University of Southern California Dissertations and Theses

Absorption And Scattering Of Thermal Radiation By A Cloud Of Small Particles

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Absorption And Scattering Of Thermal Radiation By A Cloud Of Small Particles

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Content This dissertation has been microfilmed exactly as received 6 7 -1 0 ,7 7 1 NAGY, Jr., Anthony Robert, 1932- ABSORPTION AND SCATTERING OF THERMAL RADIATION BY A CLOUD OF SMALL PARTICLES. U niversity of Southern California, Ph.D., 1967 Engineering, chemical University Microfilms, Inc., Ann Arbor, Michigan ABSORPTION AND SCATTERING O F T H E R M A L RADIATION BY A C LO U D OF SM ALL PARTICLES by Anthony R obert Nagy, J r . A D is s e r t a t io n P resen ted to the FACULTY O F THE G RADUATE SC H O O L UNIVERSITY O F SOUTHERN CALIFORNIA In P a r t ia l F u lfillm e n t o f th e R equirem ents f o r th e D egree DO CTO R OF PHILOSOPHY (Chem ical E n g in eerin g ) June 1967 UNIVERSITY O F SO U TH ERN CALIFORNIA . THE GRADUATE SCHOOL UNIVERSITY PARK LOS ANGELES, CALIFORNIA 9 0 0 0 7 This dissertation, written by under the direction of h\j&....Dissertation Com mittee, and approved by all its members, has been presented to and accepted by the Graduate School, in partial fulfillment of requirements for the degree of D O C T O R OF P H I L O S O P H Y Dean D ate June..l9.67 DISSERTATION COMMITTEE Chairman To My W ife and C h ild ren ACKNOWLEDGMENTS The author would l i k e to ex p ress h is in d e b ted n ess to the fo llo w in g p erso n s and o r g a n iz a tio n f o r t h e ir a id in t h is work* Dr* J . M. L en oir - f o r h i s i n t e r e s t , encouragem ent, and guidance d uring th e co u rse o f th e r e se a r c h . The members o f th e R esearch Comm ittee: Dr. C. J . R ebert and P r o f. R. L . Mannes f o r t h e ir c o o p er a tio n and c o n tr ib u tio n s . Mr. C. W. Brandenburg - f o r h is a id in programming the scheme fo r d a ta r e d u c tio n . Mrs. C h a r lo tte Blanchard - f o r p rep a ra tio n o f th e rough d r a ft o f th e m a n u scrip t. Mrs. Ruth Toyama - f o r h er a s s is ta n c e in prepara t io n o f th e f i n a l m anuscript and o p e r a tio n o f th e e x p e r i m ental equipm ent. The Marquardt C orp oration - f o r t h e ir tim e and f in a n c ia l support in th e form o f t u it io n co v era g e. 11 TABLE OP CONTENTS Page A C K N O W L E D G M E N T S ...................................................................... I LIST OP FIGURES .......................................................... V LIST OP TABLES ........................................................................ x NOMENCLATURE ..................................................................x i i I . INTRODUCTION .............................................................................. 1 I I . TH EO R Y O P LIGHT SCATTERING............................................ 3 A. S in g le S c a tte r in g ...................................................... 3 B. M u ltip le S c a tte r in g and th e E quation o f T ra n sfer ............................... 9 I I I . DESCRIPTION O P THE EQUIPMENT.......................... 15 A. E lu t r ia t o r ....................................................................... 15 B. M icroscope ........................ 18 € • In fr a r e d S p ectrom eter .......................................... 18 D. T e st C e ll ............................... 22 E. B alance ............................................ 2ij. IV. SELECTION O P PARTICLES AND SUSPENDING MEDIA . . 26 V. EXPERIMENTAL PROCEDURE .................................................... 28 V I. EXPERIMENTAL RESULTS ......................................................... 35 A. E lu t r ia t io n R ates ....................................................... 35 B. S iz e M easurements ............................................. 35 G. C e ll Blank M easurements ......................................... l|.l D. T ran sm ission o f th e C o llim a ted B e a m ij.6 iii iv Page V I. ( C o n 't.) E . T ran sm ission o f the D iffu s e Beam . . ................ £0 V II. CORRELATION O F RESULTS . . ................................................. 88 A . The C o llim a ted T r a n s m is s io n ................................ 88 B. The D iffu s e T ran sm ission ..................... 98 V I I I . SU M M A R Y .......................................................................................... 12fj IX . REFERENCES ......................................................................................130 APPENDICES .......................................................................................136 A . F in e P a r t ic le T echnology ...........................................137 B. D e r iv a tio n o f th e Two-Flux Model fo r D iffu s e R a d ia tio n .................................................... ll\b C. D e r iv a tio n o f T ran sm ission Param eters fo r the Sample C e ll .............. IS K D . F ortran Computer Program fo r the D e te r m in ation o f Back S c a tte r in g and A b sorp tion C ross S e c tio n s ..................... 156 LIST OP FIGURES F igu re Page 1 Mie E x tin c tio n C o e f f ic ie n t s .......................................... 8 2 E lu t r ia t o r System ........................................................... 17 3 Beckman IR -2 S p ectrom eter f o r In fra red R egion . 19 Ij. Schem atic Drawing o f T est C e l l ................................... 25 5a Measured S iz e D is t r ib u tio n f o r Aluminum O xide, 5-7*5 M icron Cut .................................................... 38 5b Measured S iz e D is t r ib u tio n f o r Aluminum O xide, 1 0 -1 2 .5 M icron Cut ....................................................... 39 6 Measured S iz e D is t r ib u tio n f o r G lass B eads, 1 0 -1 2 .5 M icron Cut ....................................................... lj.0 7 T ran sm ission Through S erv o fra x W indow ................... iflj. 8a T ran sm ission o f Aluminum Oxide P a r t ic le s in Carbon T e tr a c h lo r id e , A0 = 2 . 0 ^ . . . . . . . . 51 8b T ran sm ission o f Aluminum Oxide P a r t ic le s in Carbon T e tr a c h lo r id e , Ao = 2 . 5 / ^ ................. 5 > 2 8c T ran sm ission o f Aluminum O xide P a r t ic le s in Carbon T e tr a c h lo r id e , Ac = 3 * 0 / ^ ................. 53 8d T ran sm ission o f Aluminum Oxide P a r t ic le s in Carbon T e tr a c h lo r id e , Ao = 3*5/ * ■ ............ 8e T ran sm ission o f Aluminum Oxide P a r t ic le s in Carbon T e tr a c h lo r id e , A o = lj..Oy t l 55 v vi F ig u re Page 8 f T ran sm ission o f Aluminum Oxide P a r t ic le s in Carbon T e tr a c h lo r id e , A o = lj.*5 j i t ................... 56 8g T ran sm ission o f Aluminum Oxide P a r t ic le s in Carbon T e tr a c h lo r id e , Ao = £ . 0 ................ 57 8h T ran sm ission o f Aluminum Oxide P a r t ic le s in Carbon T e tr a c h lo r id e , A o = 6 . 0 / - . . . . . . . . 58 8 i T ransm ission o f Aluminum Oxide P a r t ic le s in Carbon T e tr a c h lo r id e , Ao = 7 * 7 /^ . . . . . . . . 59 8j T ran sm ission o f Aluminum Oxide P a r t ic le s in Carbon T e tr a c h lo r id e , Ao = 9*0 ^ .................... 60 9a T ran sm ission o f Aluminum Oxide P a r t ic le s in Carbon D is u lp h id e , Ao = 2 , 0 / A ............................ 61 9b T ran sm ission o f Aluminum Oxide P a r t ic le s in Carbon D is u lp h id e , Ao = 2 ,5^ ...................... 62 9c T ran sm ission o f Aluminum Oxide P a r t ic le s in Carbon D is u lp h id e , A o = 3 . 0 /U ............... 63 9d T ran sm ission o f Aluminum Oxide P a r t ic le s in Carbon D is u lp h id e , A o = 3 . 5 ....................... 6I 4 . 9e T ran sm ission o f Aluminum Oxide P a r t ic le s in Carbon D isu lp h id e , A o = l j . . O .............. 65 9 f T ran sm ission o f Aluminum Oxide P a r t ic le s in Carbon D is u lp h id e , Ao = i j . * 5 ...................... 66 9g T ran sm ission o f Aluminum Oxide P a r t ic le s in Carbon D isu lp h id e , Ao = 5 * 5 / * - ................. 67 v i i F ig u re Page 9h Transm ission, o f Aluminum Oxide P a r t ic le s in Oarbon D is u lp h id e , Ao = 6 * 0 ^ ............ 68 9 i T ran sm ission o f Aluminum Oxide P a r t ic le s in Carbon D isu lp h id e , Ao = 8 . 0^ ................. 69 9 j T ran sm ission o f Aluminum Oxide P a r t ic le s in Carbon D isu lp h id e , A o = 8 , $ y U .............. 70 9k T ransm ission o f Aluminum Oxide P a r t ic le s in Carbon D i s u lp h id e , A o = 9«0 71 91 T ransm ission o f Aluminum Oxide P a r t ic le s in Carbon D isu lp h id e , Ao = 9 * 5 / ^ .... 72' 9m T ran sm ission o f Aluminum Oxide P a r t ic le s in Carbon D isu lp h id e , Ao = 1 0 .0 y tC ............... 73 9n T ran sm ission o f Aluminum Oxide P a r t ic le s in Carbon D isu lp h id e , Ao = 1 0 .$ y U .............. 7if 9o T ran sm ission o f Aluminum Oxide P a r t ic le s in Carbon D isu lp h id e , Ao = 1 1 . 0 ............... 75 10a T ran sm ission o f G lass Beads in Carbon T e tr a c h lo r id e , Ao = 2 . 0 / ^ ................ 76 10b T ran sm ission o f G lass Beads in Carbon T e tr a c h lo r id e , Ao = 2 * 5 / ^ ..................... 77 10c T ran sm ission o f G lass Beads in Carbon T e tr a c h lo r id e , Ao = 3 * 0 /# , 78 lOd T ran sm ission o f G lass Beads in Carbon T e tr a c h lo r id e , A o = If.OyU, i f . 5 / / £ ................... 79 viii Figure Page lOe T ran sm ission o f G la ss Beads in Carbon T etrach loride, Ao = 5>.C, 6 .0 /A. ................ 80 lO f T ran sm ission o f G lass Beads in Carbon T etrachloride, Ao = 7 *1 / A ................................. 81 lOg T ran sm ission o f G lass Beads in Carbon T e tr a c h lo r id e , Ao =9*0 /A. ............................... 82 11a Mie E x tin c tio n C o e f f ic ie n t fo r Aluminum Oxide P a r t ic le s .......................... 93 l i b Mie E x tin c tio n C o e f f ic ie n t fo r G la ss Beads . 97 12 Back S c a tte r in g C ross S e c tio n o f Aluminum Oxide P a r t ic le s .................................................... 103 13 A b so rp tio n C ross S e c tio n fo r Aluminum Oxide P a r t ic le s . . . . . . . . ................ . « ,< > ............ 105> li}. A b so rp tio n and Back S c a t te r in g C ross S e c tio n s fo r G la ss Beads .................................................... 109 l£ a A b s o r p tiv ity o f a Cloud o f Aluminum Oxide P a r t ic le s W ith a D iam eter o f 1 2 .2 M icrons in Carbon T e tr a c h lo r id e ....................................... l l £ l£ b A b s o r p tiv ity o f a Cloud o f Aluminum Oxide P a r t ic le s w ith a D iam eter o f 6 .2 8 M icrons in Carbon T e tr a c h lo r id e .................................. I l6 i 16 A b s o r p tiv ity o f a Cloud o f Aluminum Oxide P a r t ic le s W ith a D iam eter o f 1 2 .2 M icrons in Carbon D isu lp h ld e ..................... 117 ix F igu re Page 17 A b s o r p tiv ity o f a Cloud o f G lass Beads W ith a D iam eter o f 7*75 M icrons in Carbon T e tr a c h lo r id e ................................................................. l i d 18 A b s o r p tiv ity o f V arious P a r t ic le C louds f o r a Wave Length o f 6 ,0 M icrons .............................. .. 122 LIST OP TABLES T able Page l a R ates o f E lu t r ia t io n - Aluminum Oxide .................. 36 lb R ates o f E lu t r ia t io n - G lass Beads .......................... 37 I I T ransm ission o f th e S erv o fra x W indow ..................... ij.3 H I T ran sm ission and R e f le c t io n o f Suspending M e d ia ........................ .............................................................. IVa T ran sm ission o f Aluminum O xide P a r t ic le s in Carbon T e tr a c h lo r id e W ith a C o llim a ted Source • • • • . . ............................ i|7 IVb T ran sm ission o f Aluminum Oxide P a r t ic le s in Carbon D isu lp h id e With a C o llim a ted Source lf.8 Va T ran sm ission o f Aluminum Oxide P a r t ic le s in Carbon T e tr a c h lo r id e W ith a D iffu s e Source - d = 1 2 , M icrons .......................................................... 83 Vb T ran sm ission o f Aluminum Oxide P a r t ic le s in Carbon T e tr a c h lo r id e W ith a D iffu s e Source - d ~ 6 .2 8 M icrons ................................. ... 8I 4 . VI T ransm ission o f Aluminum Oxide P a r t ic le s in Carbon D isu lp h id e W ith a D iffu s e Source - d ■ 12.21 M icrons ........................................ 8£ V II T ran sm ission o f G lass Beads in Carbon T e tr a c h lo r id e W ith a D iffu s e Source - d = 7«75> M icrons ..................... 86 x Table Page V i l l a C ross S e c tio n C o e f f ic ie n t s f o r Aluminum Oxide i P a r t ic le s in Carbon T e tr a c h lo r id e - j i d = 1 2 .2 M icrons .............................................................. 90 J VTIIb C ross S e c tio n C o e f f ic ie n t s f o r Aluminum Oxide | j P a r t ic le s in Carbon T e tr a c h lo r id e - 1 d = 6 .2 8 M icrons .............................................................. 91 IX C ross S e c tio n C o e f f ic ie n t s fo r Aluminum Oxide P a r t ic le s in Carbon D isu lp h id e ~ d - 1 2 .2 M icrons .......................................................... 92 X C ross S e c tio n C o e f f ic ie n t s fo r G lass Beads in Carbon T e tr a c h lo r id e - d = 7.75 M icrons •• 96 X Ia A b s o r p tiv ity o f Aluminum Oxide P a r t ic le s in Carbon T e t r a c h lo r i d e ................................... 112 X lb A b s o r p tiv ity o f Aluminum Oxide P a r t ic le s in Carbon D isu lp h id e • . . • • ............................................ 113 X II A b s o r p tiv ity o f G lass Beads in Carbon T e t r a c h lo r i d e ..................... 111]. N O M EN C LA TU R E 2 m . T o ta l a b so r p tio n c r o ss s e c t io n , ^ m /n + cm A C ross s e c t io n a l area o f sam ple . c e l l , cm2 b Back s c a t t e r in g c r o ss s e c t io n , cm2 B F r a c tio n o f back s c a t t e r in g , d im e n s io n le ss d D iam eter o f p a r t i c l e , /*• , cm D ” InT, d im e n sio n le ss f S c a tte r in g fu n c tio n , d im e n sio n le ss i I n t e n s it y o f forw ard r a y , e n e r g y /s te r a d , 1 I n t e n s it y , e n e r g y /ste r a d 3 I n t e n s it y o f backward r a y , e n e r g y /s t e r a d ,^ Jq,J £ B e s s e l f u n c t io n s , d im e n s io n le ss k Number o f d a ta p o in t s , d im e n sio n le ss L L ength o f sam ple c e l l , cm m Param eter (a 2 + 2 ab )^ , cm2 n P o p u la tio n d e n s ity o f c lo u d , num ber/co. R e fr a c tiv e in d e x , d im e n sio n le ss p n Legendre p o ly n o m ia ls, d im e n sio n le ss Qa Mie a b so rp tio n c o e f f i c i e n t , d im e n s io n le ss Qs Mie s c a tt e r in g c o e f f i c i e n t , d im e n s io n le ss Qe Mie e x t in c t io n c o e f f i c i e n t , d im e n sio n le ss r R e f l e c t i v i t y o f clo u d , d im e n s io n le ss R C o rr e ctio n fa c t o r f o r forw ard s c a t t e r in g , d im e n sio n le ss xii R e f l e c t i v i t y o f c e l l window, d im e n sio n le ss T r a n s m is s iv ity , d im e n s io n le ss V e lo c it y , f t / s e c W eight o f p a r t i c l e s , grams S c a tte r in g param eter t td/A » d im e n sio n le ss A b s o r p tiv ity o f c lo u d , d im e n sio n le ss A b sorp tion c o e f f i c i e n t o f su sp en d in g medium, cm "*1 - Azimuth a n g le , ra d ia n s Wave le n g th o f l i g h t , m icrons Wave le n g th o f l i g h t in a vacuum, m icrons C osin e o f th e azim uth a n g le , d im e n sio n le ss V is c o s it y , h b /P t-s e c Phase la g 2 T f d/A o 1 “p - “m l > ra d ia n s D e n s ity , gm /cc. S u rfa ce r e f l e c t i v i t y , d im e n sio n le ss o A b sorp tion c r o s s s e c t io n , cur* E x tin c tio n c r o ss s e c t io n , cm^ S c a tte r in g c r o ss s e c t io n , cm^ O p tic a l d ep th , d im e n sio n le ss T r a n s m is siv ity o f su sp en d in g medium, d im ension l e s s H a lf a n g le subtended by m onochrometer s l i t from p a r t i c l e , ra d ia n s S u b sc r ip ts bb B lack body e E xperim ental m Suspending medium p P a r t ic le 1 Front c e l l window 2 Rear c e l l window I. INTRODUCTION U n t il r e c e n t ly th e re h as been a g e n e r a l la c k o f In t e r e s t in the h e a t tr a n s fe r p r o p e r tie s o f media which ab sorb as w e ll as s c a t t e r r a d ia tiv e en er g y . Some c l a s s i c a l works in the lit e r a t u r e have d esc r ib e d th e e m is s iv it y o f sub-m icron carbon p a r t ic le s th a t occur in in d u s t r ia l fu r n a c e s . However, th e se sm all p a r t ic le s are known to absorb b u t n o t s c a t t e r ra d ia n t en erg y . R ecen t developm ents In tech n o lo g y have now g en era ted an I n t e r e s t in the more com p le x problem , th a t o f a b so rp tio n p lu s s c a t t e r in g . The r a d ia n t a n a ly s is o f a clou d o f m etal o x id e p a r t ic le s produced in a r o c k e t m otor i s one exam ple o f th e problem now b ein g i n v e s it g a t e d . The a n a ly s is o f h e a t tr a n s fe r in an e n c lo su r e con ta in in g an a b so rb in g and s c a t t e r in g medium, w hether s t a tio n a r y or in m otion , i s one o f th e m ost com plex e n g in e e r - p roblem s. The g en er a l c a s e , in w hich th ere i s m otion , in v o lv e s a system whose c o n se r v a tio n eq u a tio n s are very c l o s e l y co u p le d . The r a d ia tiv e f lu x i s a f f e c t e d n o t o n ly by geom etry, b u t a ls o by c o n v e c tiv e and co n d u ctiv e en ergy tr a n s p o r t. The p r e se n t work was r e s t r ic t e d to th e problem in w hich th e re i s no m o tion . The geom etry co n sid ered was one 1 2 o f a p la n e - p a r a lle l atm osphere. T h is atm osphere c o n s is te d o f many sm all s p h e r ic a l p a r t i c l e s , which were p a r t i a l ly tr a n sp a r e n t, suspended in a tra n sp a r en t medium. E x p er i ments were conducted to g iv e d a ta f o r th e c a lc u la t io n o f the a b s o r p tiv ity o f the atm osphere. S in c e th e re was no g en era l s o lu t io n fo r even t h is r e s t r ic t e d c a s e , a sem i-em p i r i c a l method was used to c o r r e la te the r e s u l t s . The ex p erim en ta l ta sk s in v o lv e d the c l a s s i f i c a t i o n o f the s p h e r ic a l p a r t ic le s in to u n ifo r m ly -s iz e d f r a c t io n s so th a t th e v a r ia tio n o f p a r t ic le s iz e on th e r e s u lt s cou ld be d eterm in ed . Once se p a r a te d , the p a r t ic le s iz e s were m easured. V ariou s clo u d s were prepared by u sin g d if f e r e n t s i z e s and c o n c e n tr a tio n s . In fr a r e d tr a n sm issio n was mea sured w ith b oth a c o llim a te d and a d if f u s e sou rce over a wave le n g th range o f 2 to 11 m icr o n s. The s c a t t e r in g phenomenon was c o r r e la te d by a p p ly in g the th eory o f p h y s ic a l o p t i c s . The f i n a l r e s u l t s in d ic a te d the c o n tr ib u tio n o f the v a rio u s param eters such as diam e t e r , wave le n g th , and r e f r a c t iv e in d ex to the d eterm in a tio n o f th e a b s o r p tiv ity o f a clou d o f sm a ll p a r t i c l e s . I t i s hoped th a t t h is work w i l l a id in the u n d erstan d in g o f r a d i an t h e a t tr a n s fe r in an a b so rb in g and s c a t t e r in g atm os phere • I I . TH EO RY OF LIGHT SCATTERING A. S in g le S c a tte r in g The b a s ic th e o ry o f l i g h t s c a t t e r in g was o r i g in a l ly form u lated by Mie ( 1 ) . In h is a n a ly t ic a l m odel, he con sid e r e d th e in t e r a c t io n betw een a p la n e e le c tr o m a g n e tic wave s t r ik in g a s in g le sphere o f a r b itr a r y d ia m eter. The s o lu t io n o f th e problem was a v ery com plex s e r ie s o f sp h er i c a l B e s s e l fu n c tio n s and Legendre p o ly n o m ia ls. A t la r g e d is ta n c e s from th e sp h ere, th e s c a tte r e d fie lc T C o u ld be ex p r e sse d a s a s e r i e s o f Legendre p o ly n o m ia ls. The e f f e c t o f s c a t t e r in g was to reduce th e i n t e n s i t y o f th e p la n e w ave. W ithin a d il u t e clo u d o f p a r t i c l e s , i t cou ld be assumed th a t each p a r t i c l e was in d ep en d en t o f th e o th e r . In t h is fa s h io n th e Mie th e o ry co u ld be a p p lied to each p a r t ic le s e p a r a te ly . In a d d itio n to s c a t t e r in g , th e o th er cau se o f a t te n u a tio n o f th e p la n e wave was by a b so r p tio n . By t h is p ro ce ss th e wave energy was con verted in to in te r n a l energy o f th e p a r t i c l e . The en ergy may th en be em itted a t a num ber o f d if f e r e n t wave le n g t h s . The t o t a l a tte n u a tio n o f th e p lan e wave from s c a t t e r in g and a b so rp tio n i s c a lle d e x t in c t io n . I t i s tak en t© be p r o p o r tio n a l to th e e x t in c t io n c r o ss s e c t io n o f th e p a r t i c l e , crQ, th e number o f p a r t ic le s p er u n it volum e, n , 3 the geom etric p ath le n g th , dL, and the i n t e n s i t y , I , The d i f f e r e n t i a l eq u a tio n r e la t in g th ese i s d i = - crenIdL (1 ) I n te g r a tin g = exp( - C T e nL) (2 ) For a c e l l o f le n g th L, l / l 0 i s the tr a n s m is s io n , or T = e x p (- OenL) (3 ) The e x t in c t io n c r o ss s e c t io n can be ex p re sse d as th e TT product o f the p r o je c te d area o f the p a r t ic le " and the e x t in c t io n c o e f f i c i e n t , Qe . T h is e x t in c t io n c o e f f i c i e n t can fu r th e r be broken down in to two com ponents, the s c a t te r in g c o e f f i c i e n t , Qs , and the a b so rp tio n c o e f f i c i e n t , Qa , where Qe = Qs + Qa» From o rd in a ry geom etric o p t ic s , th e l o g i c a l assump tio n fo r the e x t in c t io n c o e f f i c i e n t would be 1 .0 . T h is can e a s i l y be seen by assum ing th a t the sp h ere would remove th a t f r a c t io n o f th e l i g h t beam sw ept o u t by th e p r o je c te d a r e a . However, when th e s i z e o f the sp here approaches th e wave le n g th o f l i g h t , an oth er phenomenon occurs which can be d esc r ib e d by the th eory o f d i f f r a c t i o n . P art o f the l i g h t beam which p a sse s c lo s e to the sphere i s b en t and as a r e s u lt a c ts as s c a tte r e d l i g h t . The amount o f d if f r a c t e d l i g h t i s about eq u al to th a t removed by th e p r o je c te d area o f the sp h e re . For t h is r e a so n , as th e d iam eter o f the p a r t ic le becomes la r g e r than th e wave le n g t h , th e e x t in c t io n c o e f f i c i e n t approaches 2 .0 . S in c la ir (2 ) and Van de H u lst (3 ) d isc u sse d t h i s phenomenon a t le n g t h . A number o f in v e s t ig a t o r s have o b ta in ed num erical r e s u lt s fo r th e Mie s o lu t io n . These have req u ired th e u se o f h ig h speed com puters to e v a lu a te a l l th e term s in th e con vergen t s e r i e s . The b a s ic in p u t param eters fo r s o lu t io n are th e r e la t iv e r e f r a c t iv e in d ex and the p a r t ic le s iz e param eter, x , which i s th e r a t io o f the circu m feren ce o f the p a r t ic le to th e wave le n g th o f l i g h t in th e su r rounding medium. A sh ley and Cobb (I4.) p resen ted computa tio n s o f an gu lar s c a t t e r in g in t e n s it y fo r a r e f r a c t iv e in d ex o f 1 .2 0 and v a lu e s o f x from 5«0 to 3 5 . P angonis and H e lle r (5 ) determ ined the a n g u la r s c a t t e r in g i n t e n s i t i e s fo r r e f r a c t iv e in d ic e s up to 1 .2 0 and fo r v a lu e s o f x from 3 to ifO. C lark , Chu, and C h u r c h ill (6 ) determ ined the angu l a r s c a t t e r in g i n t e n s it y re p r ese n ted by u s in g th e eq u a tio n OO f(0) ~ I + 1Prr pn (c o s 0) (l\.) o r ig in a lly proposed by H a rtel (7)> fo r a r e f r a c t iv e in d ex o f 1*33 fo r n on -ab sorb in g p a r t i c l e s . The p a r t ic le s iz e param eter, x , was extended fo r v a lu e s from 1 to ij.0 . For th e sm a lle r v a lu e s o f x o n ly a sm a ll number o f term s in the 6 s e r i e s was needed to o b ta in r e a so n a b le a c c u r a cy . However, as th e v a lu e o f x in c r e a s e d , th e s e r ie s converged a t a much slo w er r a t e and more term s were n eed ed . These s c a t t e r in g fu n c tio n s r e s u lte d i n v er y com plex p a tte r n s w ith numerous maxima and minima f o r v a r io u s v a lu e s o f th e azim uth an gle 0 . In th e range o f la r g e r p a r t i c l e s f o r a p a r t ic le s i z e p aram eter, x , o f 20 to 1+00, Gumprecht and S lie p c e v ic h (8) d eterm ined th e s c a t t e r in g c o e f f i c i e n t f o r a number o f r e f r a c t iv e in d i c e s . B o ll, Gumprecht and S lie p c e v ic h (9) determ ined Mie c o e f f i c i e n t s f o r p a r t i c l e s whose r e f r a c t iv e in d ex was l e s s than u n ity and fo r th o se w ith v a lu e s ap p roach in g i n f i n i t y . H odkinson (10) p r e se n te d a l i s t o f r e c e n t ly pub lis h e d t h e o r e t ic a l com putations o f th e an gular d is t r ib u t io n o f th e s c a tte r e d i n t e n s i t y f o r medium and la r g e s iz e d s p h e r e s . Love and W heasler (11) summarized e a r l i e r l i g h t s c a t t e r in g work, e s p e c ia ll y t h a t p e r ta in in g to ex p erim en ta l i n v e s t i g a t io n s • K r a s c e lla (12) u sed th e Mie th eo ry to p r e d ic t the s c a t t e r in g and a b so r p tio n c r o ss s e c t io n s o f s p h e r ic a l p a r t i c l e s o f su b-m icron s i z e made o f carbon, s i l i c o n , alu m i num, c o b a lt , and o th e r m e ta ls . E x tin c tio n c o e f f i c i e n t s f o r carbon and tu n g ste n m easured by M arteney (13) were low er than th o se p r e d ic te d . The re a so n was a ttr ib u te d to 7 a g g lo m era tio n o f th e sm a ll p a r t i c l e s . Lanzo and R agsdale (H4 .) m easured th e tr a n sm issio n o f l i g h t through su sp en sio n s c o n s is t in g o f sub-m icron p a r t ic le s o f carbon and aluminum o x id e and concluded th a t th e a tte n u a tio n o f th e l i g h t beam was caused by a b so rp tio n r a th e r than s c a t t e r in g . I f the r e la t iv e r e f r a c t iv e in d ex o f th e sp h eres does n o t d i f f e r g r e a tly from u n ity , a more sim p le method i s a- v a ila b le when o n ly the s c a t t e r in g c o e f f i c i e n t and n ot th e an gu lar d is t r ib u t io n i s d e s ir e d . The th eo ry o f t h is ap proach h a s b een p resen ted by Van de H u lst (3) and Penndorf (13>) • T h is m ethod, in e f f e c t , n e g le c te d th e sm a ll r e f l e c t io n a t th e in te r f a c e and th e sm a ll d e v ia t io n o f th e l i g h t tr a n sm itte d through the sp h e re . The th e o r y reduced th e d eterm in a tio n o f th e e x t in c t io n c o e f f i c i e n t to one in d e pendent v a r ia b le , nam ely, th e phase la g s u ffe r e d by th e c e n tr a l r a y th a t p a ssed through th e sp h ere a lon g a f u l l 2 7 7 " d ia m eter. The phase la g in ra d ia n s I s eq u al to tim es th e o p t ic a l p ath d iffe r e n c e betw een a ra y w hich p a sse s through th e sphere alon g th e d iam eter and one w hich r e m ains in th e su sp en din g medium. T his d iff e r e n c e i s d |(n p - nm)( • Thus, th e phase la g becomes P = Inp - n m ! (S) A p lo t o f the t h e o r e t ic a l e x t in c t io n c o e f f i c i e n t w ith o u t a b so rp tio n i s g iv e n in F ig u re 1 . I t can be se e n E xtinction C o e f f ic ie n t 8, Phase Lag } p F igu re 1 . Mie E x tin c tio n C o e f fic ie n t s 9 th a t th e t h e o r e t ic a l curve e x h ib it s a number o f maxima and m inim a. The maxima in th e curve are due to an o u t - o f - phase in te r fe r e n c e o f d if f r a c t e d and tr a n sm itte d l i g h t ; th e minima are due to an in -p h a se in t e r f e r e n c e . For la r g e p, th e maxima occu r a t P - (k + 3/4)27T and th e minima a t P = ■ (k + l/lj.) 2.1T t where k i s an in t e g e r . Thus, th e maxima as w e ll as th e minima are p r e s e n t ev ery 2 7 T r a d ia n s . I f th e p a r t ic le s absorb as w e ll as s c a t t e r , th e max ima and minima w i l l ten d to fa d e o u t. T h is i s a lso tr u e i f th e p a r t ic le s are n e ith e r s p h e r ic a l nor m on od isp erse. P la s s (16) compared th e method o f Van de H u lst (3) by m achine c a lc u la tio n s o f th e e x a c t Mie s o lu t io n . He con clud ed th a t some e r r o r was in v o lv e d in com puting th e e x t in c t io n c o e f f i c i e n t f o r a r e f r a c t iv e in d e x g r e a te r than 1.33* alth ou gh th e shape o f th e curve w u ld rem ain th e sam e. However, as th e r e f r a c t iv e in d ex approaches u n ity th e method o f Van de H u lst would apply u n le s s str o n g ab s o r p tio n bands were p r e s e n t. I f t h is were th e c a s e , th e extrem a would be damped o u t. B. M u ltip le S c a tte r in g and th e E quation o f T ra n sfer The b a s ic th e o ry o f s in g le s c a t t e r in g by Mie (1) assumed th a t in a clou d or d is p e r s io n o f p a r t ic le s each p a r t ic le was so fa r ap art from i t s n eigh b or th a t th e r e was no in t e r a c t io n and th a t th e s c a t t e r in g o f one was independ en t o f s c a t t e r in g o f a l l th e o t h e r s . As th e s e p a r t ic le s 10 are brought c lo s e r to g e th e r , th e s c a t t e r in g p a tte r n o f one p a r t ic le a c ts as a r a d ia tio n so u rce w ith a m agnitude and d ir e c t io n f o r th e o th e r p a r t i c l e s . In an attem p t to ana ly z e t h is problem , two methods o f approach have appeared i n th e l i t e r a t u r e . H a r te l (7) proposed to f o llo w th e s c a t te r e d energy d is t r ib u t io n throughout a clou d o f p la n e - p a r a lle l geom etry, a cco u n tin g f o r a l l h ig h e r o rd er s c a t t e r in g . The o th e r approach was to c o n sid e r a c o n tr o l volume and to w r ite an energy b a la n ce around i t . T his method o f a n a ly s is h as been c a lle d r a d ia t iv e t r a n s f e r . T his problem o f r a d ia t iv e t r a n s fe r h as been o f in t e r e s t to a s t r o p h y s ic is t s fo r many y e a r s . Much work was done in an attem pt to e x p la in th e appearance o f a b so r p tio n and e m issio n l i n e s in s t e l l a r atm osp h eres. S ch u ster (17) was one o f th e f i r s t to fo rm u la te th e problem . Chandra sekhar (18) in h is e x c e lle n t book expanded th e g e n e r a l th eo ry w ith th e m ost advanced m ath em atical te c h n iq u e s . K ourganoff (19) complemented th e work o f Chandrasekhar, b u t r e s t r ic t e d th e problem to is o t r o p ic s c a t t e r in g in a p la n e - p a r a lle l atm osphere. V isk a n ta (20) p r e se n te d a thorough re v iew o f th e fundam entals in v o lv e d in ab sorb in g and s c a t te r in g m edia and in c lu d ed a d e r iv a tio n o f an e q u a tio n o f tr a n s fe r . The eq u a tio n was d eriv ed by ad o p tin g an E u le r ia n p o in t o f view and stu d y in g th e v a r ia tio n s in in t e n s i t y in 11 a f i e l d from p o in t to p o in t . The v a r ia tio n in in t e n s i t y o f a beam p a ssin g through an elem en ta l volume was co n sid er ed to be due to a number o f f a c t o r s . F i r s t , a d ecr ea se in in t e n s it y occurred b ecau se p a rt o f the beam was absorbed or s c a t t e r e d . Second, the in t e n s it y in c r e a se d b ecau se o f a s c a t t e r in g from o th er elem en ta l volum es in the d ir e c t io n o f the beam under c o n s id e r a tio n . T h ird , the volume through which the beam p assed cou ld have em itte d r a d ia tio n in the d ir e c t io n o f the beam. The r e s u lta n t eq u a tio n of tr a n s fe r d e sc rib ed the v a rio u s c o n tr ib u tio n s to the v a r ia tio n o f the i n t e n s i t y . For a p la n e - p a r a lle l atm osphere, Love (2 1 ) d eriv ed th e above eq u a tio n as where j i t was c o s in e o f th e azim uth an gle and T was th e le ft-^ a n d sid e re p rese n ted th e change in in t e n s i t y . The f i r s t term on the rig h t-h a n d s id e r e p r e se n te d the a tte n u a tio n due to s c a t t e r in g and a b so r p tio n . The second term re p resen ted the enhancement due to s c a t t e r in g from o th e r volum es in th e d ir e c t io n o f p r o p a g a tio n ,/ £ . The th ir d term accounted fo r e m is s io n . T h is e q u a tio n cannot be so lv e d in e x a c t form , but must be a tta ck ed by approxim ate m ethods. /*<re ) = - I 0 e ( r , / O + -% r-f ,y a!)d/x' -1 + <ra i bb(r) ( 6 ) o p t ic a l d epth d e fin e d as The term on the 12 In the l a s t few y e a r s , e n g in e e r s have shown an in t e r e s t in t h is problem and a number o f a n a ly t ic a l s o lu tio n s have appeared in the l i t e r a t u r e . However, th e se s o lu t io n s are u s u a lly s p e c if i c and do n o t have g e n e r a l a p p lic a t io n . The work o f Love (2 1 ) i s an example o f t h is ; he so lv e d the tr a n s fe r eq u a tio n by the method o f d is c r e t e o r d in a te s fo r p a r t ic le s w ith a s p e c i f i c in d ex o f r e f r a c t io n . The u se o f th e eq u a tio n o f tr a n s fe r to o b ta in an approxim ate s o lu t io n r a p id ly becomes r a th er d i f f i c u l t . S t u l l and P la s s (2 2 ) computed the a b so rp tio n and s c a t t e r in g c r o ss s e c t io n s fo r sm a ll carbon p a r t i c l e s . Then from an eq u a tio n o f tr a n s fe r th e y were a b le to compute th e e m is s iv it y of a d isp e r se d clou d by a f i n i t e d iffe r e n c e approach u sin g a co a rse mesh fo r th e c a lc u la t io n s . In most in s t a n c e s , the amount o f s c a t t e r in g was sm a ll so th a t the eq u a tio n of tr a n s fe r became g r e a t ly s im p lif ie d . M cA lister e t a l . (23) perform ed an a n a ly s is and e x perim ent to o b ta in th e a b s o r p t i v it i e s o f a clou d o f p a r t i c l e s u sin g z in c , fe r r o u s s u l f i d e , and cu p ric o x id e . How e v e r , th e mechanism o f s c a t t e r in g was n o t c o n sid e r e d . Morizumi and C arpenter (2ij.) approached the problem o f d e s c r ib in g the therm al r a d ia tio n from the exh au st plume o f a s o lid p r o p e lla n t r o c k e t m otor by u s in g an a n a ly s is an alogous to n eu tron s c a t t e r in g . The c o l l i s i o n p r o b a b ili ty o f a photon s t r ik in g a s p h e r ic a l p a r t ic le was in v o lv e d . 13 T his was determ ined from th e assum ption o f is o t r o p ic s c a t t e r in g . A ll o f th e a n a ly se s m entioned above e it h e r are n o t r e a l i s t i c or th e r e s u lt s are to o com plex to a llo w e x p e r i m ental c o r r e la t io n . In o rd er to p la c e th e r e s u lt s o f the p r e s e n t in v e s t ig a t io n in more tr a c t a b le form , r a th e r than p u rsu in g th e eq u a tio n o f t r a n s f e r , a sim p ler tw o -flu x method i s p rop osed . T h is m odel e s s e n t i a l l y d iv id e s th e d if f u s e r a d ia t io n f i e l d in to two f lu x e s , one fow ard, and one backward. T h is was f i r s t su g g ested by S ch u ster (17)» Kubelka and Munk (2£), and u t i l i z e d by Hamaiker (26). More r e c e n t ly , L arkin and C h u r c h ill (27) have s u c c e s s f u lly used i t to c o r r e la te r a d ia tio n through porous in s u la t io n , and Chen and C h u rc h ill (28) have u sed i t w ith packed b e d s. In th e a p p lic a tio n o f th e two f l u x m ethod, Lathrop ( 2 9 )em p h a sized th a t one o f th e b a s ic assum ptions i s th e p resen ce o f a d if f u s e f i e l d . I f th e f i e l d i s p a r t i a l l y c o llim a te d , a more com plex a n a ly s is i s r e q u ir e d . The d e r iv a tio n o f th e two f lu x m odel w ith a tte n d a n t boundary c o n d itio n s i s g iv e n in Appendix B. The f i n a l r e s u l t shows T = ------------------------------------------- (7 ) co sh (mnL) + * sin h (mnL) K o ttle r (30) in d ic a te d th a t th e v a lu e o f b , th e back s c a t t e r in g c r o s s s e c t io n was n o t co m p letely in depend en t o f th e 34 o p t ic a l depth, f o r d if f u s e g la s s but approached an asym pto t i c v a lu e as th e o p t ic a l depth in c r e a s e d . Smart e t a l. (31) in d ic a te d e x p e r im e n ta lly , th a t as th e o p t ic a l depth in c r e a s e d , th e d is t r ib u t io n o f m u lt ip le - s c a tt e r e d l i g h t b e came d if f u s e in accordance w ith th e th eo ry o f H a rtel (7)» S in c e e q u a tio n (7) i s in more t r a c ta b le form than the eq u a tio n o f t r a n s f e r , eq u a tio n ( 6 ) , th e c o r r e la tio n o f ex p erim en ta l d a ta was made by d eterm in in g th e e m p ir ic a l co n sta n ts th a t d e sc r ib e d th e a b so rp tio n and back s c a t t e r in th e form er. The r e s u lt s In t h i s form can b e t t e r be a p p lie d to e n g in e e r in g problem s. I I I . DESCRIPTION O P THE EQUIPMENT A. E lu t r la t o r The e f f o r t s rep o rted by o th e r in v e s t ig a t o r s p rovid ed a b a s is fo r th e d e sig n o f a f in e p a r t ic le c l a s s i f i e r . A lthough i t would be d e s ir a b le to make the sep a ra t io n chamber ou t o f m e ta l, so th a t i t co u ld e a s i l y be grounded to e lim in a te e l e c t r o s t a t i c e f f e c t s , i t was d e c id ed to make i t ou t o f g la s s fo r two b a s ic r e a so n s. The f i r s t was economy. The second was th a t th e g la s s co u ld be s ilv e r e d on th e in s id e in such a manner th a t a th in s t r ip a lo n g th e le n g th co u ld be exposed fo r v is u a l in s p e c t io n . The s i l v e r su r fa c e co u ld then be a tta c h e d to a ground w ir e , and thus th e e l e c t r o s t a t i c fo r c e s w hich cau se the adherence o f p a r t ic le s to the w a ll, cou ld be m inim ized . I t was d e s ir e d to have as la r g e a d iam eter as p o s s ib l e fo r th e chamber, s in c e th e se p a r a tio n r a te i s propor t io n a l to the c r o s s - s e c t io n a l a r e a . P r a c t ic a l c o n sid e r a tio n s le a d to a compromise w ith a d iam eter o f 6 in c h e s . The minimum le n g th o f the c y lin d r ic a l s e c t io n was d e te r mined by th e d is ta n c e req u ired to g iv e a f u l l y d evelop ed lam in ar v e l o c i t y p r o f i l e . The c o n ic a l s e c t io n was de sig n ed to p rovid e a gradual d if f u s io n s e c tio n w ith a h a lf a n g le l e s s than 7 ° , so th a t sep a ra ted flo w and tu rb u len ce would be a v o id ed . I t was d ecid ed to sep a ra te th e powders 1$ 1 6 in to th e fo llo w in g f r a c t io n s or c u ts : 0 -5 m icro n s, 5 “7»5 m icro n s, 7 .5 -1 0 m icro n s, 1 0 -1 2 .5 m icro n s. I t was planned to d isc a r d th e f i r s t cu t and u se the o th e r s fo r l i g h t s c a t t e r in g s t u d ie s . C a lc u la tio n s were made to d eterm in e th e b u lk v e l o c i t i e s req u ired fo r th e v a r io u s m a te r ia ls and s i z e s , in order to measure and c o n tr o l the v e l o c i t i e s in th e chamber, a s e t o f g la s s c a p illa r y tub es was c a lib r a te d w ith b oth a wet t e s t m eter and a ro ta m eter. V a rio u s j e t s were a ls o made and c a lib r a te d so th a t th ey would p rovid e a v e l o c i t y head e q u iv a le n t to about 1 .5 in c h e s Hg. T his ap peared to be a s a t is f a c t o r y v a lu e fo r s t i r r i n g up th e pow der in th e U -tu b e. P ressu re d iff e r e n c e s a c r o ss th e c a p i l la r y tu b es were m easured by a w ater manom eter. S t a t i c gage p ressu re in th e system was determ ined by u sin g a mercury manometer w ith one l e g downstream o f th e c a p illa r y and the o th e r open to the atm osphere. L aboratory a ir was used w ith a p ressu re r e g u la to r . An a ir d ryin g t r a in , c o n s is t in g o f a la r g e bed o f s i l i c a g e l and a sm a ll tube o f D r ie r it e was p la ce d in th e a ir system to dry the p a r t ic le s and thus r e duce a g g lo m era tio n . A c o tto n f i l t e r was p la ced upstream o f the j e t to e lim in a te any c a r r y -o v e r o f s o li d im p u r itie s In to th e e l u t r ia t o r . A porous Alundum thim ble was u sed to c o l l e c t th e powder c a r r ie d overh ead . The system i s shown in F ig u re 2 . C o lle c t io n Thimble P.C C a p illa r y J e t U -tu b e Manometers F igu re 2 . E lu t r ia t o r System 18 B. M icroscope Although, a number o f m ethods f o r p a r t ic le s iz e m eas urem ents were a v a ila b le in th e com m erical m arket, th e m ost a c c u r a te , but perhaps n o t th e m ost ra p id measurement was by u se o f th e o p t ic a l m icroscope* S in c e th e p a r t ic le s iz e s to be m easured f e l l in to th e range o f f > to 1$ m icro n s, no problem o f r e s o lu tio n would be ex p ecte d w ith an o p t ic a l m icr o sco p e. Such an in stru m e n t, made by S p en cer, was a - v a ila b le w ith a nom inal o v e r a ll m a g n ific a tio n o f l|lj.O power. The e y e p ie c e was marked w ith a s c a le h a v in g 100 d i v i s i o n s . A sta g e m icrom eter, w hich was a g la s s s l i d e w ith c a lib r a te d m arkings th a t d iv id e d a 2 ram. le n g th in to 100 d iv is io n s was u sed to c a lib r a te th e e y e p ie c e . By m atching th e d i v i s io n s o f th e sta g e m icrom eter w ith th o se o f th e e y e p ie c e i t was determ ined th a t each o f th e l a t t e r was eq u al to 1 .6 1 m icro n s. Thus, th e m icroscop e was p r o p e r ly c a lib r a te d fo r th e o p e r a tio n o f p a r t ic le s i z e m easurem ent. C» In fr a r e d S pectrom eter The m easuring d e v ic e used in t h is r e se a r c h was a m o d ifie d Beckman IR-2A sp ectro m eter shown in F ig u re 3« The b a s ic u n it co n ta in ed o p t ic a l components o f rock s a l t and thus p erm itted m easurem ents from 2 to If? m icro n s. I t can be co n sid ered to be broken in to fo u r compartments con s i s t i n g o fs 1) a l i g h t sou rce s e c t io n , 2) a liq u id c e l l Monitoring phototube Chopper Gas cells Liquid cell Filter Gas cell (built in) F igu re 3 . Beckman IR -2 S p ectrom eter f o r In fr a re d R egion (Courtesy; Beckman In stru m en ts, I n c .) H vO 2 0 s e c t io n , 3) a gas c e l l s e c t io n , and l\.) a monochrome t e r . The f i r s t s e c t io n co n ta in ed a N ernst g lo w er, a chopper, a m irro r, and a c o llim a tin g le n s . The glow er con s is t e d o f a h o llo w tube 3 /8 - in c h lo n g and l / 8 - i n c h d iam eter composed o f ceram ic m a te r ia l and h ea ted by a stea d y e l e c t r i c cu rren t c o n tr o lle d by a m o n ito rin g p h o to tu b e. The chopper, which had b oth g la s s and m etal shades was r o ta te d so th a t i t in te r r u p te d the l i g h t beam from th e glow er 10 tim es per seco n d . T his p rovid ed a 10 c y c le a lt e r n a t in g s ig n a l to the d e t e c t o r . The e le c t r o n ic o u tp u t from the d e te c to r was a ls o a lt e r n a t in g and thus cou ld be g r e a tly a m p lifie d . At the e x i t o f the l i g h t compartment was a c o l lim a tin g le n s which produced a p a r a lle l beam fo r the liq u id c e l l compartment. Between th e two compartments was a m etal s l i d e w hich was used to c o n tr o l th e l i g h t to th e liq u id c e l l w ith e it h e r a f u l l open or a f u l l c lo s e d p o s it io n . The liq u id c e l l compartment was a re c ta n g u la r c a v ity w ith an opening about 3*3 cm. wide and 10 cm. h ig h , la r g e enough to adm it a liq u id c e l l c o n s is t in g o f 2 rock s a l t f l a t s p ressed to g e th e r w ith a sample c a v ity in the m id d le. Between th e liq u id and gas c e l l compartments was a co n v erg in g l e n s . The gas c e l l compartment in clu d ed two c y lin d r ic a l c e l l s , one about 10 cm. lon g and the o th e r about 2 cm. At the e x i t o f t h is compartment was a con verg in g le n s which fo cu sed the image o f th e glow er upon the 21 en tra n ce s l i t o f th e m onochrom eter• The purpose o f the monochrometer compartment was to decompose th e tra n sm itted beam in to i t s wave le n g th e l e m ents and to a llo w o n ly a narrow band w idth to im pinge upon th e d e t e c t o r . The en tra n ce s l i t as w e ll as the e x i t s l i t was 20 mm. lo n g and cou ld be v a r ie d in w idth from 3 mm. to 0 .0 1 mm. Prom th e en tra n ce s l i t the beam was c o llim a te d by a curved m irror and then d is p e r s e d by a p rism . The beam tra v er sed the prism tw ic e , ow ing to th e p resen ce o f the p lan e L ittro w m irro r, which was r o t a t a b le , on the back sid e o f the p rism . The m irror was cou p led to a wave le n g th d ia l which in d ic a te d the wave le n g th o f the l i g h t le a v in g th e com partment. A fte r b ein g d isp e r s e d by the prism th e beam rev ersed i t s path and p a ssed o u t o f th e monochrometer v ia th e e x i t s l i t . Prom h ere i t was r e f l e c t e d by a p lan e m irror and fo cu sed upon a therm ocouple w hich a c te d as a d e t e c t o r . The emf s ig n a l g en era ted by the therm ocouple was then s e n t to an A .C . a m p lifie r which was tuned to a 10 c y c le freq u en cy . L The maximum p o s s ib le a m p lific a tio n was 10 . The e le c t r o n ic s ig n a l was then changed to D .C . by u se o f a synchronous r e c t i f i e r w hich c o n s is te d o f b reak er p o in ts and a cam l o ca ted on the s h a ft o f th e m otor w hich drove the chopper. The o u tp u t s ig n a l from th e r e c t i f i e r was stren g th en ed by a D .C . a m p lifie r . The o u tp u t D .C . s ig n a l was then b alanced 22 by a p o te n tio m eter fo r tr a n sm issio n r e a d in g s . B e sid e s th e o p t ic a l u n it , power su p p ly , and am pli f i e r a lr e a d y m en tion ed , a r e f r ig e r a t o r u n it was a ls o used to keep th e tem perature o f th e o p t ic a l box a t 77® ± 0 .2 ° P . D. T est C e ll The c e l l w hich was used fo r th e tr a n sm issio n m eas urem ents was c o n str u c te d from th e sm a lle r o f th e two gas c e l l s . However, s in c e th e l i g h t r a y s w ere con vergen t w ith in th e gas c e l l com partment, i t was n e c e ssa r y to p la c e th e t e s t c e l l in to th e liq u id c e l l compartment where th e y were c o llim a te d . The gas c e l l was b a s ic a l ly a h o llo w c y lin d e r made o f s t a i n l e s s s t e e l w ith two p o r ts on th e s id e w a ll f o r a llo w in g gas to flo w in and o u t. A sm a ll l i p was in clu d ed a t each end o f th e c y lin d e r to accommodate an O -r in g . A f l a t window o f rock s a l t was p la c e d a t each end o f th e c y l in d e r and s e a le d w ith th e O -rin g . The windows were h e ld a - g a in s t th e O -rin g by 2 annular d is c s th a t were t i e d t o g e th e r a t each end o f th e c y lin d e r by sm a ll te n s io n b o lt s and n u ts . The sm a ll gas c e l l had th e proper shape f o r the measurement o f p a r t ic le tr a n sm issio n b u t c e r ta in m o d ific a t io n s were n e c e s s a r y . S in c e th e c e l l was exposed to th e a ir a g r e a t p a r t o f th e tim e th e h y g ro sc o p ic n a tu re o f th e rock s a l t would p r e s e n t a problem o f f o g g in g . C onsequent- 1 6 , a new s e t o f windows made o f S erv o fra x (a r s e n ic t r i - 23 su lp h id e ) by th e Servo C o rp o ra tio n o f America was u sed . T his m a te r ia l was s e le c t e d b ecau se i t was a g l a s s , was non- h y g r o sc o p ic , and was e a sy to h a n d le . I t had th e d isa d van tage o f h a v in g a h ig h r e f r a c t iv e in d ex (2.l|.0) w ith a t ten d a n t h ig h r e f l e c t i v i t y . However, t h i s f a c t o r was taken in to a cco u n t. The gas c e l l as i t e x is t e d was too la r g e to f i t in to th e liq u id c e l l c a v i t y . T h er efo re , i t was p la ced on a la t h e and th e le n g th was reduced from 1 .9 2 cm. to 1*30 cm. The o r ig in a l 0 -r in g s were t e s t e d f o r c o m p a tib ility w ith carbon te tr a c h lo r id e by im m ersing them in th e f l u i d . W ith in a few h o u rs, th e 0 -r in g s sw e lle d to a c o n sid e r a b le e x te n t and d is c o lo r e d th e s o lu t io n , in d ic a tin g th a t th e m a te r ia l was u n s a t is f a c t o r y . T e flo n and V ito n A w ere n ex t t e s t e d In th e carbon t e t r a c h lo r id e . Both appeared to be s a t is f a c t o r y . However, when T e flo n was t r ie d as a s e a lin g m a te r ia l, i t was d isc o v e r e d th a t i t would n ot p ro p erly s e a l betw een th e window and th e m eta l u n le s s h e ld v er y t i g h t l y . I t was fe a r e d th a t th e g la s s window would crack under th e h ig h s t r e s s and th u s, th e T e flo n was d isca rd ed in fa v o r o f V ito n A. 0 -r in g s o f t h is m a te r ia l were th e n used and p ro v id ed a s a t is f a c t o r y s e a l betw een th e m eta l and th e g l a s s . However, when th e c e l l was f i l l e d w ith a su sp en sio n o f aluminum o x id e p a r t i c l e s , a ten d en cy f o r th e p a r t ic le s to s e t t l e in to th e O -rin g grooves was d is c o v e r e d . V igorous sh aking o f th e c e l l d id n ot d is lo d g e them. The 0 -r in g s were d isca rd ed and r e p la c e d by f l a t g a sk e ts Cl/3 2 in ch ) w hich made a d ir e c t s e a l w ith th e g la s s and th e m e ta l, as shown in F igu re lj.. W ith th e g a sk e t in p la c e th e c e l l le n g th was l.Ij.3 cm. and th e d ia m e te r, 2 .3 9 cm ., as m easured by a v e r n ie r c a lip e r . T h is c o n fig u r a tio n proved s a t i s f a c to r y from a l l a s p e c ts and was th e f i n a l one used in the tr a n sm issio n m easurem ents. For th e d if f u s e m easurem ents one o f th e S erv o fra x windows was roughened w ith a #80 g r ip p ap er. The roughened fa c e was exposed to th e in c id e n t c o llim a te d beam. The l i g h t tr a n sm itte d through th e window was s c a tte r e d i n a l l d ir e c t io n s and p rovid ed a d if f u s e sou rce f o r th e p a r t ic le c lo u d . B. B alance An a n a ly t ic a l beam b a la n c e -which p erm itte d w eigh in g to 0 .2 mg was used f o r w eigh in g powder a t v a r io u s s ta g e s in the ex p erim en ta l p ro ced u re. Fill ports C e ll C a v ity O p tic a l window S e a ls F igu re lj.. Schem atic Drawing o f T est C e ll IV . SELECTION OP PARTICLES A N D SUSPENDING MEDIA The p a r t ic le s stu d ie d in t h is r e se a r c h had to have a number o f c h a r a c t e r is t ic s so th a t th e d e s ir e d e x p e r i m en tal param eters co u ld be o b ta in e d . P r im a r ily , th e y had to be s p h e r ic a l, a t l e a s t p a r t i a l l y tr a n sp a r e n t, have a r e f r a c t iv e in d ex d if f e r e n t from th e su sp en d in g medium (l*lj.5>), and be in th e s i z e range from 5 to 15> m icrons fo r maximum s c a t t e r in g . S e c o n d a r ily , th ey had to be e a s i l y d isp e r se d in th e su sp en d in g medium. In ch eck in g w ith nu merous s u p p lie r s , i t was d isc o v e r e d th a t Thermal Dynamics C orp oration produced a s p h e r ic a l aluminum o x id e made from 99*7 p erc en t pure a lp h a p h a se. T his m a te r ia l was m elted in an arc fu r n a c e , form ed in to m ic r o n -siz e d d r o p le ts , and q u ic k ly quenched. T h is p rod uct was then put through a 500-mesh s i e v e , thus d e liv e r in g a f in e powder whose m axi- m iam s iz e was 25 m ic r o n s. I t was s e le c t e d as th e prim e m a te r ia l b eca u se, b ein g s im ila r to sa p p h ir e, i t would be tra n sp a ren t in th e n ear in fr a r e d , have a r e f r a c t iv e in d ex d if f e r e n t from th e su sp en d in g medium, and th u s produce maximum s c a t t e r in g . The o th e r m a te r ia l s e le c t e d was a S u p er b r ite g la s s bead made by th e 3M Company. T his m a te r ia l was s p h e r ic a l and had a maximum s i z e o f ijlj. m icr o n s. I t cou ld be e x p e c t ed to absorb in th e in fr a r e d . 26 27 A se a rch o f p o s s ib le su sp en d in g media fo r the par t i c l e s was made by u sin g v a r io u s r e fe r e n c e s such as the API R esearch .P roject l\l\. ( 3 2). The o n ly two f lu id s rea so n a b ly tra n sp a ren t in the range o f wave le n g th s (2 -1 1 m i cro n s) under c o n s id e r a tio n were carbon te tr a c h lo r id e and carbon d is u lp h id e . The form er was found to be tra n sp a ren t from 2 to 6 m icro n s. From 6 to 7*5 m icro n s, a str o n g ab so r p tio n band was p r e s e n t; a tr a n sm issio n window was ob serv ed a t 7«7 m icrons fo llo w e d by an oth er a b so rp tio n band. A seco n d , sm a lle r window was found a t 9 m icro n s. For la r g e r wave le n g th s the tr a n sm issio n was n e g l i g i b l e . Car bon d is u lp h id e was tra n sp a r en t from 2 to 6 m icrons and from 8 to 11 m icro n s. Thus, i t would be p o s s ib le to s u s pend the p a r t ic le s in th e se two media and make tra n sm is s io n m easurements over n e a r ly the t o t a l spectrum w ith in the c a p a b i l it i e s o f the sp e c tr o m e te r . V. EXPERIMENTAL PROCEDURE The procedure u sed f o r o b ta in in g th e n e c e ssa r y ex p erim en ta l d a ta was d iv id e d in to th r e e main t a s k s . These in v o lv e d th e se p a r a tio n o f th e p a r t ic le s in t o r e l a t i v e l y uniform s i z e s , th e m easurem ent o f th e s e s i z e s , and th e tr a n sm issio n o f in fr a r e d r a d ia t io n through a clou d o f th e se p a r t i c l e s . The supplem entary in fo rm a tio n reg a rd in g th e f i r s t two ta sk s i s d e sc r ib e d in d e t a i l in Appendix A. The tech n iq u es used f o r th e in fr a r e d m easurem ents are g iv e n below . B efore any in fr a r e d m easurem ents cou ld be made w ith th e sp ectro m eter, i t was n e c e ssa r y to turn on th e power su p p ly , a m p lifie r , and c o o lin g b ath and a llo w two hours f o r ev e ry th in g to come to a ste a d y c o n d itio n . The p o ten tio m e te r was th en b a la n ced by tu rn in g th e s e le c t o r sw itch to z e r o , c lo s in g th e l i g h t g a t e , and m a n ip u la tin g th e zero knob on th e a m p lifie r . F o llo w in g t h i s , th e wave le n g th and s l i t w id th were s e le c t e d , th e l i g h t g a te was opened, and th e s e le c t o r sw itch was turned to ch eck . The g a in c o n tr o l was v a r ie d u n t il th e p o te n tio m e te r was b alan ced a g a in . T his p roced u re, in e f f e c t , s e t th e band so th a t tra n sm is s io n s betw een zero and one-hundred p erc en t co u ld be r e a d . When a sample was p la c e d in th e liq u id c e l l c a v it y , th e 28 29 movement o f th e tr a n sm issio n knob to b a la n ce th e p o te n tio m e te r gave a re a d in g o f p e r c e n t tr a n sm issio n on th e tr a n sm issio n s c a l e . The s m a lle s t d iv is io n on th e s c a le was one p e r c e n t. A second s i g n i f ic a n t f ig u r e cou ld be o b ta in ed by in t e r p o la t io n . For a l l wave le n g th s l e s s than 8 m i c r o n s, th e m eta l chopper was used acco rd in g to th e manu f a c t u r e r ^ in s t r u c t io n . For lo n g e r wave le n g t h s , th e g la s s chopper was u se d . The r e a so n g iv e n f o r th e u se o f th e g la s s chopper a t lo n g e r wave le n g th s was to e lim in a te th e p o s s i b i l i t y o f th e m eta l p ie c e g e n e r a tin g s c a tte r e d l i g h t w hich would in t e r f e r e w ith th e m easurem ents. The g la s s chopper co u ld n o t be used f o r th e sh o r t wave le n g th s s in c e g la s s ten d s to be tra n sp a r en t in t h is p a r t o f th e spectrum , and’ th u s would n ot in te r r u p t th e l i g h t beam. S in c e an a l te r n a tin g beam was n e c e ssa r y f o r a m p lific a tio n , a co n tin u ous beam would n o t be sen sed by th e d e t e c t o r . D i f f i c u l t y was en cou n tered in b a la n c in g th e in s t r u ment o v er th e range o f wave le n g th from two to fo u r m i c r o n s. In te n s e n o is e was in d ic a te d by th e n e e d le o f th e p o te n tio m e te r . The n o is e was p e r io d ic and was e stim a te d to be o f th e same freq u en cy as th e l i g h t beam. A fte r some tim e , i t was d isc o v e r e d th a t i f b la ck ta p e were p la ce d on th e h o u sin g o f th e en tran ce s l i t , b oth above and below th e s l i t , in such a manner t h a t th e e f f e c t i v e s l i t h e ig h t was red u ced , t h i s p e r io d ic n o is e would d isa p p e a r . I t was 30 l i k e l y th a t th e m eta l chopper was a c tin g as a sou rce o f s c a tte r e d l i g h t w hich tr a v e r se d th e o p t ic a l t r a in and en te r e d th e monochrome t e r compartment a t th e extrem e ends o f th e s l i t * A nother anomaly was d e te c te d when th e l i g h t g a te was c lo s e d and th e a m p lifie r g a in was in c r e a se d to i t s maximum* The p o te n tio m e te r n e e d le was ob served to make la r g e n o n -p e r io d ic e x c u r s io n s . I t was assumed th a t some th in g was wrong w ith th e e le c t r o n ic equipm ent* The i n strum ent was sh u t down and a Simpson volt-o h m -m eter was u sed to tr a c e through th e power and a m p lifie r c ir c u it s * A fte r a tim e , i t was d isc o v e r e d th a t th e item g iv in g th e tr o u b le was th e synchronous r e c t i f i e r . A p p a ren tly , th e making and b reak in g o f th e p o in t s , w hich occu rred when th e A.C. o u tp u t v o lta g e o f th e a m p lifie r changed s ig n , caused a sp u rio u s s ig n a l to be s e n t to th e r e c t i f i e r . These p o in ts were clea n e d and r e s e t a t v a r io u s c le a r a n c e s but to no a v a il. T h er efo re , t h i s component o f th e in stru m en t was one o f th e lim it in g f a c t o r s fo r o b ta in in g th e maximum u s e f u l gain * The n o is e cou ld p rob ab ly be e lim in a te d by r e p la c in g th e b reak er p o in ts w ith sem i-co n d u cto r d io d e s . However, s o li d s t a t e d e v ic e s are in h e r e n tly n o n -lin e a r , and th u s would n o t be a c c e p ta b le in t h i s c i r c u i t . I t was d ecid ed to a ccep t th e n o is e lim it a t i o n , k eep in g in mind th a t I t could a f f e c t th e p r e c is io n o f m easurem ents made a t 31 lo n g wave le n g th s were the sou rce i n t e n s it y i s n o t str o n g . The f i r s t s e t o f m easurem ents made w ith the sp e c trom eter was to o b ta in the t r a n s m is s iv it y o f the S erv o fra x windows over the a v a ila b le wave le n g t h s . The n ex t m easure ments were to determ ine the t r a n s m is s iv it y o f the suspend in g m edia, carbon t e tr a c h lo r id e and carbon d is u lp h id e . The tr a n sm issio n m easurem ents f o r th e p a r t ic le clou d were to be made fo r b oth a c o llim a te d and a d if f u s e s o u r c e . The r e s u lt s fo r the c o llim a te d ca se would a llo w fo r th e d e term in a tio n o f the e x t in c t io n c o e f f i c i e n t . However, in the measurement o f l i g h t e x t in c t io n by sm a ll p a r t i c l e s , care had to be taken th a t some o f the s c a tte r e d l i g h t did n o t e n te r the monochrometer and produce a low m easured v a lu e fo r e x t in c t io n . The d ir e c t io n o f th e s c a tte r e d l i g h t i s a 7T d stro n g fu n c tio n o f th e param eter x = • The la r g e r t h is p aram eter, the more forward becomes th e s c a tte r e d l i g h t . I t has been shown by d if f r a c t i o n theory ( 8 ) , th a t a c o r r e c tio n f a c t o r to th e e x t in c t io n c o e f f i c i e n t can be o b ta in ed by m u ltip ly in g by Hj where R = 1 * J02( ^ X) * Jl2( (8) 2 0 i s the h a lf a n g le subtended by the s l i t from the par t i c l e • For th e c o llim a te d m easurem ents, th e s l i t w id th was 32 reduced to 0 .0 1 mm. A p ie c e o f b la ck tape w ith a s l i t 0 .5 mm. wide was p la ced over th e s l i t h ou sin g so th a t the s l i c e was normal to the s l i t . S in c e the sample c e l l was 18 cm. from the s l i t , a maximum subtended a n g le o f 0 .0 0 2 8 ra d ia n s was a c h ie v e d . A lthou gh the p a 'r tic le param eter, x , had a maximum o f about 28 fo r the p r e se n t r e se a r c h , the argument o f th e B e s s e l fu n c tio n s was o f th e order o f 0 .0 8 . F or t h is sm a ll argument Jq( < f > x) approached 0 and J-j_( < f ) x) approached 1 . Thus, R was n e a r ly eq u al to 1 .0 . T h er efo re, th e c o r r e c tio n fo r s c a tte r e d l i g h t was below th e accuracy o f m easurem ent. The v a rio u s p a r t ic le clo u d s were prepared by two m ethods. In b o th , an amount o f powder was f i r s t removed from a w eigh in g b o t t l e , and the amount was determ ined by w eig h in g b e fo re and a f t e r th e powder rem oval. In the f i r s t method o f p r e p a r a tio n , one window o f th e sam ple c e l l was removed and the powder was p la ced i n s id e . The second w in dow was a tta c h e d and the c e l l a ssem b led . The su sp en d in g medium was added by f i l l i n g the c e l l w ith a p ip e t through th e la r g e r o f the two tu b u la r op en ings on the to p . In the secon d m ethod, th e powder from the w eigh in g b o t t l e was p la ced in a sm a ll b ea k er. A sm a ll amount o f the su sp en din g medium was added, the beaker was a g ita te d by a s w ir lin g m o tio n , and the c o n te n ts were poured In to th e assem bled sam ple c e l l . A d d itio n a l amounts o f suspending 33 medium were added to th e beaker as a w ash. T h is was a ls o poured in to th e c e l l . The procedure was co n tin u ed u n t i l a l l o f th e powder was removed from the b ea k er. The c e l l then was topped w ith th e medium. The u se o f the second method o f p r ep a ra tio n was n e c e ssa r y w ith th e g la s s bead sample because o f i t s ten d en cy to a g g lo m era te. In f a c t , by u sin g th e f i r s t m ethod, i t was n ot p o s s ib le to d is p e r s e th e g la s s b ea d s. W ith carbon te tr a c h lo r id e th e tr a n sm issio n through th e clo u d o f alu m i num o x id e was in d ep en d en t o f the two p rep a ra tio n m ethods. W ith the second m ethod, i t was observed th a t th e la r g e r - s iz e d p a r t ic le s o f aluminum oxid e d isp e r se d much e a s ie r than the sm a lle r o n e s. T h is would be ex p ected from the in v e r se square law o f a t t r a c t io n . The second method was not used w ith carbon d is u lp h id e b ecau se o f i t s h ig h vapor p ressu re and n a u se a tin g od or. A fte r the c e l l was f i l l e d , sm all sto p p er s made o f V ito n A were u sed to cap the two p o r t s . The c e l l was shak en v ig o r o u s ly and then p la ced in to the liq u id c e l l c a v it y . The p o te n tio m eter was b alan ced and the tr a n sm issio n re a d . I t was n o tic e d th a t the in d ic a tin g n eed le would rem ain c o n sta n t fo r about e ig h t to ten se co n d s, and then g ra d u a l ly d eca y , in d ic a t in g th a t the su sp en sio n was g r a d u a lly s e t t l i n g . The a llo w a b le tim e fo r measurement was augmented by th e f a c t th a t the p a r t ic le s were n e a r ly uniform and 3J+ th u s, would s e t t l e a t th e same r a t e . In o th e r w ords, in a c o n tr o l volum e, when one p a r t ic le would s e t t l e ou t b elow , an oth er one would r e p la c e i t from ab ove. A f t e r e a c h r e a d in g , th e c e l l was rem oved , v ig o r o u s l y sh a k e n , and r e p la c e d to in s u r e r e p e a t i b i l i t y o f th e m ea su rem en t. V I. EXPERIMENTAL RESULTS A* E lu t r ia t io n R ates I n o rd er to d eterm in e when to sto p th e se p a r a tio n o f one s i z e o f p a r t i c l e s , th e accum ulator th im b le was w eighed ev ery h a lf h ou r. When th e c a r r y -o v e r r a te was l e s s than te n p e r c e n t o f th e o r ig in a l v a lu e , th e se p a r a tio n was sto p p e d . T ables l a and lb are th e r e s u l t s o f w eigh in g f o r b o th th e aluminum o x id e and th e g la s s b ea d s. The se p a r a tio n o f aluminum o x id e p rovid ed no prob lem as can be se en from th e ta b u la r r e s u l t s . The g la s s b ea d s, as in d ic a te d in th e p rev io u s s e c t io n , tended to ad h ere to th e s id e s o f th e se p a r a tio n v e s s e l . The r e l a t i v e l y slow r a t e o f e l u t r i a t io n o f th e beads was in d ic a t iv e o f th e adherence problem . As shown in T able lb , th e d e s ig n end p o in t o f each c u t was n o t a tta in e d , in d ic a t in g th e se p a r a tio n wa3 n o t o f a h ig h q u a lit y . B. S iz e Measurements The s iz e d is t r ib u t io n s o f th e e lu t r ia t e d p a r t ic le s are p r e se n te d as h isto g ra m s in F ig u r e s f?a, 5b, and 6 . The a n a ly s is o f th e s m a lle s t aluminum o x id e sam ple, th a t w hich was bounded by S tok es d ia m eters o f 5 to 7*5> m icro n s, i n d i c a te d th a t some o f th e p a r t ic le s sm a lle r than 5 m icrons were c a r r ie d over from in co m p lete se p a r a tio n o f th e 0 -5 3£ 36 TABLE l a R A T ES O F ELUTRIATIO N Aluminum Oxide Size Range Time Net Weight Normalized Rate o f microns h r s. grams Removal 0-5.0 0.5 0.137^ 1.00 1.0 0.0511 * 0.38 1.5 0.03^0 0.25 2.0 0 . 02^1 0.17 2.5 0.0217 0.16 3.0 0.0160 0.11 3.5 0.0181 0.13 U.O 0.0105 0.08 5-7.5 0.5 1.1129 1.00 1.0 0.2713 0.25 1.5 0.11*27 0.13 2.0 0.0687 0.0 6 7 .5 -1 0 .0 0.5 2.3292 1.00 1.0 0 . 0.19 1.5 0.3536 0.15 2.0 0 . 1& U 6 0.06 2.5 0.1052 0.05 10- 12.5 0.5 2.5565 1.00 1.0 0.6820 0.27 1.5 0.2827 0.11 2.0 0.159^ 0.06 37 T A B L E lb R A T E S O F ELU TR IA TIO N Glass Beads Normalized S ize Range Time Net Weight Rate o f microns hrs. grams Removal 0t 5.0 0.5 0.0288 1.00 1.0 0.0218 0.76 1 .5 0.0151 0.52 2 .0 0.0125 0.1*3 2 .5 0.0130 0.1*3 5 .0 -7 .5 0.5 0.0570 1.00 1.0 0.0350 0.61 1 .5 0.0210 0.37 2.0 0.0099 0.17 7 .5 -1 0 .0 0 .5 0.1130 1.00 1.0 0.0810 0.71 1.5 0.0680 0.60 2.0 0.0275 0 .2U ' '■ ■ ■ - ■ — 2.5 ■ 0 . 028*» - " >•■■•'■■■■■■■■• 0.25 3.0 0.0309 0.27 3.5 0.0397 0.35 1*.0 0 . 05U 0 0 .U8 U.5 O.0U 36 0.39 5.0 0.0531* 0.1*7 5.5 0.031*0 0.30 6.0 0;0322 0.28 1 0 .0-12.5 0.5 0.2330 1.00 1.0 O.O865 0.37 1 .5 0.0391* 0.17 2.0 0.0305 0.13 2 .5 0.0926 0.1*0 3.0 0.0391* 0.17 3.5 0.051*6 0.21* i*.o 0.0380 0.16 1*.5 O.OU68 0.20 5.0 0,0378 0.16 5.5 0.0561 0.21* 6.0 0 . 0U 10 0.18 6.5 0.0258 0.11 7.0 0 . 021*2 0.10 Num ber o f P a r t ic le s 38 r-TT*r Diam eter* M icresoope U n its F igu re 5a* Measured S iz e D is t r ib u tio n fo r Aluminum Oxide 5 -7 * 5 M icron Cut 39 D iam eter, M icroscope U n its F igu re 5>b. Measured S iz e D is t r ib u tio n f o r Aluminum Oxide 1 0 - 1 2 .5 > M icron Cut Num ber o f P a r t ic le s ko D iam eter, M icroscop e U n its F igu re 6 . Measured S iz e D is t r ib u tio n f o r G lass Beads 10-12*5> M icron Cut 10- m icron cut* Prom th e d is t r ib u t io n shown in F ig u re 5& > th e r o o t mean square d ia m e te r, \f d * was c a lc u la te d to be 6 .2 8 m icro n s. T his d ia m e te r, r a th e r th an the mean d iam eter was computed b ecau se th e s c a t t e r in g and a b so r p tio n o f therm al en ergy i s a su r fa c e phenomenon r a th e r than one o f le n g th . F igu re 5b in d ic a t e s th e s i z e d is t r ib u t io n fo r the sam ple bounded by S to k es d ia m eters o f 10 and 1 2 .5 m icro n s. The range o f s i z e s was g r e a te r than th e group p r e v io u s ly d is c u s s e d . Some sm a ll p a r t i c l e s were c a r r ie d over from p r ev io u s c u t s . However, th e r o o t mean square d iam eter was 1 2 .2 m icro n s, w hich was w ith in th e l i m i t s s e t by th e S to k es v e l o c i t i e s . F ig u re 6 e x p r e sse s g r a p h ic a lly some r e s u l t s o f th e problem s en cou n tered in s e p a r a tin g th e g la s s b e a d s. S iz e s ranged from 1 to over 15 m icrons w ith a r o o t mean square d iam eter o f 7*75 m icr o n s. T h is was l e s s than th e 1 0 -1 2 .5 range s p e c i f i e d . The r e a so n f o r th e in c o n s is te n c y appeared to l i e in th e i n a b i l i t y to c o m p le te ly f r a c t io n a t e th e c u ts w ith sm a lle r p a r t ic le s due to a g g lo m era tio n , as evid en ced by Table l b . Thus, th e sm a lle r p a r t ic le s were c a r r ie d over w ith th e la r g e r ones when th e S to k es v e l o c i t y was in c r e a s e d . C. C e ll Blank M easurements T ran sm ission m easurem ents were made fo r the o p tic a l window m a te r ia l, S e r v o fr a x , in order to compare them w ith p r e d ic te d v a lu e s and v a lu e s determ ined by the m an u factu rer. T able I I p r e se n ts a l i s t o f the v a rio u s tr a n sm issio n s ob ta in e d . They are p lo tt e d in F ig u re 7 and compared w ith computed tr a n sm issio n s based on F r e s n e l’ s r e f l e c t i o n la w s. The r e s u lt s in d ic a te d th a t a good com parison was o b ta in ed up to a wave le n g th o f 8 m icro n s. At t h is p o in t, some ab so r p tio n was en cou n tered in the g la s s ca u sin g the m easured tr a n sm issio n to f a l l below the t h e o r e t ic a l v a lu e . At 11 m icrons th e tr a n sm issio n in c r e a se d s l i g h t l y , but then dropped a g a in . The g e n e r a l tren d o f th e curve was in agreem ent w ith the m an u factu rer’ s d a ta (33)* and w ith B a l la r d e t a l (3 if). The t r a n s m is s iv ity o f the window was com puted from the ray tr a c in g model re p r ese n ted in Case I o f Appendix C. The m easurem ents fo r th e c e l l blank f i l l e d w ith s u s pending m edia are l i s t e d in T able I I I . Case I I o f Appendix C was d eriv ed to d e s c r ib e the tr a n sm issio n through the sample c e l l by the ray tr a c in g m ethod. W ith the tra n sm is s i v i t y , T , o f the window l i s t e d in T able I I I , eq u a tio n (if) o f Appendix C was used to compute the r e f l e c t i v i t y , R2 * fo r the back window. E q u ation s (1 ) and (3 ) were used to com pute th e t r a n s m is s iv it y , 7"c , o f the m edia. From B eer’ s law , a b so rp tio n c o e f f i c i e n t s were com puted. The r e s u lt s o f TABLE I I TRANSM ISSIO N O F T H E SE R V O F R A X W IN D O W W ave Length Transmission Microns Uncorrected T ransm issivity T 1 2 68.0 1.0 3 68.0 1.0 k 70.9 1-02 5 69.0 1.0 6 68.7 1-0 7 68.6 1.0 8 68.2 1.0 9 .......57. 9,,... ...,.0 . 8U 6...; 10 50.9 0 .7^0 11 53.0 0.772 12 39 A Percent T ran sm ission h b § m m Wave L ength, M icrons F igu re 7 , T ran sm ission Through S erv o fra x Window u s TABLE I I I TRANSM ISSION A N D REFLECTIO N O F SUSPENDING M EDIA W ave Length Measured Absorption microns Transmission Transmissivity Coefficient R eflectivity Ao T r c cm“l R2 1 CCli* cs2 CGty cs2 C C lfc cs2 CClfc cs2 2.0 63.8 60.8 l.o 6 0.995 0 0 0.217 0.202 3.5 - 61.3 - 1.00 - 0 - 0.202 1*.0 62.0 - l.Ol* 0.811* 0 0.11*5 0.217 0.202 fc.5 55-9 - 0.936 - 0.01*69 0.11*9 0.217 0.202 5.0 1*7.9 - 0.796 - 0.160 - 0.21U - 5-5 - 26.2 - 0.1*19 - 0.638 - 0.205 6.0 39.8 1*1*.8 0.652 0.737 0.30 0.193 0.21U 0.210 7.7 '1*2.9 - 0.705 - 0.21*5 - 0.21U - 8.0 - 29.0 - 0 .1 * 1 * 1 * - 0.570 - 0.190 8.5 - 52.9 - 0.972 - 0.0207 - 0.179 9.0 16.1 1*0.0 0.371 0.872 0.720 0.0965 0.188 0.168 9.5 - 3l*.8 - 0.869 - 0.0977 - 0.159 10.0 - 20.7 - 0.581+ - 0.377 - 0.151 10.5 - 29.8 - 0.792 - 0.163 - 0.153 11.0 — . 25.2 _ 0.636 _ 0.315 _ 0.155 t h e s e c o m p u ta tio n s are l i s t e d In T a b le I I I . I t can be s e e n t h a t carb on t e t r a c h l o r i d e was t r a n s p a r e n t from 2 to i|. m icron s in wave l e n g t h . A t If.5 m icro n s some a b s o r p tio n was n o t e d , Windows o f t r a n s m is s io n were o b ser v ed a t 6 , 7.7, and 9 m ic r o n s . Carbon d is u lp h id e was tr a n s p a r e n t up to a wave le n g t h o f I 4 . m ic r o n s . S m a ll a b s o r p t io n was n o t ic e d from I 4 . to 5*5 m ic r o n s . A s t r o n g ab s o r p t io n band was r e c o r d e d a t 5 * 5 and betw een 6 to 8 m i c r o n s . Beyond 8 m icro n s th e medium was s l i g h t l y a b s o r b e n t w ith a c u t - o f f a t 11 m ic r o n s . D . T r a n sm iss io n o f th e C o llim a te d Beam The m easurem ents o f t r a n s m i s s i v i t y f o r v a r io u s p a r t i c l e c lo u d s a r e g iv e n in T a b le s IV a , IV b, and I V c . T hese v a l u e s were n o r m a liz e d b y u s in g th e t r a n s m is s io n th r o u g h th e c e l l w ith o u t p a r t i c l e s . The number o f p a r t i c l e s p e r u n i t volu m e, n , was computed from th e f o l l o w i n g e q u a t io n . I n a s t r i c t s e n s e , th e d ia m e te r , d , in e q u a tio n (9) sh o u ld be b a se d upon th e v o lu m e tr ic a v e r a g e , . H ow ever, s i n c e th e p a r t i c l e s were s p h e r i c a l and in a narrow r a n g e , l i t t l e d i f f e r e n c e was n o te d b etw een th e a r ea a v e r a g e , , and th e v o lu m e tr ic a v e r a g e . F or t h i s r e a s o n th e a r e a a v e ra g e d ia m e te r was u s e d . S e v e r a l s e t s o f d a ta TABLE IVa TRANSMISSION OF ALUMINUM OXIDE PARTICLES IN CARBON TETRACHLORIDE WITH A COLLIMATED SOURCE a * 12. microns lple Weight mg. 2.0 2.5 3.0 3.5 3.6 71.6 70.2 72.9 70.6 17.3 10.2 9.^3 8.52 7.60 32.7 2.12 1.85 1.80 1.1*5 12.2 2U.8 23.1 21.5 20.2 26.1 5.15 1+.82 1*.1*2 3.81* 7.0 1 * 1 * .1 + 1 + U .1 + 1*6.3 39.1 M 32.5 30.6 23.2 a = 1 22.3 8U. 18.7 1I+.8 10.1* 9.98 8.9 13.6 9.88 7.35 6.1*8 1U.7 U.7U 3.11+ 2.21 1.93 21.2 0.803 0.521 0.331* 0.355 Wave Length U.O U.5 5.0 6.0 7.7 9.0 67.6 66.5 69.9 80.0 89.9 80.9 5.15 it.1 * 1 + 5.82 17.1 56.6 23.1* 0.956 0.752 1.28 It.98 • 3.68 6.80 15.7 13.7 16.5 3U.8 70.7 1*2.5 2.38 2.0 6 3.18 9.86 1*6.7 lit.2 35.5 3I+.O . 39.1 57.0 80.6 60.9 28 microns 25.2 35.1 1*9.6 72.0 88.1* 71*.0 12.3 16.7 28.9 57-2 87.8 69.8 8.80 lU .l 26.8 5I+.6 85.6 63.6 2.70 1+.99 12.2 33.1 77.U 1*1*.3 0.522 1.05 3.55 19.5 65.O 26.0 TABLE IVb TRANSM ISSION O F A L U M IN U M O XIDE PARTICLES IN C A R B O N DISULPHIDE W IT H A C O L L IM A T E D SO U R C E d = 12.2 microns Sample Weight W ave Length mg. 2.0 2.5 3.0 3.5 4.0 4.5 5.5 6.0 8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.8 21.8 18.2 18.0 20.8 26.1 36.7 65.5 66.8 23.1 21.4 20.2 19.9 20.1 20.3 18.5 22.1 6.15 4.46 4.32 5.50 8.48 16.6 4l.4 45.6 5.98 5.53 4.75 5-13 5.10 4.26 3.76 30.3 2 .T O 2.08 18.3 2.26 3.74 8.62 31.3 33.8 2.30 1.97 1.78 1.57 1.67 1.62 1.33 00 TABLE IVc TRANSMISSION OF GLASS BEADS IN CARBON TETRACHLORIDE WITH A COLLIMATED SOURCE d = 7.75 microns Sample Weight mg. 2.0 3.0 3 4 4.0 Wave Length i b i h ° 1 6.0 m 2*0 4.0 87.0 87.5 89.5 89.0 89.5 91.5 93.1 91.6 75.5 57.8 15.8 62.1 63.1 66.0 68.0 66.6 70.8 76.9 70.9 33.1 17.6 34.7 38.0 39.7 42.8 42.6 43.5 48.7 52.6 44.7 9.34 5.86 25.1 49.4 51.5 53.6 53.6 53.6 58.9 62.2 54.8 18.8 9.78 45.9 30.7 31.6 33.4 33.8 34.1 38.7 42.5 32.9 6.8 2.0 5 50 u sin g se m i-lo g c o o r d in a te s are p resen te d in F ig u res 8 to 10 r e p r e s e n tin g th e tr a n sm issio n as a fu n c tio n p a r t ic l e c o n c e n tr a tio n . A s t r a ig h t l i n e cou ld be drawn through th e p o in ts f o r a c o llim a te d sou rce in d ic a t in g th a t th e fu n c t io n a l r e la t io n s h ip betw een tr a n sm issio n and p o p u la tio n d e n s ity i s G-umprecht and S lie p c e v ic h (8) in d ic a te d th a t th e Mie ex t in c t i o n c o e f f i c i e n t was r e la t e d to th e tr a n sm issio n by th e fo llo w in g eq u a tio n ! m ental d a ta w ith th a t o f (1 0 a ), i t can be se e n t h a t the Mie e x t in c t io n c o e f f i c i e n t was a c o n sta n t and in depen d en t o f the p a r t ic le c o n c e n tr a tio n . From eq u a tio n (1 0 b ), i t can be seen th a t th e e x t in c t io n c o e f f i c i e n t i s p r o p o r tio n a l to th e s lo p e o f th e l i n e r e p r e s e n tin g th e tr a n sm issio n f o r th e c o llim a te d sou rce in F ig u res 8 to 1 0 . -InT = co n sta n t* n -InT = 2 ir~L Q e (10a) or (10b) By comparing th e eq u a tio n d e r iv e d from th e e x p e r i- E. T ran sm ission o f th e D if fu s e Beam The d a ta o b ta in ed w ith th e d if f u s e beam i s p r e s e n t ed in T ab les V to VII and p lo tt e d in F ig u res 8 to 10 on th e Normalized T ransm ission, P ercen t $1 GjdLlim abed Source Number o f P a r tic le s /C u b ic C en tim eter Figure 8a. Transmission of Aluminum Oxide Particles in Carbon Tetrachloride ^ o = 2 .0 /< Normalized T ra n sm issio n , P e r c e n t m m # \ . . I l :' : Number o f P a r t i c l e s / C u b i c C e n tim e te r Figure 8b* Transmission of Aluminum Oxide Particles in Carbon Tetrachloride ^ o = 2 Normalized T ransm ission, P ercen t 53 tourcc Source Number o f P a r tic le s /C u b ic C en tim eter Figure 8c• Transmission of Aluminum Oxide Particles in Carbon Tetrachloride Ao = 3.0 y U . Normalized T ransm ission, P ercen t f t m m m im&tscl Number o f P a r tic le s /C u b ic C en tim eter Figure 8d. Transmission of Aluminum Oxide Particles in Carbon Tetrachloride Normalized T ransm ission, P ercen t Number o f P a r tic le s /C u b ic C en tim eter Figure 8e. Transmission of Aluminum Oxide Particles in Carbon Tetrachloride A O = l j . , 0 Normalized T ransm ission, P ercen t t Di££M s; S ell l mafe Number o f P a r tic le s /C u b ic C en tim eter Figure Transmission of Aluminum Oxide Particles in Carbon Tetrachloride A o as i j . , 5 yCC Normalized T ransm ission, P ercen t 57 Number o f P a r tic le s /C u b ic C en tim eter Figure 8g. Transmission of Aluminum Oxide Particles in Carbon Tetrachloride Ao = 5*0/* - Normalized Transm ission, P ercen t 58 C ollLm ate i I k > 0 UfC( \ Sot r o e d= ©£8/c Number o f P a r tic le s /C u b ic C en tim eter Figure 8h. Transmission of Aluminum Oxide Particles in Carbon Tetrachloride A O = 6 .0 yU . Normalized T ransm ission, P ercen t 59 llm a tM C |U rG € D im i s e So.urea £ Number o f P a r tic le s /C u b ic C entim eter Figure 8i. Transmission of Aluminum Oxide Particles in Carbon Tetrachloride Ao — 7 * 1 yiA. Normalized T ransm ission, P ercen t 60 Number o f P a r tic le s /C u b ic C entim eter Figure 8j. Transmission of Aluminum Oxide Particles in Carbon Tetrachloride Ao = 9.0 juu Normalized T ransm ission, P ercen t <>TTIgfflESS ^ L I Number o f P a r tic le s /C u b ic C entim eter F ig u re 9&» T ran sm ission o f Aluminum Oxide P a r t ic le s in Carbon D isu lp h id e A o = 2 .0//C . Normalized T ran sm issio n , P e r c e n t 62 Goi-limat^d u se isourcis - 4 ■ ■ ■ ! - — i — ! - - I - i - - | - 1 i t - 1 - r - f i 1 — ! - — i ! • + ■ f - i - Number o f P a r tic le s /C u b ic C en tim eter F ig u re 9 b , T ran sm ission o f Aluminum Oxide P a r t ic le s in Carbon D isu lp h id e Ao = 2 , 5? yU- Normalized T ra n sm issio n , P e r c e n t So fe u r e e Number o f P a r tic le s /C u b ic C entim eter F igu re 9 c . T ran sm ission o f Aluminum Oxide P a r t ic le s i n Carbon D isu lp h id e Ao = 3 *0y<*- Normalized Transm ission, P er cen t Number o f P a r tic le s /C u b ic C entim eter F ig u re 9d . T ransm ission o f Aluminum Oxide P a r t ic le s in Carbon D isu lp h id e Ao = 3 *5 / ^ 6S Number o f P a r tic le s /C u b ic C en tim eter F ig u re 9 e . T ran sm ission o f Aluminum Oxide P a r t ic le s in Carbon D isu lp h id e Ao = )± .O yc< - Normalized T ransm ission, P ercen t 66 < fl M i gu.s Q - gouge e Number o f P a r tic le s /C u b ic C en tim eter Figure 9f. Transmission of Aluminum Oxide Particles in Carbon Disulphide Ao = Normalized T ransm ission, P ercen t 67 Source U .l.'-I' I Number o f P a r tic le s /C u b ic C entim eter Figure 9g« Transmission of Aluminum Oxide Particles in Carbon Disulphide ^o = Normalized T ransm ission, P ercen t 68 HEPS Number o f P a r tic le s /C u b ic C en tim eter F ig u re 9h. T ran sm ission o f Aluminum Oxide P a r t ic le s i n Carbon D isu lp h id e Ao = 6 , 0 / U - Normalized T ransm ission, P ercen t 69 Sourc Number o f P a r tic le s /C u b ic C en tim eter F ig u re 9 i . T ran sm ission o f Aluminum Oxide P a r t ic le s in Carbon D isu lp h id e Ao = Q .O y U 70 iimatred a ! l! Number o f P a r tic le s /O u b ic C en tim eter F igu re 9 j . T ransm ission o f Aluminum O xide P a r t ic le s in Carbon D isu lp h id e Ao = 8 . 5^ 0 . Normalized T ransm ission, P ercen t 71 aree D ifru s e Bound 3 Number o f P a r tic le s /C u b ic C en tim eter F ig u re 9k . T ran sm ission o f Aluminum Oxide P a r t ic le s in Carbon B isu lp h id e Ao * 9.0/^- Normalized T ransm ission, P ercen t 72 O Collimated Source 0 Diffuse Source O j_ XI o Number o f P a r tic le s /C u b ic C entim eter F igu re 91• T ran sm ission o f Aluminum Oxide P a r t ic le s i n Carbon D isu lp h id e Ao = 9 «5 > / + Normalized T ransm ission, P ercen t 72 Number o f P a r tic le s /C u b ic C en tim eter F igu re 91 • T ra n sm issio n o f Aluminum O xide P a r t ic le s in Carbon D isu lp h id e Ao = 9*£/ J - Number o f P a r tic le s /C u b ic C en tim eter F ig u re 9m. T ran sm ission o f Aluminum Oxide P a r t ic le s in Carbon D isu lp h id e Xo = 10.0 Normal!zed T ransm ission, P ercen t Number o f P a r t ic le s /C u b ic C en tim eter F ig u re 9 n . T ran sm ission o f Aluminum Oxide P a r t ic le s in Carbon D isu lp h id e Ao = 1 0 .£ y O C Normalized T ransm ission, P ercen t 7 5 Number o f P a r tic le s /C u b ic C en tim eter F igu re 9 o . T ra n sm issio n o f Aluminum Oxide P a r t ic le s in Carbon D isu lp h id e /( o = 11,0/W - Normalized T ransm ission, P ercen t 76 Number o f Par t i d e s/C u b ic C en tim eter Figure 10a. Transmission of Glass Beads in Carbon Tetrachloride AO = 2 . 0 yU. Normalized T ransm ission, P ercen t 77 Number o f P a r tic le s /C u b ic C en tim eter Figure 10b. Transmission of Glass Beads in Carbon Tetrachloride Ao = 2 .5 Normalized T ransm ission, P ercen t Number o f P a r tic le s /C u b ic C en tim eter F ig u re 1 0 c . T ra n sm issio n o f G la ss Beads in Carbon T e tr a c h lo r id e Ao = 3 . 0 # , 3 . ^ # . Normalized T ransm ission, P ercen t 79 Number o f P a r tic le s /C u b ic C en tim eter Figure lOd. Transmission of Glass Beads in Carbon Tetrachloride Ao = ij..0,#, T ransm ission, P ercen t Number o f P a r tic le s /C u b ic C en tim eter F ig u re lO e . T ra n sm issio n o f G la ss Beads in Carbon T e tr a c h lo r id e Ao = 6.0/* Normalized T ransm ission, P ercen t 81 Number o f P a r tic le s /O u b ic C en tim eter Figure lOf. Transmission of Class Beads in Carbon Tetrachloride Xo = 7 .7 /a. Normalized T ransm ission, P ercen t Number o f P a r tic le s /C u b ic C en tim eter Figure lOfe. Transmission of Glass Beads in Carbon Tetrachloride Ao = 9,0yU - TABLE Va TRANSM ISSION O F A L U M IN U M O X ID E PARTICLES IN C A R B O N T E T R A C H L O R ID E W IT H A DIFFUSE S O U R C E d = 12.2 microns Sample Weight mg. 2.0 2.5 3.0 - 3.5 1*.0 Wave Length U.5 5.0 6.0 7.7 9. 6.5 67.5 67.9 65.7 62.8 59.9 59.^ 62.5 73.2 87.8 66. 12.0 1 + 8.8 1*7.2 1 * 6.0 1 * 1 *.5 1*1.3 1 * 1 . 1 * 1 * 1*.6 58.1* 77.2 52. 15.6 1 * 0.0 38.0 35.8 32.5 30.6 30.7 33.7 1 * 6.9 70.5 38. 20.6 30.1 27.9 26.9 25.I* 22. 1 * 23.7 26.3 37.1 63.1 35. 25.3 21*. 2 23.0 21.0 18.5 17.2 18.2 20. 1 * 30.2 56.5 2l+. 29.7 19.2 18.8 17.8 15.6 1U.5 15.3 17.7 26.9 52.8 21. 35.^ 15.2 15.2 13.8 1 2. 1 * 11.1 12. 1 + 11+.3 22.8 1*7.3 10. 38.8 12.6 11.7 11.2 9.55 8.66 10.0 11.3 18.6 1 * 0.0 18. 1 + 1 * . 5 10.8 10.3 9.61 8.1*5 7.69 8.70 10. 1 * 16.1 36.5 10. 1*9.2 9.60 9.1*0 8.1*3 7.89 7.16 7.85 9.26 11+.7 36.7 11. 53.8 8. 9U 8.55 7.91 6.81 6.50 7.16 8.1*5 13.5 31.3 12. 56.5 7.90 6.98 6.59 5.62 5.65 6 . 1 * 8 7.51 12.6 26. 1 + - 63.2 6.78 6.95 6.12 5.61* 5.50 5-95 6.75 10.5 27.1* — 7U. 5 5.76 5.25 5.31 1 * .13 3.93 I +.89 5.1*6 8.86 19.8 - 0 0 7 0 8 0 9 9 0 0 9 0 T A B L E V a TRANSM ISSIO N O F A L U M IN U M O X ID E PARTICLES IN C A R B O N T E T R A C H L O R ID E W IT H A DIFFUSE S O U R C E d * » 12.2 microns Sample Weight mg. 2.0 2.5 3.0 - 3.5 1*.0 W ave Length U.5 5.0 6.0 7.7 9- 6.5 67.5 67.9 65.7 62.8 59.9 59. u 62.5 73.2 87.8 66. 12.0 1*8.8 1*7.2 1*6.0 1 * 1 * . 5 1*1.3 1*1.1* 1*1*.6 58.1* 77.2 52. 15.6 1*0.0 38.0 35-8 32.5 30.6 30.7 33.7 1*6.9 70.5 38. 20.6 30.1 27.9 26.9 25.1* 22.1* 23.7 26.3 37.1 63.1 35. 25.3 2U.2 23.0 21.0 18.5 17.2 18.2 20.1+ 30.2 56.5 2l+. 29.7 19.2 18.8 17.8 15.6 1U.5 15.3 17.7 26.9 52.8 21. 35.U 15.2 15.2 13.8 12.1* 11.1 12.1* ll*.3 22.8 1*7.3 10. 38.8 12.6 11.7 11.2 9.55 8.66 1 0 .Q 11.3 18.6 1 * 0.0 18. 1 + 1 * . 5 10.8 10.3 9.61 8.1*5 7.69 8.70 10. 1 * 16.1 36.5 10. 1*9.2 9.60 9.1+0 8.1*3 7.89 7.16 7.85 9.26 11+.7 36.7 11. 53.8 8.9* 8.55 7.91 6.81 6.50 7.16 8.1*5 13.5 31.3 12. 56.5 7.90 6.98 6.59 5.62 5.65 6.1*8 7.51 12.6 26. 1 * - 63.2 6.78 6.95 6.12 5.61* 5.50 5-95 6.75 10.5 27.1* - 7^.5 5.76 5.25 5.31 1+.13 3.93 1 *. 89 5.1*6 8.86 19.8 - 0 0 7 0 8 0 9 9 0 0 9 0 CD V j J TABLE Vb TRANSM ISSIO N O F A L U M IN U M O X ID E PARTICLES IN C A R B O N T E T R A C H L O R ID E W IT H A DIFFUSE S O U R C E d = 6.28 microns Sample Weight mg. 2.0 2.5 3.0 3.5 4.0 2.9 77.1 72.5 71.5 70.2 71.9 12.1 32.7 30.2 29.9 28.5 29.1 21.8 20.8 20.6 19.6 18.1 18.0 30*5 14.6 13.5 13.3 13.6 l4 .6 27.6 15.7 13.7 13.2 11.5 13.4 35.5 10.8 10.0 10.5 9.55 10.5 42.1 9-25 8.72 9.85 9.35 10.5 1+9.7 7.88 7.44 7-96 7.21 7.68 Wave Length 4.5 5.0 6.0 7.7 9.0 72.5 79.1 88.4 96.4 90.0 33.2 41.2 60.8 82.8 62.0 21.7 28.2 46.8 74.5 40.0 17.2 21.2 35.0 65.5 36.0 16.1 19.6 35.2 69.2 26.0 12.7 15.2 28.1 59.3 21.6 11. 4 lk.2 25.8 56.8 27.5 8.44 11.2 22.2 50.9 23.5 co -F * TABLE VI TRANSM ISSIO N O F A L U M IN U M O X ID E PARTICLES IN C A R B O N DISULPHIDE W IT H A DIFFUSE S O U R C E d = 12.2 microns Sample Weight W ave Length mg. 2.0 2.5 3.0 3.5 4.0 4.5 5-5 6.0 8.0 8.5 9.0 9.5 10.0 10.5 11.0 9.4 7044 68.0 69.0 69.9 71.6 75.4 82.7 82.4 53.1 52.5 51.9 51.4 39.5 51.4 46.8 20.0 45-5 43.3 43.4 44.8 49.6 55.0 67.7 66.5 23.1 25.0 23.6 25.6 19.8 17.4 18.1 31.3 27.2 29.1 29.4 30.6 34.6 4 o .l 48.4 56.3 23.7 13.9 14.6 4.2 - 16.7 - 36.3 21.1 21.5 21.6 22.6 24.7 30.2 43.4 44.0 - 7.3 - - - - - 46.9 16.7 16.3 16.0 16.3 18.0 22.4 33.0 - - - - - - - - 51.1 14.1 13.9 14.9 14.7 16.0 21.1 32.0 32.1 10.0 3.6 7.3 6.7 - - - 60.7 12.2 13.3 13.2 12.7 13.8 17.6 28.7 28.9 - - - - - - - 76.0 7.75 8.84 8.46 7.84 9.08 11.6 19.5 18.0 - - - - - - - a> vn TABLE VII TRANSM ISSIO N O F G LA SS B E A D S IN; C A R B O N T E T R A C H L O R ID E W IT H A DIFFUSE S O U R C E d = 7.75 microns Sample Weight W ave Length mg. 2.0 2.5 3.0 3.5 U.O IrO. 6.0 7VL £^0 U.O 87.0 87.5 89.5 89.0 89.5 91.5 93.1 91.6 75.5 57.8 15.8 62.1 63.1 66.0 68.0 66.6 70.8 76.9 70.9 33.1 17.6 3U.7 38.0 39.7 1 *2.8 1 *2.6 U3.5 1 *8.7 52.6 1 *1*.7 9-3U 5.86 25.1 1*9-U 51.5 53.6 53.6 53.6 58.9 62.2 5U.8 18.8 9.78 1*5-9 30.7 31.6 33. h 33.8 3U. 1 38.7 1*2.5 32.9 6.8 2.0 CD O ' 87 same c o o r d in a te s used f o r the c o llim a te d beam. I t was n o t ed th a t th e d ata p o in ts fo r n orm alized d if f u s e tr a n sm issio n f e l l above th o se fo r th e c o llim a te d beam. T h is i s ch a ra c t e r i s t i c o f m u ltip le s c a t t e r in g , a p r o ce ss in w hich i n i t i a l l y s c a tte r e d energy i s retu rn ed to the measured f i e l d . In some c a se s the lo c u s o f d a ta appeared curved w h ile o th e r s appeared n e a r ly s t r a i g h t . The method used in f i t t in g cu rves to th e se d a ta i s g iv e n in the n e x t s e c t io n . VII. CORRELATION OP RESULTS A . The C o llim a ted T ran sm ission An a ttem p t was made to c o r r e la te th e e x t in c t io n co e f f i c i e n t w ith the method o f Van de H u lst (3 )« In ord er to u se t h is approach i t was n e c e ssa r y to know the d i f f e r ence between th e r e f r a c t iv e in d ic e s o f th e p a r t ic le s and th a t o f the su sp en d in g medium. T h is v a lu e was needed to compute th e phase la g in eq u a tio n ( 5 ) . The r e f r a c t iv e in d ic e s fo r b oth carbon te tr a c h lo r id e and carbon d isu lp h id e were o b ta in ed from the rep o rted works o f Pfund (3 5 ) and K agarise ( 3 6 ) . The o n ly e x te n s iv e d ata rep o rted fo r a lu minum oxid e in the in fr a r e d r e g io n appeared to be th a t o f M a litso n (3 7 ) and were o b ta in ed from m easurements on sap p h ir e . Other d a ta were rep o rted by H arris (3 8 ) on a r t i f i c i a l l y prepared o x id e f il m s . These d a ta seem to be o f q u e stio n a b le v a lu e s in c e th ey vary depending on the method u sed to prepare the f i l m s . The v a lu e s rep o rted were low er than fo r sa p p h ir e . N euberger (3 9 ) summarized the a v a ila b le in fo rm a tio n on th e o p t ic a l p r o p e r tie s o f aluminum o x id e b u t d id n o t g iv e any more p e r tin e n t in fo rm a tio n than th a t con ta in e d in (3 7 ) and ( 3 8 ) . For the aluminum o x id e p a r t i c l e s , the d ata o f Pfund, K a g a r ise , and M a litso n were used to com pute th e phase la g . The phase la g a lo n g w ith the r e l a t i v e 80 89 r e f r a c t iv e in d ex i s in clu d ed in T ables V III and IX. The e x t in c t io n c o e f f i c i e n t s computed from eq u a tio n (10) are a ls o l i s t e d . The th r e e s e t s o f d a ta fo r aluminum o x id e are p l o t ted in F ig u re 11a to t e s t th e v a l i d i t y o f th e approxima t io n o f Van de H u ls t. Four cu rves were used to r e p r e se n t th e d a ta s in c e one s e t , w hich had carbon d is u lp h id e as a su sp en d in g medium, had r e l a t i v e r e f r a c t iv e in d ic e s both g r e a te r than and l e s s th an u n it y . I t can be seen th a t th e ex p erim en ta l d a ta in d ic a te d th e same g en er a l tren d as th e th e o r y . P r io r to th e f i r s t maximum th e m easured e x t in c t io n c o e f f i c i e n t s b ra ck et th e t h e o r e t ic a l o n e s. However, th e r e i s some d isc r ep a n c y betw een th e m easured and th e t h e o r e t i c a l maximum. There i s , how ever, good agreem ent fo r th e m easured maxima o f th e th ree s e t s o f ex p erim en ta l d a ta even though th ey occur a t s l i g h t l y d if f e r e n t phase l a g s . The v a r ia tio n o f phase la g s cou ld be due to a sm a ll erro r in th e assumed r e f r a c t iv e in d ex o f th e p a r t i c l e s , s in c e th e d iff e r e n c e s betw een th e in d ic e s o f th e p a r t ic le s and th e m edia were l e s s than 0 .3 * One p o s s i b i l i t y fo r th e low maximum v a lu e o f th e ex t in c t io n c o e f f i c i e n t would be th e la c k o f d is p e r s io n o f th e p a r t i c l e s . However, during th e sam ple p r e p a r a tio n , i t was n oted th a t th e la r g e r p a r t ic le s d isp e r s e d much e a s ie r than th e sm a lle r o n e s. I f d is p e r s io n d id in flu e n c e th e tr a n s - TABLE V illa C R O SS SECTIO N COEFFICIENTS F O R A L U M IN U M O X ID E PARTICLES IN C A R B O N T E T R A C H L O R ID E d = 12.2 microns R elative Refractive Extinction Mie ive Length Index Phase Cross Section Extinction Microns Lag cm K ^ x 10^ Coefficient Ao na P O 'e Qe 2.0 1.200 11.1 1.99 1.71 2.5 1.192 8.61 2.00 1.68 3.0 1.182 6 . 8 1* 2.03 1.71 3.5 1.176 5.60 2.19 1.87 1*.0 1.162 1 + . 1 * 5 2.61 2.21 k.5 1 . 1U 8 3.63 2.63 2.23 5-0 1.130 2 . 8U 2.26 1.93 6.0 1.092 1.31* 1.50 1.28 7.7 1.031* 0.1*95 0.538 0 . 1*6 9.0 0.87 1.58 1.1*7 1.26 Back Fraction Absorption Cross Scattering o f Back Section * y * Absorption Cross Section Scatter cm-2 x 10b C oefficien t cm ' 2 x 106 B Ua 1 * (T jrr d2 0.51*18 0.272 0.02096 0.0179 0.5767 0 . 281* 0.02001 0.0171 0.6387 0.316 0.01802 0.0151* 0.7109 0.328 0.01812 0.0155 0.8311* 0.320 0 . 01U 06 0.0120 0.7718 0.295 0.00952 0.0082 0.6021 0.266 0.00679 0.0058 0.0257 0.017 0.1531* 0.1330 0.0163 0.0298 0.08781* 0.0751* v O o TABLE VXIIb C R O SS SECTION COEFFICIENTS FO R A L U M IN U M OXIDE PARTICLES IN C A R B O N TETR A C H LO R ID E d = 6.28 microns W ave Length Relative Refractive Index Phase Extinction Cross Section Extinction Back Scattering Fraction of Back Absorption Cross Section Absorption Microns 8m Lag cm"2 x 10° Coefficient Cross Section Scatter cm"2 x 10° Coefficient ko P < r e Q e cm"2 x 10^ B < T a 1 * < r& /ir&2 2.0 1.20 5.72 o.i*6 1.75 0.U6U 1.01 0.00568 0.021U 2.5 1.192 1*.1*2 0.U9 1.85 0.521* 1.07 0 . 00U 6I * 0.0171* 3.0 1.182 3.53 0.53U 2.01 0.572 1.07 0.00227 O.OO86I * 3.5 1.176 2.87 0.582 2.20 0.6156 1.06 0.00231 0.00872 U.O 1.162 2.29 0.582 2.20 0.580 0.99 0.00189 0.00712 1+.5 1.1U8 1.86 0.536 2.02 0.1*28 0.80 0.00236 O.OO89O 5.0 1.130 1.1*6 0 . 1*26 1.61 0.295 O.69 0.00098 0.00370 6.0 1.072 O.692 0.310 1.17 0.118 0.038 0.06819 0.257 7.7 1.03U 0.253 0.01*1 O.15I * 0.0301* 0.71*6 0.00976 0.0369 9.0 0.87 0.810 0.119 0.U5 - 0.0556 - - v O H TABLE IX C R O SS SECTIO N COEFFICIENTS F O R A L U M IN U M O X ID E PARTICLES IN C A R B O N DISULPHIDE d = 12.2 microns tve Length Relative Refractive Index Phase Extinction Cross Section Extinction Back Scattering Fraction o f Back Absorption Cross Section Absorption Microns n p Lag cm x 106 Coefficient Cross Section Scatter cm"2 x 10^ Coefficient U C T J 7 / d h o n& P O e Q e cm x 10 B O 'a . 2.0 1.090 5 . 7 3 2.1U 1 . 8 3 0 . 3 0 7 8 0 . 1 U 3 0 . 0 2 6 7 0.0228 2 / 5 1.090 U.U6 2.30 1 . 9 6 0 . 3 5 2 0 0 . 1 5 3 0 . 0 1 8 3 O .O I56 3.0 1 . 0 8 5 3 . U 3 2.62 2.2U 0 . 3 3 1 5 0.126 0.0211 0.0181 3 . 5 1.080 2.50 2.22 1 . 8 9 0.2986 0 . 1 3 5 0.0258 0.0221 U.O 1.068 2.01 1 . 9 3 1 . 6 5 0 . 2 1 6 3 0.112 0 . 0 3 3 2 0.028U U .5 1 . 06l 1.61 l.UU 1 . 2 3 0 . 1 5 5 8 0.108 0.038U 0.0328 5 . 5 1.052 1.08 0.66 0 . 5 6 V 0.00910 0 . 01U 0 . 0 8 8 7 0.0760 6.0 1 . 0 5 0 . 9 5 5 0.526 0.U50 0.01708 0.032 0 . 08UU 0.0721 8.0 0.81 3 r 0 3 3 1 .1 1 — 1.88 - - - - 8 . 5 0 . 7 7 7 2.22 1 . 9 0 0.2781 0 . 1 2 5 0 . 1 2 5 5 0 . 1 0 7 9 . 0 0 . 7 U 3.61 2 . 3 1 1 . 9 7 0.5866 0 . 2 5 3 0 . 0 1 9 5 1 0 . 0 1 6 3 9 . 5 0.70U 3 . 8 $ 2 . 3 3 1 . 9 9 ( 0 . 9 3 1 2 ) ( 0 . 3 9 8 ) (0.00912) (0.0078) 10.0 0.666 U.7U 2 . U 5 2 .0 9 ( 0 . 6 7 7 8 ) ( 0 . 2 7 5 ) ( 0 . 0 0 U 2 3 ) ( 0 . 0 0 3 6 ) 1 0 . 5 0.615 U.56 2 . 3 5 2.01 - - - - 11.0 0.617 U . 3 2 2 . 3 3 1 . 9 9 - - - v O ro M Ie E xtin ction C o e f f ic ie n t 93 Phase L ag,/0 F ig u re 1 1 a . Mie E x tin c tio n C o e f f ic ie n t fo r Aluminum Oxide P a r t ic le s J 914- m issio n r e a d in g , i t would be ex p ec ted th a t a d iff e r e n c e would be n oted in the r e s u lt s o f the two s iz e s * A check o f| i F ig u re 11a in d ic a te d no d iffe r e n c e * F urtherm ore, I r a n i (1 4 -0 ) s p e c i f i c a l l y recommended carbon te t r a c h lo r id e as a d is p e r s in g a g en t fo r aluminum o x id e . i The p o s s i b i l i t y o f th e r e c e iv e r d e t e c t in g s c a tt e r e d ' l i g h t has been d is c u s s e d p r e v io u s ly and was r e j e c t e d . P rob ab ly, the m ost im portan t rea so n fo r the d is c r e p ancy in th e maximum v a lu e s i s th a t th e powder sam ples were n o t m o n o -d isp e rse . S in c e th e extrem a in th e e x t in c t io n cu rves a re caused by the in te r fe r e n c e betw een th e d if f r a c t - ; ed rays and the tr a n sm itte d r a y s , th e p resen ce o f any non- ' s p h e r ic a l, p o ly -d is p e r s e m a te r ia l would tend to reduce the extrem a. The n o n -sp h e r ic a l n a tu re w i l l make the i n t e r f e r ence phenomena l e s s sh a rp , and the p o ly -d is p e r s e n atu re w i l l cau se the extrem a to occu r a t d if f e r e n t wave le n g th s fo r d if f e r e n t p a r t ic le d ia m e te r s . j A second reason f o r th e d iscr ep a n c y l i e s in the f a c t th a t th e powder was h ig h ly c r y s t a l l i n e and in clu d ed two j I form s, o i and y , w ith th e l a t t e r b ein g th e m ajor form , as ; shown by an X -ray d if f r a c t i o n p a tt e r n . S in c e th e se two i forms are known to vary s l i g h t l y in r e f r a c t iv e in d e x , j t h e ir e x is te n c e cou ld a f f e c t the tr a n sm itte d ra y s by in - i te r n a l r e f r a c t io n so th a t th e Bharpness o f the in te r fe r e n c e p a tte r n s cou ld n o t be a t t a in e d . 9 5 The p r e c i s i o n o f th e m ea su red e x t i n c t i o n c o e f f i c i e n t f o r v a r i a t i o n s i n s i z e and r e l a t i v e r e f r a c t i v e in d e x was v e r y good a s s e e n by th e c l o s e a g r e e m e n t among th e e x p e r i m e n ta l m axim a. T h is f a c t com bined w it h th e p h y s ic a l and d i s t r i b u t i v e p r o p e r t i e s o f th e c lo u d c a n e x p la in th e d i s c r e p a n c y b e tw e en th e t h e o r e t i c a l and m easu red m axim a. A fo u r th s e t o f d a ta , h e r e to fo r e unm entioned, i s th a t o b ta in ed by u sin g carbon d is u lp h id e in the wave le n g th range from 8 to 11 m icro n s. The maximum e x t in c t io n c o e f f i c ie n t was s l i g h t l y below the o th e r d a ta . However, two con d it io n s were d if f e r e n t fo r t h is s e t . F i r s t , th e r e la t iv e r e f r a c t iv e in d ex was l e s s than u n ity ( s e e Table V i l l a ) ; s e c o n d ly , in t h is p a rt o f the spectrum a b so rp tio n becomes im p o rta n t. T his phenomenon tended to redu ce the i n t e r f e r ence extrem a. The computed e x t in c t io n c o e f f i c i e n t s fo r the g la s s beads are g iv en in T able X . A problem e x is te d in the d e term in a tio n o f the r e f r a c t iv e in d e x . A d ata s h e e t from the m anufacturer (i\. 1) rep o rted a r e f r a c t iv e in d ex ©f 1*52 fo r the sodium D l i n e . The m a terial„w as claim ed to resem ble p la te and window g la s s in co m p o sitio n and n o t b o r o s ilic a t e or fu sed q u a r tz . However, in view o f th e la c k o f d ata o f t h is g la s s in th e in fr a r e d r e g io n , th e d is p e r s io n d ata on q uartz was used to compute the phase l a g . These computed r e s u lt s are l i s t e d in T able X and p lo t t e d in F ig u re l i b . TABLE X C R O SS SECTIO N COEFFICIENTS F O R G L A SS B E A D S IN C A R B O N T E T R A C H L O R ID E d = 7.75 microns R elative Absorption R efractive E xtinction Back Fraction Cross W ave Length Index Phase Cross Section E xtinction Scattering o f Back Section . O l L Absorption Microns ?P Lag cm"2 x 10° C oefficien t Cross Section Scatter cm " '2.jX,10° C oefficien t Ao m P ^e Qe cm -2 x 10^ B 1 + <7^/ • 7 7 'd2 2.0 1.032 1.25 0.260 0.592 0.079^ 0.305 0.00939 0.0211+ 2.5 1.025 0.85^ 0.233 0.530 O.O6986 0.299 0 . 01101+ 0.0235 3.0 1.023 0.632 0.197 0. M + 8 0.05371* 0.273 o.oii+6i 0.0312 3.5 1.02 0.1+17 0.153 . 0.31+8 0.01+809 0.315 0.01680 0.0360 1 + /0 1.01 o.ii+o 0.112 0.256 0.05561 0.1+96 0.01316 0.0282 U.5 1.00 0 0.080 0.182 0.00876 0.110 0 . 031+ 1 + 5 0.0737 5.0 0.981 0.262 0.0685 0.156 0.00691 0.101 0.03155 0.0675 6.0 0.93 0.829 0.0870 0.198 0.0071+8 0.086 0 . 01+176 0.0895 7.7 0.80 1.7*+ 0.268 0.609 0.20185 0.7l+9 0.02179 0.01+61+ 9.0 0.83 1.19 0.321+ 0.736 0.01378 0.01+3 0 . 161U 0 0 . 31+50 v O O E xtinction C o e f f ic ie n t 97 H T riT 7 : 1 'mzm Phase Lag, p F ig u re l i b , Mie E x tin c tio n C o e f f ic ie n t fo r G la ss Beads 98 Only f a i r agreem ent was o b ta in ed w ith the th eo ry o f Van de H u ls t . B . The D iffu s e T ran sm ission The r e s u lt s o f n orm alized d if f u s e tr a n sm issio n l i s t e d in T a b les V, V I, and V II were an alyzed by u sin g eq u a tio n (7 ) w hich d e s c r ib e s th e tw o -flu x m odel. The d ata p lo tte d in F ig u res 8 to 10 were u sed to c a lc u la t e the ab so r p tio n c r o ss s e c t io n s and th e back s c a t t e r in g c r o ss s e c t io n s . The method o f l e a s t sq u ares was s e le c t e d as an ap p ro p r ia te means fo r d eterm in in g th e s e c o e f f i c i e n t s . To m inim ize th e sum o f sq u a r e s, eq u a tio n (1 1 ) was d if f e r e n t ia t e d f i r s t w ith r e s p e c t to a , and then w ith r e s p e c t to b , so th a t The sum o f sq u ares can be ex p re sse d as ( 11) k ^ fC ln T e U ) - l n T ( i ,a ,b ) ] ) T ( i , a , b ) ( 12) T ( i ,a ,b ) / C ln T e (i) - lnT( " "2 i= lL T ( i ,a ,b ) - ln T ( i,a ,b ) J < jT (i,a ,b ) 9 ( i 3 ) 9 9 For the sura o f squares to be a minimum, the two e - q u a tio n s above each must eq u al z e r o . T h is r e s u lte d in two n o n -lin e a r a lg e b r a ic eq u a tio n s in two unknowns, a and b . S in c e th e e x tr a c tio n o f th e se two e m p ir ic a l c o n sta n ts cou ld n ot be done d i r e c t l y , a t r ia l- a n d - e r r o r method was u se d . By a llo w in g n , the number o f p a r t ic le s p er u n it volum e, to becomes very la r g e , i t can be shown th a t eq u a tio n (7 ) d eg en er a tes to ^ a s 2m exp C-(°Si + m n)lJ m + a ( l- p ) b Taking th e lo g a rith m o f b oth s id e s , InT = -mnL + + In Cm + a + T h is in d ic a te d th a t as the clo u d becomes v ery d e n se , the p lo t o f tr a n sm issio n a g a in s t p a r t ic le p o p u la tio n on sem i lo g paper w i l l become a s t r a ig h t l i n e . T his tren d was n oted in F ig u re s 8 to 1 0 . By e x tr a p o la tin g t h is s t r a ig h t l i n e , i t was p o s s ib le to o b ta in a s lo p e , fm, where m - (a^ + 2 a b )^ /^ , and an in t e r c e p t , w hich i s the second term on th e r ig h t hand s id e o f eq u a tio n ( 1 5 ) . T his gave two eq u a tio n s in two unknowns th a t were e a s i l y so lv e d to o b ta in i n i t i a l e s tim a te s fo r a and b to be used to s o lv e eq u a tio n s (1 2 ) and (1 3 ) when th e y were b oth equated to z e r o . W ith the i n i t i a l e s tim a te s , eq u a tio n s (1 2 ) and (1 3 ) 100 were so lv e d in th e fo llo w in g m anner. The e s tim a te s were in s e r te d in eq u a tio n ( 12 ) , and a n o n -zero r e sid u e was n o t e d . The e s tim a te f o r a was changed d i f f e r e n t i a l l y and the new r e sid u e was n o te d . These two p o in ts were p lo tt e d on r e c ta n g u la r co o r d in a te paper; a s t r a ig h t l i n e was drawn betw een two p o in ts and e x tr a p o la te d to th e v a lu e o f a , where th e r e sid u e was eq u al to z e r o . T h is v a lu e o f a was then th e n e x t e s tim a te fo r a . The p ro ce ss was rep ea ted u n t i l the r e sid u e became v ery sm a ll and approached z e r o . The r e s u lt in g v a lu e o f a was then used in the second equa tio n w ith the i n i t i a l e s tim a te f o r b . The r e s id u e o f equa tio n ( 13) was n o ted ; b was in crem en ted d i f f e r e n t i a l l y to o b ta in a n oth er r e s id u e . A new v a lu e o f b was computed in the same manner a s fo r a in eq u a tio n ( 1 2 ) . W ith the new v a lu e o f b and the l a s t v a lu e o f a , the f i r s t eq u a tio n was u sed a g a in to o b ta in a new v a lu e o f a , fo r th e new v a lu e o f b . T h is p r o c e ss was rep ea ted u n t i l the v a lu e s o f a and b s a t i s f i e d b o th e q u a tio n s . In ord er to p r o c e ss th e d a ta , a com puter program was w r itte n in F o rtra n IV f o r th e IBM 70ij.O d i g i t a l com puter. The d e t a i l s o f th e computer program are in clu d ed in A ppendix D . The method o f i t e r a t i v e c a lc u la t io n was fou n d , in some c a s e s , to be s e n s i t i v e to i n i t i a l e s tim a t e s . For e x am ple, in th e e x tr a p o la tio n p r o c e ss i t was p o s s ib le to e v o lv e n e g a tiv e v a lu e s fo r a and b . S in c e square r o o ts 101 were needed to be taken o f fu n c tio n s c o n ta in in g th e se p a ram eters, erron eou s s o lu t io n s were som etim es o b ta in e d . T h is d i f f i c u l t y was overcome by u sin g more c a r e f u lly s e le c t e d i n i t i a l e s tim a te s and r e p e a tin g the p r o c e s s . Once th e v a lu e s o f a and b were o b ta in e d , the com p u ter program was d esig n ed to compute t r a n s m is s iv it ie s fo r v a r io u s p a r t ic le c o n c e n tr a tio n s . These v a lu e s were p lo t t e d on F ig u r e s 8 to 1 0 . Smooth cu rves were drawn through th e computed p o in ts and r e p r e se n te d the b e s t f i t o f th e e x p e r i m ental d a ta . A good f i t was o b ta in ed fo r n e a r ly a l l o f th e wave le n g t h s , p a r t ic le s i z e s , and su sp en d in g media c o n sid e r e d . However, as the p a r t ic le d e n s ity in c r e a s e d , th e s c a t t e r o f p o in ts tended to in c r e a s e . T h is was p r im a r ily due to th e low tr a n sm issio n through th e c e l l and to the r e d u c tio n o f s ig n a l- t o - n o is e r a t io o f th e sp e c tr o m e te r . Some d i f f i c u l t y was en cou n tered in o b ta in in g v a lu e s o f a and b fo r Ao ~ 6.0 m icrons in carbon t e t r a c h lo r id e . A good f i t was n o t o b ta in e d , as shown in F ig u re 8h . T h is p o s s ib ly was caused by th e r e l a t i v e l y h ig h a b so r p tio n co e f f i c i e n t f o r th e medium. S in c e the v a lu e s o f a (a = -21® n + ^ a ) are s tr o n g ly in flu e n c e d by th e a b so rp tio n c o e f f i c i e n t , a s l i g h t e r r o r in w i l l cau se a s i g n i f i c a n t e r r o r 0^. The s c a t t e r o f d a ta fo r A0 - 9»0 m icrons (F ig u r e 8j) was q u ite wide and was p r im a r ily due to n o is e in th e 102 sp ectrom eter. These r e s u lt s are q u e stio n a b le . For the c a s e s u sin g carbon d isu lp h id e , some o f the data obtained a t lo n ger wave le n g th s ( Ao > 8 .0 m icrons) a ls o showed co n sid er a b le s c a t t e r . For some runs the e l e c t r i c a l n o ise from the spectrom eter was so high th a t read in gs could not be o b ta in ed . However, c o n s is te n t data were obtained fo r wave le n g th s o f 8 .£ and 9.0 m icrons. The data for the g la s s beads in d ic a te d much l e s s s c a t t e r than fo r the ca se s p r e v io u sly d is c u s s e d . From the v a lu es of a and b , the v a lu es of the ab so rp tio n cr o ss s e c t io n , ^ a , the fr a c tio n o f sc a tte r e d ra d ia tio n d ir e c te d backwards, B (where b = B 0"e) » a^d the ab so r p tio n c o e f f i c i e n t , which i s the r a t io o f the ab sorp tion cro ss s e c t io n to the geom etric cr o ss s e c t io n , were comput ed . These are l i s t e d in T ables VI to X. The back s c a tt e r in g cro ss s e c tio n fo r the aluminum oxide i s given in F igure 12. I t can be seen t h a t , although there was a gen era l c o r r e la tio n fo r the co llim a te d beam, the r e s u lt s o f d if f u s e beam tran sm ission in d ic a te d th a t the maxima of the back s c a t t e r in g are q u ite d i f f e r e n t . This f a c t was ex p ec te d . The e x t in c t io n o f a co llim a te d beam accounted fo r rays th a t were d e fle c te d or s c a tte r e d , w hile the back s c a t t e r accounted fo r d ir e c t io n as w e ll . S in ce the s c a tt e r in g fu n ctio n cannot be c o r r e la te d by a sim ple parameter such as phase la g , n e ith e r can the amount o f back 103’ Wave Length., /*- Figure 1 2 . Back S c a tte r in g Cross S e c tio n o f Aluminum Oxide P a r t ic le s IOIj . sc a tte r * In comparing th e f r a c t io n o f back s c a t t e r , B, some gen eral r u le was apparent* Comparing th e r e s u lt s o f the two s i z e s measured in carbon t e t r a c h lo r id e , the f r a c t io n o f back s c a t t e r v a r ie d in v e r s e ly w ith p a r t ic le siz e # A lso , i n comparing th e 1 2 .2 m icron p a r t ic le s in carbon t e t r a c h lo r id e and in carbon d is u lp h id e , th e la r g e r r e l a t i v e r e f r a c t iv e in dex produced more back s c a t t e r in g . This com p a riso n i s i n q u a lit a t iv e agreement w ith s c a tt e r in g theory* As the p a r t i c l e s iz e param eter, 1T'd/A, became la r g e r , the f r a c t io n o f forward s c a tte r in g in c r e a se d . As th e r e l a t i v e r e f r a c t iv e in d ex in c r e a se d fo r a f ix e d p a r t ic le s i z e , the l i g h t rays which en tered th e sp h e r ic a l p a r t i c l e were more str o n g ly r e fr a c te d and th u s , b en t more towards the r e v er se d ir e c t io n . The valu e o f the back s c a tt e r in g f r a c t io n f o r 6 .2 8 micron p a r t ic le s ( ^ 1 * 0 ) (Table V U I b ), was comparable to th a t ob tain ed by R o e ssle r and H arlacher (lj.2). In t h e ir work, a powder o f magnesium oxid e was d ep o sited on a g la s s s lid e * Transm ission measurements w ith both a d if f u s e and a c o llim a te d source r e s u lte d i n a valu e f o r th e e x t in c t io n cro ss s e c t io n equal to th a t o f the back s c a tt e r in g cro ss s e c t io n . The ab sorp tion cro ss s e c t io n f o r the aluminum oxid e p a r t ic le s i s p resen ted in Figure 13. I t can be seen th a t reason ab ly good agreement was ob tain ed fo r th e 1 2 .2 m icron io £ a o •H •P O C O N. m m o U o C ! o •H •P P. U o m 5 Wave Length, F igure 13* A bsorption Cross S e c tio n fo r Aluminum Oxide P a r t ic le s io 6 p a r t ic le s in the sh o rter wave le n g th s . In the lo n g er wave le n g th s , some d iscrep an cy was e v id e n t but the g en era l trends were good. The comparison o f the data fo r 1 2 .2 micron p a r t ic le s w ith the 6 .2 8 micron p a r t ic le s was in good- q u a lit a t iv e agreem ent. However, the comparison w ith pub lis h e d data on sapphire in d ic a te d th e a b sorp tion to be h ig h er in the p resen t stu d y . G i l le s p ie e t a l. (ij.3) measured the tra n sm issio n through a p ie c e o f sapphire 2.8 mm. th ic k . The Mie a b sorp tion c o e f f i c i e n t computed fo r A0 = 6 was J ^.,6 x 10“3 . The work o f McCarthy (/4 J+ .) agreed q u a li t a t iv e l y w ith t h is d a ta . However, e a r lie r work by McCarthy (i|5) in d ic a te d a stro n g ab sorp tion band a t 2 .7 m icrons. This was claim ed to be due to im p u r itie s in the sample of sap p h ir e . P la ss (lj.6 ) used the a b sorp tion data on sapphire from Gryvnak and Burch (i|.7) to compute Mie a b so rp tio n co - e f f i c i e n t s from 7 x 10 ^ f o r a wave le n g th of 2 microns to 5 x 1 0 for 6 m icrons. However, e m is s iv it y data (I4 .7 ) on p o ly c r y s t a llin e alumina was observed to be g re a te r than fo r s in g le c r y s t a l sap p h ire. Carlson e t a l. (I4 .8 ) measured the e m is s iv it y o f a ro ck et plume w ith aluminum oxide in the liq u id s t a t e and found i t to be two orders of magnitude g r e a te r than pre d ic te d from data on sapphire in the s o lid s t a t e ( ip7) . This was probably due to the h ig h er m o b ility o f e le c tr o n s in the liq u id s t a t e . 107 A comparison of the ab sorp tion between a d is c of p o ly c r y s t a llin e magnesium oxide and a s in g le c r y s t a l was made by Hanna (l+9 )» The former m a teria l was found to have a h ig h er ab sorp tion owing to im p u r itie s entrapped a t the g rain b ou n d aries. Lee and K ingery (50) found t h is same e f f e c t when comparing aluminum o x id e . P lo r io ( 5 1) measured the d i e l e c t r i c p r o p e r tie s o f the s in g le c r y s t a l and p o ly c r y s t a llin e aluminum oxide and found the e l e c t r i c a l conduc t i v i t y fo r the l a t t e r to be h igh er by two orders o f magni tu d e. The former was found to be 9 9*99% pure, w h ile the l a t t e r had im p u ritie s of 0.5% c o n s is tin g o f ir o n , s i l i c o n , sodium, magnesium, and calciu m . Prom electro m a g n etic theory ( 1 6 ) , the Mie ab sorp tion cro ss s e c t io n was shown to be p ro p o rtio n a l to the e l e c t r i c a l c o n d u c tiv ity . T his f a c t im p lied th a t the r e l a t i v e l y impure p o ly c r y s t a llin e phase would have a h igh er ab sorp tion cr o ss s e c t io n . Morizumi and Carpenter ( 2l\.) concluded th a t the data o f sapphire was n ot r e p r e se n ta tiv e of the aluminum oxide p a r t ic le s in ro ck et ex h a u sts. Thus, I t has been shown th a t p o ly c r y s t a llin e alum i num oxide i s not o p t ic a lly id e n t ic a l to sa p p h ire. The h ig h er ab sorp tion c o e f f i c i e n t s obtained in the p resen t work were n ot in c o n s is t e n t w ith those obtain ed in oth er i n v e s t i g a tio n s d e a lin g w ith the p o ly c r y s t a llin e phase. The summary o f the r e s u lt s fo r the d if f u s e tra n s- 108 m issio n o f g la s s beads l i s t e d in Table X i s p lo tte d in F igu re 1I 4 .• The back s c a tte r in g cr o ss s e c tio n was observed to d ecrease w ith in c r e a sin g wave le n g th . A t 7*7 m icrons, a peak was observed fo llo w ed by a drop to the p reviou s l e v e l a t 9 m icrons. The ab sorp tion c o e f f i c i e n t was found to gra d u a lly in c r e a se s l i g h t l y w ith wave le n g th to 6.0 m icrons, fo llo w ed by a dip a t 7.7 m icrons. At 9*0 m icrons i t in crea sed by an order o f m agnitude. I t i s p o s s ib le th at in r e a l i t y , the ab sorp tion cro ss s e c t io n i s h ig h er than measured a t 7*7 m icrons. This would have the e f f e c t of reducing the back s c a tte r in g cr o ss s e c t io n , somewhat. The la r g e in cr ea se in ab sorp tion from 7*7 to 9*0 microns i s in agreement w ith the data of N ich o ls (52) and Boeckner (53) who measured the o p tic a l c h a r a c t e r is t ic s o f quartz in the in fr a r e d r e g io n . The v a lu es o f B, the fr a c t io n of back s c a t t e r f o r the g la s s beads, l i s t e d in Table X were in q u a lit a t iv e agreement w ith those fo r aluminum o x id e . S in ce the r e la t iv e r e fr a c t iv e index fo r g la s s beads in carbon te t r a c h lo r id e was l e s s than th a t o f aluminum oxide in carbon t e t r a c h lo r id e , i t would be expected th a t the valu e o f B fo r the beads would be l e s s . However, the comparison o f Tables V i l l a and X in d ic a te d th a t the v a lu es of B are about the same. The com pensating f a c to r appeared to be the sm aller < / s iz e o f the g la s s beads ( 7*75 microns vs 12*2 ) . 109 M M ■ H i Wave L e n g th ,^ F igure lij.. A bsorption and Back S c a tte r in g Cross S e c tio n s f o r Glass Beads 110 U sing the co n sta n ts B, 0"e , and C T a , i t was p o s s ib le to ob tain the a b s o r p tiv ity o f a cloud o f p a r t ic le s w ith a fr e e su rfa ce w ithout ab sorp tion by the suspending medium. The r e f l e c t i v i t y o f the cloud can be exp ressed as r = o where i 0 i s the in c id e n t i n t e n s i t y in the forward d ir e c tio n and j 0 i s the backward in t e n s it y a t the cloud boundary. U sing eq uation (B -20) d erived in Appendix B fo r f = 0, b sinh(mnL) r = m cosh(mnL) + (a+b) sinh(mnL) The a b s o r p tiv ity ; & - 1 - t - r m + b sinh(mnli) , or oc = 1 ------------------- (16) m cosh(mnL) + (a+b) sinh(mnL) The lim it in g c o n d itio n s fo r equation (16) were of p a r tic u la r i n t e r e s t . For example, i f the number o f par t i c l e s per u n it volume approached zero, then the a b so r p ti v i t y approached zero . I f the cloud became extrem ely dense, then equation (16 ) became = l - _________ iL_________ (17) (a^ + 2a.b)^/^+ a + b I f the back s c a tt e r in g cr o ss s e c tio n was much la r g e r than th a t fo r ab sorp tion or b ^ a , then the equation fo r a th ic k cloud became o C = 1 12a/b 111 ( 18 ) This aquation in d ic a te d the trend o f the a b s o r p tiv ity o f a weakly absorbing but h ig h ly s c a t t e r in g clo u d , such as aluminum o x id e . The ab sorp tion c r o ss s e c tio n n a tu r a lly in crea sed the a b s o r p tiv ity w hile the back s c a tt e r in g tend ed to reduce i t . The back s c a t t e r in g d escrib ed the f a c t th a t some of the energy was r e f le c t e d back to the fr e e sur fa ce which bounded the c lo u d . In a s e n s e , t h is energy was r e f le c t e d from th e clo u d , thus redu cing the a b s o r p tiv ity . I f the o p p o site case occurred, namely where a ^ b , the a b s o r p tiv ity d egenerated to An example o f t h is r e la t io n s h ip m ight be found w ith sm all carbon p a r t i c l e s . I f the s i z e s were very much sm aller than the wave le n g th o f the in c id e n t l i g h t , the s c a t t e r in g would be very sm a ll, w h ile the a b so rp tio n would be h ig h . U sing the v a lu es of b and o " a l i s t e d in T ables V III to X, the a b s o r p t iv it ie s o f aluminum oxide and g la s s beads were computed f o r va rio u s v a lu es o f nL, the number of par t i c l e s per square c e n tim e te r . The r e s u lt s o f th e se compu t a tio n s are p resen ted in T ables XI and X II. The r e s u lt s are p lo tte d in F igu res l £ to 17 f o r v a lu es o f nL = 10^ cm “2 , 107 cm"2 and i n f i n i t y . A v alu e o f 10^ cm"2 would TABLE X Ia ABSORPTIVITY OF ALUMINUM OXIDE PARTICLES IN CARBON TETRACHLORIDE No. Particles/cm^ H O O N l o t 0 0 106 10? Diameter; Mi crons 12.2 12.2 12.2 6.28 6.28 Wave Length Microns 2.0 0.0213 0.157 0.238 — 0 0.0529 2.5 0.0193 0.15k 0.220 — 0 0.01*32 3.0 0.0175 o.iko 0.210 — 0 0.0189 3.5 0.0180 0.139 0.199 ~ 0 0.0223 k.O 0 . 01U 1 0.112 0.168 — 0 0.0183 k.5 0.009 0.081 0.1U3 ~ 0 0.0189 5-0 0.007 0.060 o.iko 0 0.0097 6.0 0.275 0.766 0.928 0.065 0.355 7.7 0.298 0.578 0.923 0.0763 oo 6.28 o.nM 0.136 0.086 0. 08k 0.076 0.099 0. 07k 0.926 0.k3k H 1 1 3 TABLE Xlb ABSORPTIVITY O P A L U M IN U M O X ID E PARTICLES IN C A R B O N DISULPHIDE d = 12.2 microns No. P articles/cm 2 10^ 10^ 0 ° n l W ave Length, microns 2.0 0.0258 0.210 0.3^5 2.5 0.0238 0.151 0.272 3.0 0.0207 0.151 0.299 3.5 0.0252 0.209 0.358 1*.0 0.0312 0.255 0.1*23 U.5 0.0362 0.296 O.U98 5.5 . 0.0825 0.632 0.953 6.0 0.0766 0.561 0.911 8.5 0.1160 0.558 0.599 9.0 0 . 020U 0.169 0 . 21*1 9.5 (0 . 008) (0.077) (0.130) 10.0 (o.ooi*) (0.039) (0 . 101*) 114 TABLE XII ABSORPTIVITY O F G LA SS B E A D S IN C A R B O N T E T R A C H L O R ID E d = 7.75 microns No. Particles/cm ^ 10^ 10^ o» n l Wave Length, microns 2.0 < .01 0.0886 0 . 38U 2.5 < . 0 1 - 0.103 0 .U2U 3.0 < .01 0.13U 0.51^ 3.5 ^ .01 0.152 0.556 k.O < .01 0.130 0.1*90 h.5 0.0131 0.270 O.898 5.0 0.0310 O .267 0.909 6.0 0 . 0^08 0 . 3^0 0.923 7.7 0.017^ 0.175 0.360 9.0 0 . 15! + 0 . 78U 0.960 A b so r p tiv ity 1 1 5 Wave Length, Microns F igure lj?a. A b s o r p tiv ity o f a Cloud o f Aluminum Oxide P a r t ic le s With a Diameter o f 1 2 .2 Microns in Carbon T etra ch lo rid e 116 Wave Length, Microns Figure l£b. Absorptivity of a Cloud of Alpainum Oxide Particles With a Diameter of 6.28 Microns in Carbon Tetrachloride Wave Length, Microns F igure 1 6 . A b so r p tiv ity o f a Cloud o f Aluminum Oxide P a r t ic le s With a Diameter o f 1 2 .2 Microns in Carbon D isu lp h id e A b so r p tiv ity 118 Wave Length, Microns Figure 17• Absorptivity of a Cloud of Glass Beads With a Diameter of 7*75 Microns in Carbon Tetrachloride. 119 correspond to a cloud 1 cm. In depth, whose co n cen tra tio n was 10^ p a r t i c l e s / c c . The a b s o r p tiv ity of aluminum oxide in carbon te tr a c h lo r id e w ith a p a r t ic le s iz e of 1 2 .2 mi crons showed a r e l a t i v e l y low a b s o r p tiv ity fo r wave le n g th s l e s s than 6 m icron s. At 6 microns the ab sorp tion cro ss s e c tio n was a maximum w hile the back s c a tte r in g cross s e c tio n was low . T his r e s u lte d in a maximum a b s o r p tiv ity o f 0.928 fo r an i n f i n i t e l y th ic k clo u d . This valu e may be h igh due to the r e s u lt s of the curve f i t of the tran sm is sio n data fo r th is wave le n g th . At a wave le n g th of 7 .7 , the a b s o r p tiv ity was lower for a d ilu t e cloud but grad u ally approached the valu e measured fo r 6 m icron s. This occurred because the back s c a tte r in g was lower a t 7.7 m icrons. Us in g the s im p lif ie d formula (18) fo r an i n f i n i t e l y th ic k clou d , an a b s o r p tiv ity o f 0.278 was c a lc u la te d for a wave len gth o f 2 m icrons. This compared favorab ly w ith a value o f 0.238 in Table XIa; For the 6.28-m icron p a r t ic le s , the shape of the ab s o r p t iv it y curve was o f the gen eral shape produced by the la r g e r p a r t i c l e s . The valu es o f a b s o r p tiv ity were g e n e r a l l y lower because o f the la r g e r back s c a tte r in g cro ss s e c tio n r e la t iv e to the absorp tion cro ss s e c t io n . A la rg e peak was obtained a t 6 microns in a fa sh io n sim ila r to th a t fo r the la r g e r p a r t i c l e s . However, the value f o r 7*7 microns was sm aller than fo r the la r g e r p a r t ic le s because 120 the back s c a tt e r in g cr o ss s e c t io n was la r g e r . The v a lu es f o r the a b s o r p tiv ity o f aluminum oxide in carbon d isu lp h id e shown in F igure l 6 in d ic a te d the same gen eral trend as th a t fo r carbon t e t r a c h lo r id e . In the range o f wave le n g th s l e s s than 5 m icrons the a b s o r p tiv ity was s l i g h t l y h igher fo r the former suspending medium b e cause of the lower back s c a t t e r in g . For the i n f i n i t e cloud a peak a b s o r p tiv ity o f 0.953 was computed. At la r g e r wave le n g th s a s l i g h t l y d ecr ea sin g value o f a b s o r p tiv ity was noted because o f in crea sed s c a t t e r in g . At a wave le n g th o f 8.5 microns a peak a b s o r p tiv ity was noted fo r a more d ilu t e clo u d . However, as the cloud became more d en se, t h is peak tended to disappear r e la t iv e to the v a lu e s computed fo r s l i g h t l y sm a ller wave le n g th s . T his was caused by the h ig h s c a tte r in g th a t was a tten d a n t w ith the h ig h ab sorp tion a t 8.5 m icrons. The r e s u lt s fo r the g la s s beads shown in F igure 17 in d ic a te d an a b s o r p tiv ity o f a grad u ally in c r e a s in g nature w ith wave le n g th u n t i l the range o f i|..5- 6.0 m icrons was reach ed . At t h is part of the spectrum the r e f r a c t iv e index o f the g la s s was n ea rly equal to th a t o f the suspending medium. The back s c a t t e r was low w h ile the ab sorp tion was g ra d u a lly in c r e a s in g . At 7«7 microns the s c a t t e r in g b e came in te n s e and the a b s o r p tiv ity dropped. At 9 microns the s c a tt e r in g was reduced and the ab sorp tion cr o ss s e c t io n 121 in c r e a se d , g iv in g a maximum a b s o r p tiv ity o f O.96O fo r an i n f i n i t e clo u d . A s im ila r it y in the g en era l shape o f F igu res 15 to 17 was n o te d . T his was p rim a rily due to the f a c t th a t fo r a l l fo u rca a ses rep resen ted in the f ig u r e s , back s c a t te r in g was predominant fo r the sh o rter wave le n g t h s , w hile ab sorp tion was predominant fo r the lo n g er wave le n g th s . The reg io n o f maximum a b s o r p tiv ity was in the p roxim ity o f a wave le n g th o f 6 m icrons. In the fo u r c a s e s , the asymp t o t i c v a lu es of a b s o r p tiv ity fo r i n f i n i t e l y th ic k clouds were from 0 .9 1 to O.9 2 . T his s im ila r it y o f va lu es was due to the f a c t th a t back s c a tt e r in g was n e g lig i b l e and caused the r e f l e c t i v i t y o f the clou d s to be s m a ll. S in ce the tra n sm issio n through an i n f i n i t e l y th ic k cloud approached z ero , the a b s o r p tiv ity approached a valu e between 0 .9 and 1 .0 , as d escrib ed by eq uation (19)* Although f o r the lim it o f a th ic k cloud the four ca se s have the same a b s o r p tiv ity , the v a lu es fo r thin n er clouds are d i f f e r e n t . As an i l l u s tr a tio n fo r the fou r c a s e s , the a b s o r p tiv ity was p lo tte d as a fu n c tio n o f the number o f p a r t ic le s per cm.^ in Figure 1 8 . T his fig u r e ex p resses g r a p h ic a lly the d iffe r e n c e s between the a b s o r p t iv itie s fo r the v a rio u s cloud concen t r a t io n s . The methods and d ata p resen ted h erein can be used to compute the a b s o r p t iv it ie s o f va rio u s p a r t ic le Number o f P a r tic le s/c m ^ F igure 1 8 . A b so r p tiv ity o f Various P a r t ic le Clouds f o r a Wave Length o f 6 .0 Microns 123 c o n c e n tr a tio n c lo u d s , provided the same p a r t i c l e m a t e r i a l, p a r t i c l e s i z e , and su sp en d in g medium are u s e d . E q uation ( 16) can be used w ith the proper v a lu e s o f a , b, n, and 1 . The o n ly unknowns in the e q u a tio n s are a and b . These can be o b ta in ed by lo o k in g in the a p p ro p ria te ta b le f o r (Ta , (T e , and B, and computing the v a lu e s o f a and b . I f the p a r t i c l e s i z e i s d i f f e r e n t but in betw een the s i z e s u sed in t h i s work, i n t e r p o l a t i o n sh ould g iv e v a lu e s fo r the param eters th a t are n o t too f a r o f f . However, i f the com putation i s to be made f o r a d i f f e r e n t su sp en ding medium, c a u tio n sh o u ld be e x e r c i s e d . A l though a g e n e r a liz e d c o r r e l a t i o n o b ta in ed f o r the Mie e x t i n c t i o n c o e f f i c i e n t proved to be s a t i s f a c t o r y f o r the c o l lim a te d so u r c e , i t was n o t p o s s i b l e to g e n e ra te one f o r the d i f f u s e s o u r c e . S in c e the r e l a t i v e r e f r a c t i v e i n d i c e s f o r the p a r t i c l e s and su sp en ding medium would be d i f f e r e n t , the a s s o c i a t e d l i g h t s c a t t e r i n g p r o p e r t ie s would be d i f f e r e n t . P rob ab ly, th e s a f e s t method o f approach would be to o b ta in e x p e rim en ta l data u s in g the d e s ir e d su sp en ding medium. In l i e u o f t h i s , i t m ight be p o s s i b l e to u se the a b s o r p tio n c r o s s s e c t i o n a l data o b ta in ed in t h i s work, determ ine the e x t i n c t i o n c o e f f i c i e n t from the th eory of Van de H u l s t , and e s tim a te the back s c a t t e r i n g f r a c t i o n , B, k eep in g in mind t h a t t h i s work has In d ic a te d in a q u a l i t a t i v e se n se t h a t B 12i|. i s d i r e c t l y p r o p o r tio n a l to r e l a t i v e r e f r a c t i v e in d ex and i n v e r s e l y p r o p o r tio n a l to p a r t i c l e s i z e . i V I I I . SU M M A R Y A survey was made to o b ta in more e f f e c t i v e te c h n iq u es f o r f i n e p a r t ic le c l a s s i f i c a t i o n . A fter c o n sid e r in g variou s schemes, the method o f a ir e l u t r ia t io n was s e le c t e d as th e most advantageous. A system in c lu d in g flo w measuring d e v ic e s was d esig n ed , f a b r ic a te d , and c a lib r a te d . The major p ie c e o f equipment was a la r g e g la s s s e t t l i n g chamber, 6 in ch es in diam eter x lji8 in ch es lo n g . Aluminum oxid e and g la s s beads were s e le c t e d as the candidate m a te r ia ls f o r study s in c e th ey were exp ected to have la r g e s c a tte r in g p r o p e r tie s a t some p o rtio n o f the in fr a r e d spectrum . These p a r t ic le s were separated b atch- w ise in to the fo llo w in g cu ts: 0 -5 m icron s, 5-7 •£ m icrons, 7«f>-10 m icrons, and 1 0 -1 2 .5 m icron s. The aluminum oxid e e a s i l y separated and did n o t adhere to the s id e s o f the s e t t l i n g chamber. C onsiderable adherence was encountered w ith the g la s s b ead s. The p a r t ic le s were s iz e d by measurements taken w ith an o p t ic a l m icroscop e. The mean diam eters o f th e f r a c tio n s o f aluminum oxide agreed w e ll w ith those p red ic te d from Stokes s e t t l i n g law . The g la s s beads were sm aller than p r e d ic te d . This was caused by the adherence of p a r t ic le s to th e w a ll o f the s e t t l i n g v e s s e l . 125 126 L ight tran sm ission measurements were made u sin g a m odified Beckman IR-2A sp ectrom eter in the wave le n g th range from 2 to 11 m icron s. A sample c e l l u sin g a rsen ic tr is u lp h id e windows was d esign ed and b u i l t . Carbon t e t r a c h lo r id e and carbon d isu lp h id e were used as suspending media fo r preparing the v a rio u s p a r t ic le c lo u d s . T ransm ission measurements were f i r s t made u sin g a co llim a te d so u rce. The experim ental tra n sm issio n through the a rsen ic tr is u lp h id e windows c o r r e la te d w e ll w ith pre d ic te d v a lu e s . V arious cloud s were prepared and tr a n s m issio n measurements were made. A p lo t o f norm alized tran sm ission a g a in st p a r t ic le co n cen tra tio n s produced a s tr a ig h t lin e on se m i-lo g paper. Prom the slo p e s o f the l i n e , Mie e x tin c t io n c o e f f i c i e n t s were computed and were compared w ith the d if f r a c t i o n work of Van de H ulst ( 3 ) . Good agreement was obtained f o r the s e v e r a l samples o f aluminum oxid e when the e x t in c t io n c o e f f i c i e n t was p lo tte d a g a in st the phase la g 2 r r d , — i» p - m Good agreement was a ls o ob tained when compared to the th e ory of Van de H u lst, ex cep t f o r th e extrema o f the e x t in c tio n c o e f f i c i e n t . T his d iscrep an cy was claim ed to be caused by, 1) non-uniform p a r t ic le s i z e , 2) a m ixture o f 127 two p o ly c r y s t a llin e p h a se s, and 3 ) n o n -sp h e r ic a l p a r t ic le sh ap e• The r e s u lt s of the g la s s beads agreed reason ably w e ll w ith the th eory, but for the most part included on ly r e l a t i v e l y sm all v a lu es fo r the phase la g . A d iff u s e window was i n s t a l l e d in the sample c e l l and the tra n sm issio n measurements were re p e a te d . The n or m alized tran sm ission was g re a te r than fo r the case o f the co llim a te d source because of m u ltip le s c a t t e r in g . I n i t i a l l y , the data did not l i e on a s t r a ig h t l in e in the d ilu t e range, but a t higher co n ce n tra tio n s tended to be lin e a r on a se m i-lo g p lo t . As the cloud in crea sed in p o p u la tio n , the s c a t t e r of data became la r g e r because o f n o ise e f f e c t s from the sp ectro m eter. A tw o -flu x model proposed by S h u ster (17)» Kubelka and Munk (2S>), and Hamaker (26) was used to c o r r e la te the d a ta . Two em p irical c o e f f i c i e n t s , the back s c a tte r in g cro ss s e c t io n and the a b so rp tio n c r o ss s e c t io n , were ob tain ed by se p a r a te ly ap p lyin g the method o f l e a s t squares to each s e t of experim ental d a ta . A more gen eral c o r r e la tio n was attem pted by combining th ese s e t s to g e th e r .. The param eters o f importance were wave le n g th , d iam eter, and r e fr a c t iv e in d e x . T h is e f f o r t proved to be u n s u c c e s s fu l, in d ic a tin g th a t the s p e c if i c a t io n of on ly the th ree param e te r s mentioned above i s not s u f f i c i e n t to determ ine the 128 two em p irica l c o n s ta n ts . Thus, fo r each ca se to be in v e s t ig a t e d , some experim ental data are n e ce ssa r y to ob tain the c o n s ta n ts . T his la c k o f a g e n e r a liz e d c o r r e la tio n fo r back s c a t t e r was a ls o observed by Twomey and Howell (5^)» In t h e ir work, an attem pt was made to determ ine the v i s i b i l i t y o f the atmosphere by back s c a tte r in g measurements. T h eir co n clu sio n was th a t they were unable to o b ta in a g e n e r a liz e d c o r r e la tio n between e x t in c t io n and back s c a t t e r . The a b s o r p t iv it ie s o f the cloud s were computed from the tw o -flu x model and the two em p irica l c o n s ta n ts . The gen eral trend in d ic a te d a r i s e o f a b s o r p tiv ity w ith a r is e in ab sorp tion cr o ss s e c tio n and a d ecrease w ith a r i s e in back s c a t t e r in g . The r e s u lt s were fu n c tio n s of p a r t ic le s i z e , wave le n g th , and r e la t iv e r e f r a c t iv e in d e x . T his resea rch endeavor has in v e s tig a t e d the in fr a re d tra n sm issio n c h a r a c t e r is t ic s o f two s o lid m a te r ia ls , alum i num oxide and window g l a s s , f i n e l y d isp e r s e d , in the shape o f u n ifo r m ly -siz e d sp h eres, whose diam eters were in the range o f 6 to 12 m icrons. These c h a r a c t e r is t ic s were meas ured in two d if f e r e n t tran sp aren t m edia, carbon t e t r a c h lo r id e and carbon d is u lp h id e . By u sin g a tw o -flu x , d i f fu se model, i t was p o s s ib le to determ ine two em p irica l con sta n ts which d escrib ed the a b sorp tion and s c a t t e r in g char a c t e r i s t i c s o f the p a r t i c l e s . U sing th ese c o n s ta n ts , i t 129 was p o s s i b l e to compute the a b s o r p t i v i t y o f a c lo u d o f th e se p a r t i c l e s w ith an a r b it r a r y p o p u la tio n d e n s i t y . Thus, i t i s p o s s i b l e f o r a d e s ig n e r to o b ta in clo u d a b s o r p t i v i t i e s from the d a ta g iv e n h e r e i n . However, when the su sp en d in g medium i s d i f f e r e n t from th e one u sed in t h i s work, the back s c a t t e r i n g cannot be determ ined p r e c i s e l y , s in c e a g e n e ra l c o r r e l a t i o n does n o t appear to e x i s t . T h e r e fo r e , a d d i t io n a l work must be done by r e p e a t in g the ex p erim en ta l work r ep o rted h e r e i n w ith a d i f f e r e n t su sp en d in g medium such as a i r . In a d d i t io n , the e f f e c t o f u s in g la r g e r p a r t i c l e s co u ld a l s o be i n v e s t i g a t e d . S in c e many i n d u s t r i a l p r o c e s s e s do n o t u se s p h e r ic a l p a r t i c l e s , the r e se a r c h probab ly sh ou ld be extend ed to par t i c l e s o f a r b it r a r y sh a p e . F i n a l l y , i t may be d e s ir o u s to vary the tem perature o f the p a r t i c l e s . The a b s o r p tio n c h a r a c t e r i s t i c s o f th e m a t e r ia l sh o u ld change w ith temper a tu r e and th u s , g iv e d i f f e r e n t a b s o r p t i v i t i e s f o r the c lo u d . IX. REFERENCES 1 . Mie, G ., Ann. P h ysik , 25>, 377 (1 9 0 8 ). 2 . 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M., Journal o f the O p tica l S o c ie ty of America, iiij., No. 1 , 18-21 (January 195>if) • 1 0 . Hodkinson, J . R ., A pplied O p tic s, No. 5 , 839*“Slflf. 130 131 11. 1 2 . 13. 1 1 1-. 15- 16 . 17. 18. 19. 20. 2 1. 22. (May 1 9 6 6 ). Love, T. J . , and W heasler, R. A ., Aerospace R esearch j L ab oratories Report 61j.-109 (June 196^ ). K r a s c e lla , N. L •< » United A ir c r a f t Report C -910092-1, j September I96I 4 .. Marteney, P. J . , U nited A ir c r a ft Report C -910092-2, September 196I|-. Lanzo, C. D ., and R agsdale, R. G. , NASA TN D-lli.05, September 1962. Penndorf, R. B ., Journal o f the O p tica l S o c ie ty o f i America, k-7, No. 7 , 603“603> (J u ly 1957)* | P la s s , G. N ., A pplied O p tic s, 5 , No. 2, 279 -283? | (February 1966)• ; S ch u ster , A.» A s tr o . P hys. , 2 1 , 1 (1 9 0 5 ). Chandrasekhar, S . , R a d ia tiv e T r a n sfe r , Dover P u b lic a t io n s , I n c ., New York, N. Y. ( i 960) . j Kourganoff, V ., B asic Methods in T ransfer Problem s, ! Dover P u b lic a tio n s , I n c ., New York, N. Y. ( 1963) . j V isk an ta, R ., Argonne N a tio n a l Laboratory Report ANL-6170 ( i 960) . Love, T. J.» A eron au tical R esearch L ab oratories ! ---------------------------------------------- j Report ARL 63“3» January 1963. | S t u l l , V. R ., and P la s s , Journal o f the O p tica l j S o c ie ty o f America, $ 0 , 2 , 121-129 (February i 960) . j 132 23* M cA lister, J . A ., Keng, E . Y. H ., and Orr, C ., NASA, CHR-325* November 1965 • 2l*. Morlzuml, S . J . , and C arpenter, H. J . , P r e p r in t, No. 61*-6l, Aerospace S cien ce M eeting, New York, N. Y ., January 2 0 -2 2 , I 96I 4 .• 2 5 . Kubelka, P ., and Munk, F . , Z . Tech. P h y s ic s, 1 2 , 593 (1 9 3 1 ). 2 6 . Hamaker, H. C ., P h i l l i p s R esearch R ep o rts, 2 , 55*103# 112,1*20 (191*7). 27. L arkin, B. K ., and C h u r c h ill, S . W., AIChE Jou rn al, £ , No. 1+, 1*67-1*71* (December 1959)* 2 8 . Chen, J . C ., and C h u r c h ill, S . W., AIChE Jou rn al, No. 1 , 35-1*1 (January 1963)* 2 9 . Lathrop, A. L ., Journal o f the O p tical S o c ie ty o f America, 5 £ , No. 9 , 1097-HOl* (September 1 9 6 5 ). 30. K o ttle r , F . , Journal o f the O p tica l S o c ie ty o f Am erica, 5 0 , No. 5* 1*83-1*90 (May i 960) . 31. Smart, C ., Jacobsen, R ., K erker, M., K r a to h v il, J . , and M a tije v ic , Journal o f the O p tica l S o c ie ty o f America, 5 5 , No. 8 (August 1965)• 3 2 . API R esearch P r o je c t 1*1*, In fra red S p ectra D ata, Carnegie I n s t i t u t e o f T echnology, P ittsb u r g h , P a ., June 30, 1952. 33* Servo. Corporation B u lle t i n , S erv o fra x , A rsenic T r is u lp h id e . 1 3 3 ! 3I 4 .. B a lla r d , S . , McCarthy, K ., and W olfe, W., S t a t e - o f - | th e-A rt R ep o rt. O p tical M aterials fo r In frared In stru m en tation , U n iv e r s ity o f M ichigan, January | 1959 • | 35* Pfund, A. H ., Journal of the O p tica l S o c ie ty of America, 25, No. 11, 351 (November 1935)- 3 6 . K agarise, R. E ., Journal o f the O p tical S o c ie ty o f America, 5 0 , No. 1 , 36 (January i 960) . 3 7 . M a litso n , I . H ., Journal o f the O p tical S o c ie ty o f America, 5 2 , No. 12, 1377 (December 1962) . 38. H a r r is, L ., Journal o f the O p tica l S o c ie ty o f America, ij5, No. 1 , 27 (January 1955)* 39* Neuberger, M., "O ptical P r o p e r tie s and Thermal Con d u c t iv it y o f Aluminum O x id e ,1 ' EPIC R eport, No. S- 6 (February 1965) • lj.0. I r a n i, R. R ., and C a l l i s , C. F . , P a r t ic le S iz e ; Measurement, I n te r p r e ta tio n , and A p p lic a tio n , John W iley and Sons, I n c ., New York, N. Y. (1963)* lj.1. 3M "Superbrite" G lass Beads, T ech n ical Data S h eet, 3M Company, February 1 , 1961. I4.2. R o e s s le r , V. F . , and H orlacher, O ptlk, 1 9 , No. 9* il5l~ I 4-62 (September 1962) . 1^ .3• G i l l e s p i e , D. T ., O lesen , A. L ., and N ic h b ls, L. W., A pplied O p tic s, [j., No. 11, llj.88-ll4.93 (November 1 9 6 5 ). .................................................. i 3 h : Ijlj.. McCarthy, D. E ., A pplied O p tic s, ij., No, 3> 317-320 (March 1965)* I L j.^ o McCarthy, D. E ,, A pplied O p tic s, 2 , No. 1 4 ., 591 (A p ril | 1 9 6 3 ). I 1|6. P la s s , G. N«, A pplied O p tica, Ij., No. 12, l 6 l 6 - l 6 l 9 I (December 1965)* I 4 .7 • Gryvnak, D. A ., and Burch, D. E ., Journal o f the O p tica l S o c ie ty o f America, 5 5 , 625 (1965)* I 4.8• C arlson, D. J . , L ew is, C. H ., Du P u is, R. A ., and i I Bauer, A. B ., S o lid P r o p e lla n t Exhaust R ad iation S tu d ie s , A pplied R esearch L a b o ra to ries, P u b lica tio n , No. U-30I 4 .I 4 ., March 10, 1965. j I 4 . 9 • Hanna, R ., Journal of the American Ceramic S o c ie t y , M . No. 7 , 376-380 (J u ly 1 9 6 5 ). 5 0 . L ee, D. U ., and K ingery, U. D ., Journal o f the American Ceramic S o c ie t y , ijj, No. 11, 59^“607 j i (November i 960) . j 1 5 1 . F lo r io , J . V ., Journal o f the American Ceramic ! S o c ie t y , I 4 .3 , No. 5> 262-267 (May i 960) . 5 2 . N ic h o ls , E. P ., P h y sica l R eview, [j., 297-313 ( I 897) • 53* Boeckner, C ., Journal o f the O p tica l S o c ie ty o f Am erica, ! £ , 7-15 (1 9 2 9 )- 5^ 4-• Twomey, S . , and H owell, H. B ., A pplied O p tic s, ij., No. ifc, 501-506 (A p ril 1 9 6 5 ). 135 B o lla r , P . S . , U. S . Bureau o f Mines T ech n ical Paper U90 (1 9 3 1 ). 5 6 . Schweyer, H. E ., and Work, L. T . , "Methods fo r D eter mining P a r t ic le S iz e D is t r ib u t io n ,” ASTM Symposium on New Methods fo r P a r t ic le S iz e D eterm ination in the Subsieve Range. March 1914-1. 5 7 . Stairraand, C. J . , "Some P r a c tic a l A spects o f P a r tic le 1 S iz e A n a ly sis," Symposium on P a r tic le S iz e A n a ly sis by the I n s t it u t e o f Chemical E ngineers and the S o c ie ty o f Chemical I n d u str y , February L\., 19^4-T* 5 8 . R o lle r , P. S . , ASTM Symposium on Metal Powders, S p e c ia l T ech n ical P u b lic a tio n No. 1I 4 .O (1 9 5 2 ). 5 9 . P o lla r d , R. E ., Journal o f R esearch. N ation al Bureau o f S tan dard s. B h No. 1 (J u ly 1953). 60. R e if , A. E ., W hite, C. S . , and G ib lin , M. E ., A M A A rchives o f I n d u s tr ia l H e a lth . i l l , iji+2 (November 19 5 6 ). 61 . Matheson, G. L ., O il and Gas J ou rn al, November 15> 1914-7. 6 2 . Wen, C ., and H ashinger, R. F . , AIChE Jou rn al, 6 , No. 2 , 220-226 (June i 960) . APPENDICES 1 3 6 APPENDIX A j FINE PARTICLE TECHNOLOGY j I . Theory o f C la s s if ic a t io n i The p a r t ic le s iz e d e sir a b le for t h is research was I in the 2-15 micron range where s c a tt e r in g o f in fr a re d r a d i a tio n w i l l be la r g e . Since p a r t ic le s do n ot o r d in a r ily come in a uniform s i z e , a method was d ev ise d to c l a s s i f y them in to uniform groups. Because of the sm all s iz e s in v o lv e d , i t was not p o s s ib le to use s ie v e s fo r the separa t io n . i A fte r some stu d y, i t appeared th a t e l u t r ia t io n pro- ; vided the b e s t means fo r s i z i n g . The p rocess o f e l u t r i a tio n i s an a p p lic a tio n o f Stokes Law by which a batch of p a r t i c l e s , having a wide s iz e d is t r ib u t io n , can be se p a r a t ed in to cu ts having a r e l a t i v e l y narrow s iz e d is t r ib u t io n . ! The p rocess i s accom plished by p a ssin g a f l u i d v e r t i c a l l y ! through a bed of p o ly d isp e rse p a r t i c l e s . I f th ese par t i c l e s are fa r enough apart so th a t they do not in t e r a c t , S I the v a r ia tio n of the f lu i d v e l o c i t y can sep a ra te th ese par-! t i d e s in to d if f e r e n t s iz e ra n g es. E quating the drag on a | i sphere in Stokes flow to the w eight shows | i v = T§"^cd2( " P ) (A -l) : 137 138 The theory in d ic a te s th a t i f a p a r t ic le has a diam eter l e s s than s p e c if ie d by the above eq u a tio n , i t w i l l be removed from the b ed . I f la r g e r , i t w i l l be r e ta in e d , a p rocess in which the l i g h t components tend to m igrate to the top o f a sep a ra tio n tower, w h ile the h e a v ie r ones remain a t the bottom . E lu t r ia t io n methods have been s u c c e s s f u lly used as an a n a ly tic a l t o o l fo r s iz e a n a ly s is o f f in e p a r t ic le s in the su b siev e s iz e ran ge. Perhaps, one of the f i r s t in v e s tig a to r s to apply t h is method was P . S . R o lle r (55) • Even t u a ll y , h is apparatus became accep ted by ASTM as a standard fo r a n a ly s is and i s now marketed by the American Instrum ent Company. The apparatus which was d esign ed and b u i l t fo r t h is resea rch was based p rim a rily upon the R o lle r appara t u s . Figure 2 shows the b a sic elem ents of the equipment. The powder to be analyzed was p laced in a U -tu b e, which was attached to the bottom o f a se p a r a to r . A j e t of d ried a ir was made to impinge on the powder, cau sin g i t to c i r c u la te and d e-agglom erate. The a i r was d ried to reduce agglom eration . In the s e t t l i n g chamber, the v e l o c it y pro f i l e was d evelop ed. P a r t ic le s whose term inal v e lo c it y (g iv en by Equation A -l) was l e s s than the gas bulk v e l o c it y were ca r rie d out o f the chamber overhead in to a porous th im b le. During the se p a r a tio n , an o s c i l l a t i n g hammer was 139 used on both the sep arator and the U-tube to prevent ad herence of p a r t ic le s to the w a lls . The sep arator was elec-^ t r i c a l l y grounded to reduce e l e c t r o s t a t i c e f f e c t s . The j se p a ra tio n was i n i t i a t e d by s e t t in g the v e l o c i t y o f the air! equal to th a t p red icted by equation ( A - l ) . Every 30 min u t e s , the thim ble was removed and w eighed. When the ra te of c o l le c t io n dropped below 10$ o f the o r ig in a l r a t e , the sep a ra tio n fo r th a t cut was con sid ered com p lete. A fr e s h thim ble was in s t a lle d and the v e l o c it y was in creased fo r the n ext c u t. One problem in the a p p lic a tio n o f the R o lle r -ty p e sep arator was the sharpness o f se p a r a tio n . Schweyer and Work (56) reported on e l u t r ia t io n techniques and found a 15 to 20$ overlap o f s iz e s above and below the s p e c if ie d fr a c tio n by a R o lle r a n a ly ze r. This overlap was claim ed to be caused by p a r t ic le shape and a non-uniform v e l o c i t y d is - j t r ib u t io n . Stairmand (57) performed a p a r t ic le s i z e an aly-j i s i s by u sin g R o lle r equipment and compared the cut w ith a m icroscop e. I t was found th a t se p a ra tio n s were fa r from i sharp, e s p e c ia lly fo r the f in e c u t, and su ffe r e d from j marked sy stem a tic e r r o r . A d isadvantage was noted in the ! f time requ ired fo r complete fr a c tio n a tio n o f c u t s . For ex- ! ample, the 10 micron fr a c tio n was n ot complete a f t e r 8 j hours o f o p e r a tio n . I t was concluded th a t the overlap of la r g e p a r t ic le s was caused by an uneven v e l o c it y 1 1 4 - 0 d is t r ib u t io n . A lso , some o f the f in e s were l e f t in the bed by in e f f e c t i v e scrubbing by the f l u i d i z i n g g a s. I t was in t e r e s t in g to note th a t th ese two e f f e c t s tended to compen sa te each o th e r , sin c e the mean p a r t ic le s i z e , as measured by the e l u t r ia t o r , was q u ite c lo s e to the mean o f the m icroscop ic measurements, even though the in d iv id u a l f r a c tio n s were not sharply c l a s s i f i e d . S p e c i f i c a l l y , the 0-5 micron cu t fo r the R o lle r an alyzer contained 89$ p a r t ic le s l e s s than 5 microns in d iam eter, w h ile the 10-20 micron cu t contained p a r t ic le s w ith in th a t ran ge. Further data regardin g the v e lo c it y p r o f ile in the R o lle r an alyzer were reported by R o lle r ( 5 8 ) . S ep aration chambers were made o f cellop han e so th a t the su rfa ce con tour o f the ascending stream could be observed. Photo graphs in d ic a te d an in te r fa c e th a t was q u ite f l a t . R o lle r exp lain ed th a t in the presence o f suspended d u st, the mo mentum tra n sfe rr ed from the a ir to the w a lls was n e g lig ib le compared to th a t tra n sferred to the d u s t. S in ce the l a t t e r was uniform ly d is tr ib u t e d , as w e ll as b ein g the major r e c ip ie n t o f momentum, the v e l o c it y p r o f ile would a ls o be uniform . Towards the end o f a se p a r a tio n , the d u st con c e n tr a tio n would become very sm a ll, and th u s, the v e l o c it y p r o f ile would d ev elo p . However, in ev a lu a tin g t h is l a t t e r cla im , i t could be sta te d th a t the in te r fa c e may a c t u a lly be the one which e x i s t s between dense and d ilu t e phases o f llj.1 a f lu i d iz e d bod. P o lla rd (59) conducted a c r i t i c a l review o f the R o l l e r apparatus and concluded th a t the b e s t technique was to perform w eighings o f the r e c e iv e r every 30 m inutes and pro ceed to the n ex t cu t when the ca rry -o v er r a te was reduced to 10% o f the i n i t i a l r a t e . R e if e t a l. (60) measured the s iz e d is t r ib u t io n o f a cu t as a fu n c tio n of tim e. He’ concluded th a t the sm aller s i z e s w ith in a cu t came over f i r s t . A ls o , i t was concluded th a t althou gh there i s a gen eral agreement w ith Stok es Law, com plete sep a ra tio n f o r p a r t ic le s under 10 microns i s not p o s s i b l e « Matheson ( 6 l) performed se p a ra tio n s tu d ie s w ith the R o lle r apparatus, hum idifying the a ir by p a ssin g i t f i r s t through a l±0% s o lu tio n o f s u lf u r ic a c id . The h ig h er m ois ture c o n ten t was b e lie v e d to reduce the powder holdup on the w a lls by m inim izing the e l e c t r o s t a t i c ch a rg es. Wen and Hashinger (62) conducted an in v e s t ig a t io n to augment the understanding o f e l u t r ia t io n o f p o ly d isp e r se sy stem s. The e f f e c t o f freeboard space above the f lu id iz e d bed was evalu ated as i t a f fe c te d th e r a te o f e l u t r i a t i o n . I t was d isco v ered th a t i f the freeboard space were g re a te r than the d ista n c e requ ired to f u l l y develop the gas v e lo c i t y p r o f i l e , the e l u t r ia t io n ra te was independent of freeboard sp a c e . 1 k 2 The work reported above provided a number o f c r i t e r ia fo r the d esig n o f the apparatus which w i l l c l a s s i f y as f in e as p o s s ib le , the s p h e r ic a l p a r t ic le s to be used in the in fra red s t u d ie s . I I . E lu t r ia t io n Techniques The c o l le c t io n thim ble was weighed and placed in p o s itio n a t the top o f the e l u t r l a t o r . The U-tube was charged w ith about 30 cc o f powder and the gas tr a in was attach ed to the U -tu b e. The a i r v a lv e on the la b o ra to ry bench was opened, the pressure r e g u la to r was a c t iv a te d , and the globe v a lv e which c o n tr o lle d the a ir flo w was crack ed. The v a lv e was opened fu r th er u n t i l the wet manometer reached a predeterm ined valu e corresponding to the Stokes v e l o c i t y fo r 50 micron p a r t i c l e s . The powder in the U-tube was a g ita te d and f lu id iz e d in the c o n ic a l s e c tio n le a d in g to the s e t t l i n g chamber. Through the s l o t in the s ilv e r e d su rface i t was p o s s ib le to observe the bed, where p a r t ic le s tended to a tta c h them selves to the g la s s w a ll in the c o n i c a l s e c t io n . The powder would con tin u e to b u ild up u n t i l th ere was no more in the U -tu b e, thus ren d erin g the separa tio n p rocess i n e f f e c t i v e . During t h is p ro cess the e x i s t ence o f stron g e l e c t r o s t a t i c fo r c e s was d e te c te d in the U -tu b e. An attem pt to r e c t i f y t h is s it u a t io n was made by Removing the drying system from the gas t r a in . The in 343 crea se in the hum idity o f the f l u l d i z i n g a ir had a profound e f f e c t upon the p r o c e ss. Then, the p a r t ic le s b u i l t up to a f i n i t e th ic k n e ss and s l i d down in to the U-tube to be f lu id iz e d a g a in . At no time were there observed any par t i c l e s b ein g attach ed to the w a ll o f the c y lin d r ic a l s e c tion* T his p art of the bed was extrem ely d i l u t e , and i t was im p o ssib le to d e t e c t any evid en ce o f the p a r t ic le s ' b ein g p resen t in t h is s e c t io n . I n sid e the goose-neck which connected the top of the c o n ic a l s e c tio n to the c o l l e c t i o n th im b le, the p a r t i c le s tended to a tta c h them selves to the low er p o rtio n of the su r fa c e . This was due to the f a c t th a t the a ir was now b ein g d ir e c te d h o r iz o n ta lly through the goose-n eck and thus could not support the w eight o f the p a r t i c l e s . A fte r t h ir ty m inutes, the f lu i d iz in g a ir was shut o f f and the goose neck and c o l le c t io n thim ble were removed from the s e t t l i n g chamber. The goose-neck was c a r e f u lly tapped so th a t the adhering powder would come lo o s e and drop in to the th im b le. The thim ble was then removed and weighed on the a n a ly t ic a l b a la n ce. The n e t gain in w eigh t fo r the i n i t i a l t h ir t y minute run was computed. The apparatus was put to g eth er a- g a in , the a ir flow ra te was s e t a t the same v a lu e , and the p rocess was repeated a g a in . When the n e t in c r e a se in the w eight of the thim ble and co n ten ts fo r a t h ir t y minute p e-- i l A riod was l e s s than ten p ercen t o f the i n i t i a l r a t e , the sep aration was considered to be com p lete, A fr e s h thim ble rep laced the previous one, and the c a p illa r y tube and j e t were replaced by new ones whose flow c h a r a c t e r is t ic s were p r e v io u sly determ ined. The a ir flow was then in crea sed to a p r e v io u sly determ ined valu e correspon ding to the Stokes v e lo c it y fo r 7 •5-micron p a r t i c l e s . The same procedure was repeated again and again u n t i l b atch es o f p a r t ic le s were obtained w ith the t h e o r e t ic a l s iz e ranges o f 0-5 > 5 “7»5> 7*5-10, 1 0 -1 2 .5 m icrons. A t o t a l o f 22 hours was required to ob tain the four c u t s . The resid u e l e f t in the U-tube was removed, the equipment was clea n ed , and a new charge o f powder was in s t a l l e d . The above procedure was rep eated u n t i l enough p a r t ic le s were obtained fo r the in fr a re d tra n sm issio n measurements• The g la s s beads were tr e a te d in a s im ila r fa sh io n as the aluminum o x id e . However, the problem o f powder ad herence to the w a ll could n o t be e lim in a te d . I t was n e c e s sary to co n tin u o u sly tap the e l u t r ia t o r to remove the pow der from the c o n ic a l s e c t io n o f the s e t t l i n g chamber. I l l • P a r t ic le S iz e Measurement Techniques A very minute sample o f the powder was p laced on a m icroscope s li d e w ith a s p a tu la . A drop of TW EEN 20, the ilf5 trade name fo r a d is p e r s in g agent made by the A tla s Powder G o., was mixed w ith th e sample o f powder. A cover s l i p was placed over the m ixtu re. U sin g the e r a se r on the end o f a p e n c il, the cover s l i p was c a r e f u lly moved back and fo r th to provide a sh earin g fo r c e th a t would sep arate the par t i c l e s . The s li d e was then mounted onto the m icroscope and the p a r t ic le s were brought in to fo c u s . U sing the p re v io u s ly c a lib r a te d d iv is io n s in the e y e p ie c e , the sample o f powder was s iz e d , p a r t ic le by p a r t i c l e . APPENDIX B DERIVATION OP THE TW O-FLUX M O DEL FOR DIFFUSE RADIATION The tw o -flu x model assumes th a t th e d if f u s e r a d ia - ■ t io n f i e l d can be sep arated in to two in te r a c tin g f lu x e s , i one t r a v e llin g i n the forward d ir e c t io n , and the o th e r in j th e backward d ir e c t io n . An E u le ria n p o in t o f view i s tak en so th a t th e v a r ia tio n o f i n t e n s i t y o f each f l u x can be con sid ered from p o in t to p o in t. A s im ila r d e r iv a tio n was i j o b tain ed by Larkin and C h u rch ill (3$) • j ! C onsider now an accoun tin g o f each o f th e two f l u x - j i e s as th ey pass through an elem en tal volume fo r stea d y I i s t a t e c o n d itio n . •rl •H J - f 5 - dx dx dx i + | i d x dx where i i s the in c id e n t f l u x , forward d ir e c t io n ; lil.6 lltf dt i + dx i s the emergent f lu x ; InB o " edx i s the l o s s from the forward f l u x due to back s c a t t e r . I t , th e r e fo r e , i s a g a in by the backward f l u x . i ( n c Tq , + otm)dx i s th e l o s s from th e foward f lu x due to ab sorp tion w ith in the elem en tal volume. The f i r s t term, incr*adx r e p r e se n ts the l o s s by the ab sorp tion by the p a r t ic le s and the second term, io^dx r e p r e se n ts a l o s s by th e absorp tio n by the suspending medium, j i s the in c id e n t f lu x , backward d ir e c tio n ; j - 4^- dx i s the emergent f l u x , backward d ir e c tio n ; dx jnB Q -'edx i s the l o s s from th e backward f l u x due to back s c a t t e r . I t , th e r e fo r e , Is a ga in by the forward f l u x . jCnc^ + o J ft)dx i s the l o s s from th e backward f lu x due to ab sorp tion w ith in th e elem en ta l volume, s im ila r to th a t f o r th e forward f l u x . An accoun ting f o r th e foward f lu x in d ic a te s i + jnB crQ dx = i ( n < T a + otm)dx + inB cr0dx + i + H dx (B -l) ° r H = -i(n B cre + n cra + < *m) + jnB cre 1 1 4 - 8 For the backward f lu x j + inB o 'e d x = -3(n cra + <*m)dx + jnB credx + j - dx (B-2) or M = j(nB cre + n cra +<*m) - inB cre As a check on the o v e r a ll energy b a la n c e, eq u ation s (B -l) and (B -2) may be added to g e th e r to g iv e i + j = i( n cra + ^ m)dx + j(n < ra +c*m)dx + i + d i + j - dj This i s c o n s is te n t w ith the o v e r a ll energy balance around the elem en tal volume, which to e f f e c t , s t a t e s th a t the ab so r p tio n w ith in the volume i s equal the n e t change o f the two flu x e s in c id e n t upon i t . By a llo w in g a = cra + <*m / n b = B cr© | | = - ( a + b )in + bjn (B -3)a - | | = - ( a + b )jn + bin (B -3)b Equations (B -3)a and (B -3)b can be uncoupled by d i f f e r e n t i a tin g each to o b ta in = - ( a + b)n H + bn (B-l|.)a - = - ( a + b)n 1 1 + bn ~ (B-ij.)b dx dx dx I n s e r tin g e x p r e ssio n s f o r the f i r s t order d i f f e r e n t i a l s from (B -3 )a and (B -3)b in to (B-ij.)a and (B-lj.)b 2 “ -(a+ b )n [-(a + b )in + + bn [(a+b) jn - b in j - “ “(a+b)n £+(a+b)jn - b i n j + b n [-(a + b )in + bjn] By combining terms | | | = [(a + b )2n2 -(bri)2 ] 1 = [(a+b)2n2 -(brtpj J o r & - dx£ S im p lify in g = [ a 2 + 2ab] in 2 (B -£ )a dx - ra2 + 2ab 1 jn2 (B-5>)b d x ^ L E quations (B -5 )a and (B -5)b in d ic a te th a t the dependent v a r ia b le s i and j have been separated in to two lin e a r , second order d i f f e r e n t i a l eq u a tio n s. The s o lu tio n s fo r eq uations (B -£ )a and (B-f>)b are i * A sin h mnx + E cosh mnx (B-6) j = C sin h mnx + D cosh mnx (B-7) where ra - \|a2 + 2ab The boundary co n d itio n s fo r these eq u ation s are x = 0 , i = i 0 x = L, J * P i In oth er words, a t the end o f the c e l l , the back* i5o ward f lu x i s equal to the forward f lu x tim es the r e f l e c t i v i t y . . E xp ression s fo r A and E can be ob tain ed by f i r s t d if f e r e n t i a t in g eq u ation s (B -6) and (B-7) • d i ^ = A mn cosh mnx + E ran sin h mnx (B -8 )a = C mn cosh mnx + D ran sin h mnx (B -8)b At x = 0 d i/d x ) x=0 = A mn (B-9) d j/d x )x=0 = C a n (B-10) j ) x =0 = D ( B - l l ) i ) x=0 = E (B-12) E v a lu a tin g eq uation (B -3)a a t x = 0 and s u b s t it u tin g the e x p re ssio n from eq uation ( B - l l ) d i/d x)xsso = - ( a + b )n io + bn D Comparing t h is to eq uation (B -9) in d ic a te s Am = - ( a + b ) io + bD (B -13) E valu atin g (B -3)b a t x = 0 and s u b s tit u t in g the ex p re ssio n from eq uation ( B - l l ) -d j/d x ) x = q - ~ (a + b)Dn + bion Comparing t h is to equ ation (B -10) shows -Cm = - ( a + b)D + b i 0 (B-lij.) U sing the boundary co n d itio n a t x = L and eq u ation s (B -6) and (B -7) 1*1 p [ A sin h mnL + io cosh mnL ] = C sin h mnL + D cosh mnL ( b -1 5 ) E xp ression s (B-13)> (B -llj.), and (B -l5 ) r e p r ese n t a s e t o f th ree eq u ation s in th ree unknowns. The co n sta n t C can be elim in a ted from eq u ation (B -l£ ) by u sin g equation (B-llO or p [A sin h mnL + io cosh mnL] D - H s j s i n h mnL + D cosh mnL (B -l6 ) S u b s titu tin g the e x p re ssio n f o r D from equ ation (B-13) in to equ ation (B -l6 ) { (?[A sin h mnL + io cosh mnL ] = S . [ 4 5 + i o ] - Sinh m a . + £ i 0 ] cosh mnL By combining terms A [ sin h mnL - l a- ^~I sin h mnL - 3 j j j cosh mnL] = i0 [ - cosh mnL + sin h mnL + (-a^?.l cosh mnL J io {Ca + b ( l - P )] cosh mnL + m sin h mnL] or ^ -m cosh mnL - [ a + b ( l - p )J sin h mnL (B-17) S u b s t itu t in g the ex p re ssio n fo r A in to eq u ation (B-6) 152! , _ Ca4b(l"<°)3 cosh mnL + m sin h mnL , 0 m cosh mnL + [ a + b d - p ) ] sin h mnL n ranx + i 0 cosh mnx E v a lu a tin g i a t x = L Ca+bCl-z^lcosh mnL sin h mnL + m sinh^ mnL - 1(L) = _ m cosh^ mnL ■ Ca+bd-/?) J sin h mnL cosh mnL io m cosh mnL + fa + b d -^ J J sin h mnL i(L ) _ ________________ 1___________________ oi» j j _ a+b( l - p ) o cosh mnL + C J sin h mnL m N orm alizing 'with r e s p e c t to the tr a n s m is s iv ity of the su s pending medium, T = : ----------------------------— .------------------------------- (B-18) T . a + (l-i°)b . , cosh mnL + ------- sin h mnL m The r e f l e c t i v i t y o f the cloud can be obtained by e v a lu a tin g D, sin c e from eq uation (B-r7) j (0 ) = D Prom eq uation (B-13) n = Am _ (a+b) A D “ “ b b “ io U sing eq u ation (B-17) j, B m . Ca+b(l-P)J cosh mnL + m sin h mnL + a+b * b ° -m cosh mnL - C a+bd-fO J sin h mnL b 0 D * i0 £ fa+b( 1-/3)-a -b j cosh mnL+(m-^~^§t+b( l-<o)j)sinh mnL b -m cosh mnL - [a+b(l-p)J sin h mnL 153 D = io{-m poosh *** ^ ( 1 - P H . * ^ ( l - p ) ^ sin h m n h } -m cosh mnL - £ a + b (l-p )] sin h mnL iofm p cosh mnL + C~a. P + M ItP )7 sin h mnL} D r = — — .................„ - . — ........... ........... ............(B -19) m cosh mnL + ^a+bCl-fO "J sin h mnL o . „ _ J(0) S in ce r - the r e f l e c t i v i t y r becomes _ f>m cosh mnL + [ b ( l - p ) - a f J sin h mnL m cosh mnL + j " a+b( 1-f ) ] sin h mnL (B-20) APPENDIX C DERIVATION O P TRANSMISSION PARAM ETERS FO R THE SAMPLE CELL Case I - T ransm ission through the window w ith d if f e r e n t r e f l e c t i v i t i e s a t the g la s s in t e r f a c e . r = m-PiKi-Pj.) [ i + e-fz?2 + (P!p2)2r ^ + j _ ru*Pi)d-p2) Ti = ( 1-P1P 2 r 2> R 1- Pxp2r* + (c -i) 1 = Pg r ^ i - P i ) 2 [1 + Pj.P2r+ (PjP2>2r+ ■■■■]* px (0-2) 1 5 1 ) 1 5 5 Case I I - Transm ission through th© sample c e l l TcT T = 7 ''c t 12[ 1 + T o r 2 + ^ *2^ * ----- J 2 T = r 0Ti ‘ i - r 2oE22 p (0 -3 ) (0 -^ ) APPENDIX D FORTRAN CO M PUTER PR O G R A M FOR THE DETERMINATION OF BACK SCATTERING AND ABSORPTION CROSS SECTIONS FORTRAN SOURCE LIST 0 6 /0 6 /6 6 ISN SOURCE STATEM ENT 0 $IBFTC BNGJOB LIST,REF ^ 1 D IM EN SIO N AG (2 ),SIGA(2 ),BG(2 ) ,SIGB(2 ),T A U (100),RHO(100),EN(100), IC(IOO),EM(100),EPLUS(100),EM INUS(100),C S H M N L (100),SN H M N L (100), 2XA(100),XB(100),XC(100) 2 1000 READ1, N, ND, EL, ALPHA, DIA, XLAMB,FACT, EPSA, EPSB,TAUC,AG(l),BG(l) 5 1 F0RMAT(234/(6E12.8)) 6 NDIAGS = ND 7 BEAD 2 9 , (TA U (I),R H O (I),EN(I),I=1,N) 14 29 FORMAT(3E12.8) 15 NBLOOP = 0 16 2 BG(2) = FACT#BG(1) 17 DO 3 1= 1 .2 20 B = BG(I) 21 NALOOP = 0 22 4 AG(2) = FACT*AG(1) 23 D O 5 J=1.2 24. A = AG(J) 25 SIGA(J) = 0 . 0 26 DO 8 K=1,N 27 C(K) = (A+ALPHA/EN(K)) 30 EM(K) = SQRT(C(K)#*2+2.«C(K)*B) 31 EPLUS (K) = EXP(EM(K)*EN(K)*EL) 32 EMINUS(K) « 1 ./EPLUS(K) APPENDIX D (c o n 1t . ) SOURCE STATEM ENT CSHMNL(K) = .5*(EPLUS(K)+EMINUS(K)) SNHMNL(K) = .5*(#PLUS(K)-EMINUS(K)) XA(K) = l./(CSHMNL(K) + (C(K)+B*(l.-RHO(K)))*SNHMNL(K)/EM(K)) XB(K) = (EM(K)**2*EN(K)*EL*(C(K)+B)-CC(K)+B*(1.-RH0(K)))*(C(K)+B) 1+EM(K)**2)/EM{K) #*3'*SNHMNL(K) +EN(K)*EL*(C(K)+B*( 1 • -RHO(K)) ) * (C ( K) 2+B)*CSHMNL(K)/EM(K)**2 SIGAA » ALOG(TAU(K)/(TAUC*XA(K)))*XB(K)*XA(K) SIGA(J) = SIGA(J)+SIGAA 8 CONTINUE IF(ABS(SIGA(J)).LT.EPSA) G O T O 6 5 CONTINUE G O TO( 3 0 ,3 1 ) ,NDIAGS 31 PRINT 27,AG(1),SIGA(1),AG(2),SIGA(2) 27 P0RMATC2X,5HA1 = E13.6,2X,6HSA1 = E13.6,2X,£HA2 a E13.6,2X,6HSA2 = 1 E 1 3 .6 /) 30 AG(1) = A G (l)-SIG A (l)*(A G (2)-A G (l))/(SIG A (2)-SIG A (l)) NALOOP = NALOOP+1 IP(NAL00P.LT.30) G O T O Ij. PRINT 25 25 FORMAT(/5X,15HA LOOP OVERFLOW ) G O TO 1000 6 SIGB(I) = 0 .0 D O 9 K=1,N XC(K) a (EM(K)#*2*ENCK)*EL*C(K)-(C(K)+B*(1.-RH0(K)))* C(K)+EM(K)** 12*(1.-RHO(K)) ) *SNHMNL(K)/EM(K)**3+EN(K)*EL*C(K)*(C(K) +B*(1.-RHOCK 2)) )#CSHMNL(K)/EM(K)**2 SIGBB = ALOG(TAU(K)/(TAUC*XA(K)) )*XC(K)*XA(K) , 9 SIGB(I) = SIGB(I)+SIGBB ' ISN 71 77 100 1 0 1 102 103 106 10? 110 1 1 1 112 117 120 121 APPENDIX D ( c o n 't .) SOURCE STATEM ENT IF(ABS(SIGB(I)) .LT.EPSB) G O T O 7 3 CONTINUE G O T0(i{.0,ij.l) ,NDIAGS lj.1 PRINT 28,BG (1),SIG B(1),BG (2) ,SIGB(2) 28 FORMAT(2X,5HBltsgl3.6 , 2X,6HSB1 = E13.6,2X,£HB2 = E13.6,2X,6HSB2 = 1 E 1 3 .6 /) ij.0 BG(l) = BG(1)-SIGB(1)*CBG(2)-BG(1))/(SIGB(2)-SIGB(1)) NBLOOP = NBLOOP+1 IF(NBL00P.LT.30) G O T O 2 7 PRINT 20 20 FORMAT(1H1/2OX,33HB0B NAGY SPECIAL DATA CORRELATION) PRINT 10* ALPHA, DIA,XLAMB, TA U C , A, B 10 FORMAT(//5X,8HALPHA = E13.6,3X,7HDIAM = E13.6,3X,9HLAMBDA = E 1 3 .6 / l/9X,7HTAUC = E13*6,6X,1]JHA = E13.6,8X,ljHB = E13.6///26X,2H XA,l6X,2H 1EN/) PRINT 11,(X A (I),E N C I),I= 1,N ) 11 F0RMAT(20X,E13.6,5X,E13.6) G O T O 1000 END i-» \n c»

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University of Southern California Dissertations and Theses

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Creator Nagy, Anthony Robert, Jr. (author)

Core Title Absorption And Scattering Of Thermal Radiation By A Cloud Of Small Particles

Degree Doctor of Philosophy

Degree Program Chemical Engineering

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

Tag engineering, chemical,OAI-PMH Harvest

Language English

Contributor Digitized by ProQuest (provenance)

Advisor Lenoir, John M. (committee chair), Mannes, Robert L. (committee member), Rebert, Charles J. (committee member)

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c18-135894

Unique identifier UC11360212

Identifier 6710771.pdf (filename),usctheses-c18-135894 (legacy record id)

Legacy Identifier 6710771.pdf

Dmrecord 135894

Document Type Dissertation

Rights Nagy, Anthony Robert, Jr.

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the au...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus, Los Angeles, California 90089, USA