t a (16)(8.34) • 134 d.ynes/crrl-. U2 • (47•16)(51.6) • 36 poises (42) Figura 15 r c (15)(8.34) • 125 d.ynes/om2. U1 • (37•16)(61.5) c 40.5 poises {28) U2 a (50-16)(51.5) = 46.2 poises (39) Mb• (2)(40.5-46.2) • -17.2 dynas/cm2. ln (39 2 ) (282) Figure 39 r - (10.5)(8.34} = 87.5 dynes/c~. 115 Figure 40 r • (21)(8.34) • 175 dynes/cm2. u = 1 (32.5-21)(51.5) • 21.2 poises (28) U2 • (46-21)(51.5) = 30.6 poises (42) Mb• (2)(21.2-30.6) • -23.2 dynes/cm 2 • ln (422) (2a 2 ) Figure 41 f = (16)(8.34) • 134 dynes/cm 2 • U1 • (33-16)(51.5) • 31.3 poises (28) U2 = (46-16)(51.5) = 36.8 poises (42) ~ = (2)(31.3-36.8) • -13.7 dynes/om 2 • ln (422) (282) Figure 42 r = (23)(8.34) • 192 dynes/cm 2 • U2 = (50-23)(51.5) = 33.1 poises (42) Figure 17 r = (10)(8.34) • 83.4 dynes/cm 2 • u = 1 (25.6-10)(51.5) = 28.5 poises {28) U2 = (31-10)(51.5) • 25.8 poises (42) M • (2)(28.5-25.5) • 6.66 dynes/cm 2 • ln (42 2 ) (282) 116 Figure 43 t = (16.5)(8.34) = 138 dynes/cm 2 • u 1 = (28-16.5)(51.5) • 21.2 poises (28) u 2 = (Sl-16.5)(51.5) • 17.8 poises (42) M = (2)(21.2-17.8) • 8.4 dynes/cm 2 • ln (42 2 ) (28 2 ) Figure 44 r = (11.0)(8.34) • 92 dynes/cm 2 • U1 • (26-11)(51.5) • 27.6 poises (28) • U2 = (30-11.0)(51.5) • 23.3 poises (42) M • (2)(27.6-23.3) • 10.6 dynes/cm2. ln (422) (2a2) Figure 45 f = (15)(8.34) • 125 dynes/cm 2 • u 1 = (27.5-15)(61.5) • 23 poises (28) U2 • (31.16)(51.5) • 19.6 poises (42) M • (2)(23-19.S) = 8.7 dynes/cm2. ln (42 2 ) (2a2) 117 Figure 46 f • (16.5)(8.34) • 130 dynes/cm 2 • U1 • (33-15)(51.5) • 32.3 poises (2a) U2 • (35-16.5)(51.5) = 23.9 poises (42) M = (2)(32.2-23.9) = 20.3 dynes/cm2. ln (422) (282) Figure 47 t • (17.5)(8.34) • 146 dynes/cm 2 • u 1 • (36-17.6)(51.6) • 32.2 poises (28) u 2 • (38-17.5)(51.5) = 25.2 poises (42) M • (2)(32.2-25.2) • 17.4 dynes/cm2. in (422) (28 2 ) Figure 19 t • (5)(2.1)(10-2)(0.59)(4334) • 268 dynes/cm 2 • Since (2.1)(10-2)(0.69)(4334) • 63.5 then f • (5)(53.5) • 268 dynes/cm2. U1 = (8.25-5)(9.55)(13.58)(10- 3 )(4334)(0.59): 38.5 poises ·-··· (28)' Since (9.55)(13.56)(10- 3 )(4334){0.59) • 332 then U1 = (8.25-5)(332) • 38.5 poises (28) U2 • (9.5-5)(332) • 35.5 poises (42) M • (2)(38.5-35.5) • 7.16 dynes/om 2 • ln (422) (2a2) 118 Figure 48 Not calculated due to curve irregularities. Figure 49 f • (25)(53.5) • 1340 dynes/cm 2 • U1 • (30-24)(332) • !1.2 poises (28) u 2 = (33-24)(332) = 71.2 poises {42) M • 0 Figure 50 r • r • Figure 22 t • (24)(63.5) • 1315 dynes/cm 2 • (30-24.5)(332) • 65.2 poises (28) (S:5-24.5)(332) (42) (2)(65.2-67 .. 2) ln °(42 2 )- (282) • 67.2 poises • -4.9 dynes/cm 2 • (20.5)(53.5) = 1100 dynes/cm 2 • (30-20.5)(332) • 75.0 poises (42) (15)(53.6) • 804 dynes/cm 2 • (19-15)(332) • 47.5 poises (28) U2 • (20-15)(332) • 41.5 poises (40) M = (2)(47.5-41.5) • 14.8 cynes/om 2 • 1n (402) (282) 119 Figure 61 r = (19)(53.5) • 1020 dynes/cm 2 • u 2 • {28-19)(332) = 71.0 poises {42) U1 • 71.0 poises M • 0 Figure 5~ f = (22)(63.5) • 1180 dynes/cm 2 • J4 • 0 Figure 23 f • (28)(53.5) • 1500 dynes/cm2. M • Negative Figure 53 f = (26)(53.5) • 1400 dynes/om2. M • Negative 120 121 CONSISTE~CY CURVE DATA FIGURE 9 FIGURE 29 FIGURE 30 FIGURE 31 RPM UP DOVfN UP DOWN UP DOWN UP DOWN 12 10 7 10 7 13 8 10 9 14 13 9 10 9 13 9 12 10 19 15 13 13 15 17 11 13 14 24 19 18 17 18 19 17 16 17 28 22 22 20· 24 22 20 17 23 32 26 27 27 27 24 24 25 28 36 29 29 29 Sl 27 27 29 32 40 32 34 33 36 30 33 32 36 42 36 38 34 38 FIGURE 32 FIGURE 33 FIGURE 12 FIG URE 34 12 13 9 11 9 12 9 15 10 14 15 11 12 11 14 11 17 12 19 17 13 16 15 16 16 20 16 24 20 18 19 19 20 20 21 20 28 24 22 21 22 23 26 25 26 32 25 26 24 25 25 30 27 30 36 30 30 27 30 27 33 30 35 40 33 34 32 34 32 36 35 39 42 35 35 37 41 FIGURE 36 FIGURE 36 FIGURE 37 FIGURE 38 12 14 13 16 12 17 12 17 14 14 17 17 17 15 17 13 18 17 19 21 23 19 19 20 18 20 22 24 24 29 22 25 24 21 22 26 28 27 35 25 31 26 26 24 30 32 30 38 29 35 28 30 31 36 36 36 40 33 39 30 35 35 38 40 38 42 38 42 86 39 39 43 42 45 42 40.' 44 122 FIGURE 14 FIGURE 39 FIG URE 40 FIGURE 41 RPM UP DOWN UP DOWN UP DOWN UP DOWN 12 25 19 14 15 17 19 21 18 14 25 22 15 16 19 23 22 22 19 26 29 16 19 24 30 24 29 24 28 32 20 22 27 34 30 33 28 33 34 21 22 30 38 31 37 32 41 38 25 25 36 40 35 38 36 45 40 31 27 40 42 41 40 40 47 44 31 28 45 44 44 44 42 47 32 46 46 FIGURE 42 FIGURE 15 FIGURE 17 FIGURE 43 12 30 28 30 23 18 15 17 18 14 30 30 30 26 20 17 20 19 19 32 35 31 33 22 20 23 23 24 34 37 34 38 25 22 24 25 28 39 40 37 42 25 23 27 28 32 47 43 43 46 27 25 29 27 36 49 45 48 48 29 26 30 29 40 50 46 61 50 30 28 31 30 42 50 53 31 31 FIGURE 44 FIGURE 45 FIGURE 46 FIG URE 47 12 21 15 22 17 25 18 29 20 14 21 16 24 19 28 20 31 22 19 23 19 25 22 30 23 32 24 24 24 21 27 23 32 25 34 26 28 26 23 27 24 33 26 36 27 32 27 25 29 26 34 28 36 29 36 28 26 29 27 34 28 36 31 40 30 27 30 28 35 31 38 34 42 31 31 34 38 123 Fiu-tJRE 19 FIG URE 20 FI G URE 48 FIGURE 49 RPM UP DOWN UP DOWN UP DO iN UP DOWN 12 7 6 26 23 19 27 27 27 14 7 s½ 25 24 20 27 27 28 19 8 7 26 25 22 28 28 29 24 8 7½ 26 26 22 29 29 30 28 8 8 27 27 23½ 30 30 31 32 9 8 28 28 25 30 31 32 36 9 a½ 29 28 27 30 31 32 40 9 9 30 30 28 30 32 32 42 ~ 30 29 33 FIGURE 50 FIGURE 22 FIGURE 23 FIGURE 51 12 27 26 17 16 25 25 23 22 14 27 27 18 16 25 25 23 22 19 28 28 18 17 25 27 24 24 24 28 29 19 18 25 28 24 24 28 29 30 19 18 26 28 25 25 32 30 31 19 19 26 28 26 25 36 31 32 19 19 27 28 26 26 40 32 32 20 19 29 28 27 27 42 33 21 29 28 FIGURE 52 FIG URE 53 12 23 19 23 23 14 22 20 23 23 19 22 21 23 24 24 22 21 23 25 28 22 22 24 26 32 22 22 25 26 36 23 23 25 26 40 24 24 26 26 42 25 27 124 M ISCELLANEOUS OffiERVATIONS During the preliminary runs it was noted that the viscometer had a pronounced wobble in the suspension assembly during testing. This was eliminated by inserting a soft brass collar in the center bracing point. The collar had 0.002 inches clearance between itself and the assembly and was kept lubricated with oil. On a future instrument this ooJlar should be replaced with a precisiLn bearing. The speed range of the instrwnent was not wide enough. A future instrument should have a range from Oto 200 rpm.

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Asset Metadata

Creator McKenzie, Russell G. (author)

Core Title A rheological study of an alkyl aryl sulfonate slurry

School School of Engineering

Degree Master of Science

Degree Program Chemical Engineering

Degree Conferral Date 1958-06

Publication Date 01/01/1958

Defense Date 01/01/1958

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

Tag OAI-PMH Harvest

Format theses (aat)

Language English

Contributor Digitized from microfilm by the USC Digital Library in 2023 (provenance)

Advisor Robert, Charles G. (committee chair), Benson, C. M. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-oUC113172848

Unique identifier UC113172848

Identifier Ch '58 M157 (call number),etd-McKenzieRussell-1958.pdf (filename)

Legacy Identifier etd-McKenzieRussell-1958

Document Type Thesis

Format theses (aat)

Rights McKenzie, Russell G.

Internet Media Type application/pdf

Type texts

Source 20230616-usctheses-microfilm-box8 (batch), University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

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