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The viscosity of liquids (a) Normal octanol at atmospheric pressure (b) An equipment for high pressures De Verteuil, Georges Francois 1958

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THE VISCOSITY OF LIQUIDS (a) Normal Octanol at Atmospheric Pressure (b) An Equipment f o r High Pressures by GEORGES FRANCOIS DE VERTEUIL B. A., Cambridge U n i v e r s i t y , 1956 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF. THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of CHEMICAL ENGINEERING We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA December 1958 i i ABSTRACT Theories of L i q u i d V i s c o s i t y lead to equations g i v i n g the v a r i a t i o n of the v i s c o s i t y w i t h temperature and pressure, but give poor agreement w i t h experimental v a l u e s , p a r t i c u l a r l y f o r a s s o c i a t e d compounds such as normal a l c o h o l s . The l a c k of accurate measurements under pressure f o r these compounds i s being p a r t i c u l a r l y f e l t i n the development of such t h e o r i e s . Apparatus has been assembled and c a l i b r a t e d f o r c a r r y i n g out measurements on the normal a l c o h o l s over a range of pressures to 10,000 p s i and temperatures to 100°C. P a r a l l e l w i t h the development of t h i s pressure viscometer, the v i s c o s i t y of n-octanol at atmospheric pressure has been determined i n standard c a p i l l a r y viscometers f o r a range of 15° to 90°C. The data have been examined and c o r r e l a t e d on the b a s i s of standard v i s c o s i t y - t e m p e r a t u r e equations w i t h emphasis on t h e i r relevance i n an important homologous s e r i e s . The r e s u l t s have l a i d the groundwork f o r measurement under pressure. In presenting t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree that the L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r reference and study. I f u r t h e r agree that permission f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e . I t i s understood that copying or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission. George F. de V e r t e u i l Department of Chemical Engineering The U n i v e r s i t y of B r i t i s h Columbia, Vancouver S, Canada. Date 19th December, 1958. i i i TABLE OP CONTENTS ABSTRACT i i TABLE OP CONTENTS i i i LIST OP TABLES v LIST OP FIGURES v i LIST OP APPENDICES v i i NOMENCLATURE v i i i ACKNOWLEDGMENT x i I INTRODUCTION 1 I I THEORY AND CORRELATION OP LIQUID VISCOSITIES (a) General Theory 16 (b) Theory of Corresponding States 26 (c) E f f e c t of Temperature on the V i s c o s i t y of L i q u i d s 30 (d) E f f e c t of Pressure on the V i s c o s i t y of Li q u i d s 35 (e) Theory i n R e l a t i o n to the Normal Al c o h o l s 42 I I I APPARATUS AND PROCEDURE (a) C a p i l l a r y Viscometers • 47 (b) The Pressure Viscometer 66 (c) D e n s i t y Determinations 85 (d) Pressure Equipment 87 (e) Transfer Apparatus 91 ( f ) Procedure f o r I n t r o d u c t i o n of Sample, and P r e s s u r i z i n g 92 i v IV NORMAL OCTANOL PURIFICATION AND CHARACTERIZATION 95 V RESULTS (a) V i s c o s i t i e s at Atmospheric Pressure 98 (b) D e n s i t y Determinations 102 (c) C a l i b r a t i o n of R o l l i n g - B a l l Viscometer 102 VI DISCUSSION (a) The Pressure Apparatus 112 (b) . V i s c o s i t y Measurements at Atmospheric Pressure 115 (c) The P u r i t y of n-octanol 117 (d) The V i s c o s i t y of n-octanol 118 LITERATURE CITED 121 APPENDICES 130 i V LIST OP TABLES Table Page 1 Approximate Values of Surface Tension-Density R a t i o f o r Common Organic L i q u i d s 60 2 P h y s i c a l P r o p e r t i e s of n-Octanol from the L i t e r a t u r e 97a 3 C a l i b r a t i o n of C a p i l l a r y Viscometers by Comparison 104 4 C a l i b r a t i o n of- C a p i l a r y Viscometers w i t h D i s t i l l e d Water at 20°C 105 5 V i s c o s i t i e s and D e n s i t i e s of O i l s D,E and P 106 6 V i s c o s i t y and Density of n-Octanol 107 7 C o r r e l a t i o n of Viscosity-Temperature Data f o r n-Octanol 108 8 C a l i b r a t i o n of Pyknometers 109 9 C a l i b r a t i o n of Pressure Viscometer 110 10 C o r r e l a t i o n f o r Pressure Viscometer 111 v i LIST OP FIGURES To Follow Figure Page 1 Cannon-Fenske Viscometer 47 2 Drying System f o r C a p i l l a r y Viscometer 48 3 R o l l i n g - B a l l Viscometer 68 4 Timing System f o r Pressure Viscometer 71 5 C r i t i c a l Reynold's No. f o r R o l l i n g - B a l l Viscometer 77 6 C o r r e l a t i o n Factor f o r R o l l i n g - B a l l Viscometer 77 7 Assembly of Pressure System 87 8 Transfer Bomb 89 9 Transfer Apparatus 91 10 V i s c o s i t y of n-Octanol 100 11 C a l i b r a t i o n of Pressure Viscometer 103 12 C a l i b r a t i o n of Thermometers 136 13 Pulse Generator 143 / v i i APPENDICES Page I . B i b l i o g r a p h y on Pressure Viscometry. 130 I I . C a l i b r a t i o n C e r t i f i c a t e f o r C a p i l l a r y Viscometer, B78. 133 I I I . C a l i b r a t i o n of Thermometers 135 IV. Operating I n s t r u c t i o n s f o r Pressure Viscometer. 137 V. E l e c t r o n i c Timer 142 VI. Design of Pressure Bombs 144 v i i i NOMENCLATURE A = atomic weight, pre-exponential f a c t o r B = E/R i n v i s c o s i t y — t e m p e r a t u r e equation C = c a l i b r a t i o n constant f o r viscometer D = d i f f u s i v i t y , tube diameter ( r o l l i n g - b a l l ) E = energy of a c t i v a t i o n E^ = i s o c h o r i c energy of a c t i v a t i o n P = shearing f o r c e , e f f e c t i v e f o r c e on b a l l due to g r a v i t y ^P* = f r e e energy of a c t i v a t i o n (Eyring Theory) H = X-^  — X2 = d r i v i n g head i n c a p i l l a r y viscometer AH* = enthalpy of a c t i v a t i o n (Eyring Theory) I = Souders' c o n s t i t u t i v e f a c t o r K = a d i a b a t i c c o m p r e s s i b i l i t y , c o r r e l a t i o n f a c t o r f o r r o l l i n g - b a l l viscometer L = le n g t h of c a p i l l a r y , l e n g t h of viscometer tube M = molecular weight P = pressure Q, = volume flow through c a p i l l a r y R = r a d i u s of c a p i l l a r y , gas constant, f l u i d r e s i s t a n c e AS^ = entropy of v a p o r i z a t i o n AS* = entropy of a c t i v a t i o n (Eyring Theory) i x T = absolute temperature V = atomic vaolume, e f f e c t i v e volume of c a p i l l a r y viscometer, b a l l v e l o c i t y W = constant i n B a c h i n s k i i equation, c o r r e c t i o n to Stokes Law f o r w a l l - e f f e c t A,B,C,D,G, and K are used as constants a = l a t t i c e parameter (Eyring Theory) d = diameter, b a l l diameter d^ = diameter of lower r e s e r v o i r of c a p i l l a r y viscometer g = g r a v i t a t i o n a l constant h = mean h y d r a u l i c diameter, Plank's constant k = Botlzmann constant, thermal c o n d u c t i v i t y k^ = absolute r e a c t i o n r a t e (Eyring Theory) m = mass of a molecule, k i n e t i c energy f a c t o r , mass of b a l l n = number of molecules / u n i t volume n^ - = pressure c o r r e l a t i o n f a c t o r f o r E y r i n g Theory p = pressure q 0 = constant i n Lederer equation r = l e n g t h parameter, r a d i u s of a molecule r-|_ = r a d i u s of e f f l u x bulb = r a d i u s of lower r e s e r v o i r t = time, e f f l u x time, r o l l time u = mean f l u i d v e l o c i t y v = point v e l o c i t y , s p e c i f i c volume x a,b,c,and n are used as constants X constant i n Andrade e q u a t i o n ? c o e f f i c i e n t of thermal expansion = v a r i a b l e defined i n equation (72) S = surface t e n s i o n S = l a t t i c e parameter (Eyring Theory) 6 = bond energy, constant i n molecular p o t e n t i a l f u n c t i o n * l = absolute v i s c o s i t y ^M = absolute v i s c o s i t y at m.p. v i s c o s i t y at law pressures = reduced v i s c o s i t y ( r e l a t i v e to c r i t i c a l p o i n t ) +• T j = reduced v i s c o s i t y (Comings and Elgy) reduced v i s c o s i t y (De Boer) d = angle of r o l l v = kinematic v i s c o s i t y , v i b r a t i o n frequency <? = d e n s i t y , d e n s i t y of l i q u i d <?. = d e n s i t y of b a l l <r = average distance between molecules, constant i n molecular p o t e n t i a l f u n c t i o n t = shearing s t r e s s f l u i d i t y , f u n c t i o n of (~) f o r r o l l i n g - b a l l viscometer, equation (81) a n d ^ were used as constants x i ACKNOWLEDGMENT The author wishes to express h i s thanks to Dr. L.W. Shemilt, and other members of the s t a f f at the Department of Chemical Engineering, U n i v e r s i t y of B r i t i s h Columbia, f o r advice and help during the course of t h i s work, and to the N a t i o n a l Research C o u n c i l f o r f i n a n c i a l a s s i s t a n c e . 1 I , INTRODUCTION (a) V i s c o s i t y The e x i s t e n c e of f r i c t i o n i n t h e f l o w o f f l u i d s was f i r s t r e c o g n i z e d by Newton (1) a t the end of the 1 7 t h c e n t u r y , when he p o s t u l a t e d t h a t t h e f r i c t i o n a l f o r c e between two l i q u i d s u r f a c e s was p r o p o r t i o n a l t o the a r e a and t o t h e r e l a t i v e v e l o c i t y of the f l u i d s u r f a c e s . L a t e r , Newton's assumptions were v e r i f i e d and e x p r e s s e d i n a f o r m w h i c h d e f i n e s t h e c o e f f i c i e n t of v i s c o s i t y as f o l l o w s . where,, = c o e f f i c i e n t of v i s c o s i t y , = s h e a r i n g s t r e s s ^Z' = v e l o c i t y g r a d i e n t e x i s t i n g a t same d r " ' p o i n t , r,. a l e n g t h parameter d e f i n e d I n a d i r e c t i o n p e r p e n d i c u l a r t o t h e f l o w d i r e c t i o n . I n c.g.s. u n i t s , the u n i t o f v i s c o s i t y i s t h e p o i s e = gm. cm."''' s e c . ^ . The c e n t i p o i s e i s the common p r a c t i c a l u n i t o f v i s c o s i t y . The r a t i o o f the v i s c o s i t y t o the d e n s i t y i s c a l l e d the k i n e m a t i c v i s c o s i t y and i s a f u n d a m e n t a l v a r i -a b l e i n hydrodynamics. The c.g.s. u n i t of k i n e m a t i c v i s c o s i t y i s the s t o k e = cm. s e c . (b) Newtonian and Non-Newton!an V i s c o s i t y For many f l u i d s , i n equation (1) i s a true constant at any p a r t i c u l a r value of,say, temperature and pressure i . e . i t i s a true f u n c t i o n A s t a t e and independent of the magnitude and nature of the imposed shearing s t r e s s , Those f l u i d s f o r which ^ i s a t r u e constant of s t a t e are r e f e r r e d to as Newtonian f l u i d s and T[ i s c a l l e d the Newtonian V i s c o s i t y . Most pure l i q u i d s , homogeneous l i q u i d mixtures, and gases show Newtonian behavior. On the a p p l i c a t i o n of an e x t e r n a l s t r e s s many substances do not obey the simple Newton law, but show anoma lous e f f e c t s which are included i n the general term of non-Newtonian behavior. I n f a c t a general r e l a t i o n s h i p between dv the imposed shearing s t r e s s , , and the r a t e of shear, — , can be w r i t t e n i n the form = K#J (2) f o r any m a t e r i a l , f l u i d or s o l i d , and Newton's law, equation (1), i s merely a p a r t i c u l a r example of t h i s general r e l a t i o n s h i p which i s found to apply f o r most pure gases and l i q u i d s A general d i s c u s s i o n of the r e l a t i o n , equation ( 2 ) ? i s g i ven by Burgers (2) and Oldroyd ( 3 ) . (c) Importance of V i s c o s i t y The concept of v i s c o s i t y i s now of great importance i n pure science and engineering. I n a n a l y t i c a l and p h y s i c a l chemistry i t i s a property which i s u s e f u l i n ch a r a c t e r -i z i n g m a t e r i a l s . For t h i s purpose, the i-Theochor, u-, .of F r i e n d and Hargraves (4) and l a t e r m o d i f i c a t i o n s by Ch a c r a v a r t i (5) and Jones and Bowden (6) i s p a r t i c u l a r l y u s e f u l . I t i s found to be l a r g e l y independent of temperature and, s i m i l a r to the parachor of Sugden (7)^ i s an a d d i t i v e p roperty of organic compounds. During recent years, i n t e r e s t i n t h i s f i e l d of chemistry seems to have been c o n s i d e r a b l y reduced. However, i n the more r e c e n t v f i e l d of h i g h polymer chemistry the use of v i s c o s i t y i n e s t i m a t i n g molecular weight and s t r u c t u r e has a t t a i n e d a new prominence as i s shown by the vast l i t e r a t u r e on the v i s c o s i t y of polymer melts and s o l u t i o n s I t i s i n r e l a t i o n to t h i s f i e l d that non-Newtonian V i s c o s i t y i s p a r t i c u l a r l y developing. i s a l so very important and an accurate knowledge of the v i s c o s i t y i s e s s e n t i a l to the s o l u t i o n of many design problems p a r t i c u l a r l y those a s s o c i a t e d w i t h f l u i d motion. I t i s p a r t i c u l a r l y important i n Chemical Engineering Science f o r the c o r r e l a t i o n of data i n the f i e l d of heat, mass,and momentum t r a n s f e r . I n these c o r r e l a t i o n s the use of dimensionless groups i s standard p r a c t i c e , and the v i s c o s i t y i s represented i n many of these groups, f o r example, In the f i e l d of engineering, the v i s c o s i t y of f l u i d s Reynolds No. Re = - Heat, Mass, Momentum P r a n d t l No. Pr = Y[C^ - Heat Transfer I t i s a l s o important i n other engineering f i e l d s , such as aerodynamics and h y d r a u l i c s and i n other f i e l d s where the flow of f l u i d s i s of importance (d) V i s c o s i t y a3 a Transport Property of F l u i d s V i s c o s i t y , along w i t h d i f f u s i v i t y and thermal c o n d u c t i v i t y , i s termed a t r a n s p o r t property of f l u i d s . I t i s the most e a s i l y and a c c u r a t e l y measurable of the t r a n s -p o r t p r o p e r t i e s of f l u i d s and f o r t h i s reason, more r e l i a b l e data are a v a i l a b l e f o r v i s c o s i t y than f o r e i t h e r of the other t r a n s p o r t p r o p e r t i e s . At the present time, a l o t of t h e o r e t i c a l work Is being done on the theory of the gaseous and l i q u i d states,and when (these t h e o r i e s are a p p l i e d to the t r a n s p o r t p r o p e r t i e s of f l u i d s they are almost i n v a r i a b l y t e s t e d w i t h v i s c o s i t y data, ( f o r example, B i r d , H i r c h f e l d e r and C u r t i s s ( 8 ) ). Thus v i s c o s i t y a f f o r d s a means of pene-t r a t i n g i n t o many d e t a i l s of the molecular s t r u c t u r e of matter. (e) Theories of V i s c o s i t y Many t h e o r i e s and mathematical r e l a t i o n s have been proposed to e x p l a i n the v i s c o s i t y of l i q u i d s and i n p a r t i c u -l a r the e f f e c t of temperature and pressure. U n t i l r e c e n t l y , these r e l a t i o n s have been mainly e m p i r i c a l , or s e m i t h e o r e t i -LTV c a l and have been l i m i t e d A a p p l i c a b i l i t y , i . e . s u i t a b l e to c e r t a i n types of compounds and not others. During the l a s t 5 .20 y e a r s t h e r e have been a t t e m p t s t o r e l a t e v i s c o s i t y t o a more g e n e r a l t h e o r y of t r a n s p o r t p r o p e r t i e s , and more f u n d a m e n t a l l y t o g e n e r a l t h e o r i e s o f the gaseous and l i g u i d s t a t e s . As i n o t h e r f i e l d s , t h e r e has been g r e a t e r s u c c e s s w i t h gases t h a n w i t h l i q u i d s , and i n f a c t w i t h the s i m p l i e r gases agreement of t h e o r y and experiment i s w i t h i n the e x p e r i m e n t a l e r r o r . U n f o r t u n a t e l y , the agreement of e x p e r i -ment and t h e o r y w i t h l i q u i d s i s s t i l l i n t h e r e a l m o f " o r d e r s o f magnitude." However, t h e r e do e x i s t many e m p i r i c a l cor-r e l a t i o n s r e l a t i n g the v i s c o s i t y o f l i q u i d s w i t h the f u n d a -m e n t a l i n t r i n s i c p r o p e r t i e s of p r e s s u r e and te m p e r a t u r e , w h i c h show good agreement w i t h experiment and a r e v e r y u s e f u l f o r e n g i n e e r i n g a p p l i c a t i o n s . The v i s c o s i t y of f l u i d s i s a v e r y s t r o n g f u n c t i o n o f t e m p e r a t u r e , gases showing a de c r e a s e i n v i s c o s i t y and l i q u i d s an i n c r e a s e w i t h d e c r e a s e of t e m p e r a t u r e . F o r l i q u i d s , t he e f f e c t i s p a r t i c u l a r l y marked, many l i q u i d s showing a 1 0 0 $ change w i t h 20 - 30°C change i n t e m p e r a t u r e . A l l gases and l i q u i d s so f a r . i n v e s t i g a t e d , w i t h t h e e x c e p t i o n o f water, have shown an i n c r e a s e i n v i s c o s i t y w i t h p r e s s u r e ( a t c o n s t a n t t e m p e r a t u r e ) . Water shows a minimum i n the v i s c o s i t y p r e s s u r e curve a t c e r t a i n t e m p e r a t u r e s , i . e . , the v i s c o s i t y d e c r e a s e s w i t h p r e s s u r e a t f i r s t and a f t e r a c e r t a i n p r e s s u r e b e g i n s t o i n c r e a s e . The p r e s s u r e e f f e c t oia. v i s c o s i t y i s quit-e s m a l l up t o one hundred atmospheres !•• 6 but shows very marked increase at h i g h and extreme pressures, ( f ) Viscometry and l i q u i d s are e s s e n t i a l l y the same, d i f f e r e n c e s e x i s t i n g only i n the d e t a i l s of the a n c i l l a r y equipment. The methods are best summarized under the f o l l o w i n g headings, suggested by Bingham (9), page 6. Many of these are r e a d i l y and e x a c t l y analysed mathemati-c a l l y and are t h e r e f o r e absolute methods. However, i n many cases, the a p p l i c a t i o n of the appropriate equations i n v o l v e s f u r t h e r l a b o r i o u s work and the use of a d d i t i o n a l experimental data which are u n c e r t a i n . As a r e s u l t , the m a j o r i t y of p r a c t i c a l viscometry i s done on a r e l a t i v e s c a l e . For example, the c a p i l l a r y ^ t u b e viscometer i s an absolute i n s t r u -ment, i n that the e f f l u x time can be r e l a t e d e x a c t l y w i t h the dimensions and the v i s c o s i t y by a p p l i c a t i o n of the P o i s e u i i l l e Law ( 1 0 ) , The methods f o r measuring the v i s c o s i t i e s of gases 1) Flow methods, 2) Methods based on r e s i s t a n c e o f f e r e d to s o l i d bodies, 3) Other methods. (3) where, volume flow pressure drop: r a d i u s of tube time of flow l e n g t h of c a p i l l a r y U 7 However, the a p p l i c a t i o n of t h i s equation to determine Y|_ would r e q u i r e , f o r example, a very accurate value f o r the rad i u s of the tube, R, which i s d i f f i c u l t to o b t a i n w i t h s u f f i c i e n t accuracy. Other methods f o r measuring the v i s c o s i t y cannot be analysed e x a c t l y and are t h e r e f o r e n e c e s s a r i l y r e l a t i v e methods. With most viscometers, care i s taken to ensure t h a t operation i s w i t h i n the viscous regime of flow and i n general that i n e r t i a l e f f e c t s are n e g l i g i b l e . With some viscometers, however, i n e r t i a l e f f e c t s are cons i d e r a b l e , but the method i s designed to take these i n t o account and to ensure determi-n a t i o n of the c o r r e c t v i s c o s i t y as defined by Newton's Law f o r viscous f l o w . B r i e f l y , the f o l l o w i n g are some examples of the viscometers i n common use: 1. Flow Methods (a) E f f l u x through h o r i z o n a l c a p i l l a r i e s e.g. Thorpe and Rodger (11) and Bingham and White (12). (b) E f f l u x through v e r t i c a l c a p i l l a r i e s . The most important are the Ostwald viscometer; (13) f o r l i q u i d s w i t h I t s m o d i f i c a t i o n s by Cannon and Fenske (14) Ubbelhode (15), and the Rankine viscometer (16) f o r gases. 2. Methods based on Resistance to s o l i d bodies (a) R o t a t i n g bodies i n the f l u i d . D i s c s , c y l i n d e r s and spheres have been used commonly, because these ,8 are r e a d i l y analysed mathematically. (b) O s c i l l a t i n g bodies — a l s o d i s c s , c y l i n d e r s and spheres. (c) Free f a l l of a sphere through a l i q u i d — Stoked'; law. (d) F a l l of bodies i n confined spaces. These in c l u d e the f a l l i n g c y l i n d e r instrument of Bridgman-(17) (and o t h e r s ) , the f a l l i n g sphere of Hoppler (18) and the r o l l i n g b a l l of Flowers (19) and Hersey and Shore (20) 3. Other Methods, i n c l u d e (a) Decay of o s c i l l a t i o n s of l i q u i d i n a U-tube (b) Measurement of the v e l o c i t y of sound i n a l i q u i d . For accurate work at atmospheric pressure, c a p i l -l a r y flow methods are most f r e q u e n t l y used f o r l i q u i d s , but r o t a t o r y and o s c i l l a t o r y methods are common. For h i g h pressure s t u d i e s , the c a p i l l a r y method of Rankine i s i m o s t common f o r gases. For l i q u i d s , some form of f a l l i n g body method Is u s u a l , s i n c e t h i s i s p a r t i c u l a r l y s u i t e d to h i g h pressure design, although the c a p i l l a r y method has been used (21). (g) V i s c o s i t y Standards and Viscometer C a l i b r a t i o n i Although the use of r e l a t i v e viscometers i s p r e f e r -able even f o r accurate experimental determinations, neverthe-l e s s , absolute viscometxry i s e s s e n t i a l i n order to determine 9 the c o r r e c t absolute b a s i s to which to r e f e r the r e l a t i v e measurements. Furthermore, i t i s p r e f e r a b l e to use v i s c o -meters which can be mathematically analysed e x a c t l y , because the a n a l y s i s i s o f t e n u s e f u l , and sometimes e s s e n t i a l , i n c a l c u l a t i n g the c o r r e c t i o n s and e r r o r s due to various e f f e c t s . Since most commonly used methods f o r v i s c o s i t y measurement are r e l a t i v e , the viscometers must be c a l i b r a t e d . Great care should be taken w i t h the c a l i b r a t i o n i n order t o ensure c o r r e c t v i s c o s i t y measurements as an absolute b a s i s . The absolute standard f o r v i s c o s i t y i s u n i v e r s a l l y accepted as the v i s c o s i t y of water at 20°C. As a r e s u l t of the recent work of Swindells and co-workers (22) at the N.B.S. the v i s c o s i t y of water at t h i s temperature Is now known very a c c u r a t e l y . The value i s given as 0.010019 - 0.000003 c.g.s. u n i t s or 1.0019 cp. at 20.00°C. Since most viscometers w i l l not give values to b e t t e r than 0.1%, i t has been recommended (22) that t h i s value be correc t e d to 1.002 cp. f o r use as a standard f o r r e l a t i v e determinations. I t i s s u r p r i s i n g that commonly accepted values p r i o r to t h i s determination are d i f f e r e n t by as much as 0.6$, which c o n t r i b u t e s to some extent to the l a c k of consistency i n the v i s c o s i t y determinations of var i o u s experimenters. I t i s u s u a l l y p r e f e r a b l e to c a l i b r a t e viscometers w i t h watery I n order t o minimize e r r o r s i n the c a l i b r a t i o n by reducing the number of experimental determinations between the 10 absolute standard and the f i n a l c a l i b r a t i o n . However, Cannon (23) has described a proceedure based on the use of s p e c i a l l y designed c a p i l l a r y viscometers as absolute standards f o r v i s c o s i t y measurements. These "Master viscometers" are c a l i b r a t e d w i t h d i s t i l l e d water and used to determine the v i s c o s i t y of other l i q u i d s which are used f o r r o u t i n e c a l i -b r a t i o n s . This proceedure has r e c e i v e d the s a n c t i o n of the N a t i o n a l Bureau of Standards (24) and the American S o c i e t y f o r T e s t i n g M a t e r i a l s (25), and i s now w i d e l y accepted. (h) The Importance of Den s i t y Measurements In much work on v i s c o s i t y , the a v a i l a b i l i t y of accurate d e n s i t y i s e s s e n t i a l to c a l c u l a t e the absolute v i s c o s i t y from the other experimental measurements. For example, i n the c a p i l l a r y viscometer, the product of the e f f l u x time and the c a l i b r a t i o n constant gives the kinematic v i s c o s i t y V = ~ , and i n the va r i o u s f a l l i n g body instruments, the d e n s i t y d i f f e r e n c e ( <PS f ) between the f a l l i n g body and the f l u i d must be known before *^  can be evaluated from the experimental r e s u l t s . I n order that the experimental e r r o r i n <f w i l l not be a l i m i t i n g f a c t o r i n the o v e r a l l e r r o r i n the absolute v i s c o s i t y , y\ , i t i s u s u a l l y s u f f i c i e n t to keep the e r r o r I n ^ l e s s than 0.1$. This u s u a l l y r e q u i r e s accuracy of o n l y three s i g n i f i c a n t f i g u r e s i n the d e n s i t y measurements^ which i s e a s i l y a t t a i n a b l e w i t h standard equipment. ( i ) The A v a i l a b i l i t y of V i s c o s i t y Data 11 There e x i s t s a v a s t l i t e r a t u r e on the v i s c o s i t y of f l u i d s . A p a r t i c u l a r l y l a r g e amount of r e s u l t s i s a v a i l a -b l e f o r pure l i q u i d s and l i q u i d mixtures, although there have a l s o been a l a r g e number of measurements on gases and vapours. Most of the s i g n i f i c a n t data up to 1938 ctjie presented i n the I n t e r n a t i o n a l C r i t i c a l Tables (26) and i n the 5 t h E d i t i o n of Landolt - B o r n s t e i n (27). Unfortunately, there has been no complete c o m p i l a t i o n of data since 1938. The 6 E d i t i o n (1955)of Landolt - B o r n s t e i n (28) l i s t s the v i s c o s i t y of about 150 pure l i q u i d s and gases over q u i t e wide temperature ranges, but compared to the volume of published data, t h i s i s s m a l l . A c e r t a i n amount of data at a few temperatures i s a v a i l a b l e i n some of the standard works on the p h y s i c a l p r o p e r t i e s of pure organic compounds (29, 30), but the scope i s l i m i t e d . The data on hydrocarbons has been brought up to date by the American Petroleum I n s t i t u t e ' s P r o j e c t 44 "Selected Values of Thermodynamic P r o p e r t i e s of Hydrocarbons and Related Compounds"(31). I t Is to be hoped that compilations of data on many other compounds w i l l be a v a i l a b l e through t h i s p r o j e c t . Vogelpbhl ( 2 8 ) , i n an i n t r o d u c t i o n to the data presented i n Landolt - Bornstein,estimates that absolute pre-c i s i o n of the v i s c o s i t y data Is seldom gr e a t e r than 1%. Measurements by d i f f e r e n t workers are o f t e n I n much greater disagreement than 1$,since the v i s c o s i t y i s s t r o n g l y a f f e c t e d by i m p u r i t i e s . He notes that i t i s u s u a l l y very d i f f i c u l t to 12 assess v i s c o s i t y data, because there i s seldom w e l l - d e f i n e d data on the degree of p u r i t y . Extensive temperature ranges have been covered at atmospheric pressures. For l i q u i d s , the m a j o r i t y of data covers the temperature range from room temperature to the b o i l i n g p o i n t , but the c l a s s i c a l lowtemperature work of Tonomura and M i t s u k u r i (32) has served to extend the range of a v a i l a b l e data on many l i q u i d s to near the f r e e z i n g p o i n t s . Whereas the temperature e f f e c t of the v i s c o s i t y of l i q u i d s has been e x t e n s i v e l y i n v e s t i g a t e d , the e f f e c t of pressure has r e c e i v e d comparatively l i t t l e a t t e n t i o n . This i s almost c e r t a i n l y due to the r e l a t i v e l y s m a ll e f f e c t of pressure,up to moderate pressures. Since most i n d u s t r i a l operations are c a r r i e d on at r e l a t i v e l y low pressures (below 100 Atm.) where the e f f e c t i s s m a l l , there has been l i t t l e i n c e n t i v e f o r experimentation. In the petroleum i n d u s t r y a knowledge of the pressure e f f e c t of v i s c o s i t y i s u s e f u l f o r s o l v i n g problems a s s o c i a t e d w i t h the production of crude o i l and w i t h l u b r i c a t i o n , and a c e r t a i n amount of data i s a v a i l a -b l e i n t h i s f i e l d . Apart from the experiments on petroleum products the work of Bridgman (17 ,33,34,35) at Harvard stands supreme, the number of l i q u i d s s t u d i e d i n h i s experiments exceeding t h a t of a l l other experimenters. I n t h i s work, the pressure range covered was from 0 to 30,000 Atms. but temperatures are l i m i t e d to 30° and 75°C. 1 3 There has a l s o been l i t t l e work i n the range of temperatures above the b o i l i n g p o i n t s of l i q u i d s ? a n d measurements near the c r i t i c a l p o i n t are very scarce. Indeed, there remains a great d e a l to be done before i t w i l l be p o s s i b l e to c o n s t r u c t a complete v i s c o s i t y - temperature -pressure surface f o r other than a very few substances. The l a c k of such data i s being p a r t i c u l a r l y f e l t i n the develop-ment of t h e o r e t i c a l work i n the f i e l d of v i s c o s i t y and i s c e r t a i n l y c o n t r i b u t i n g to the slow development of the theory of the l i q u i d s t a t e . ( j ) Purpose and Scope of t h i s Work The l a c k of extensive and r e l i a b l e data on -the e f f e c t t of pressure on v i s c o s i t y of l i q u i d s , means t h a t the assembly of an apparatus f o r o b t a i n i n g such data would be of great use. A l i t e r a t u r e survey of the a v a i l a b l e data and equipment used f o r such determinations was made, and i s presented i n Appendix I . I t became obvious that the R o l l i n g - b a l l Viscometer f i r s t developed by Flowers ( 1 9 ) and l a t e r used by Hersey and Shore ( 2 0 ) and by Sage and a s s o c i a t e s ( 3 6 - 3 9 ) would be a convenient form of apparatus to use f o r t h i s r esearch, and s i n c e such an apparatus had been donated to t h i s l a b o r a t o r y by I m p e r i a l O i l L t d . i t was decided to adopt I t . M o d i f i c a t i o n s were made to o b t a i n more accurate measurements than were p o s s i b l e i n i t s o r i g i n a l form. 14 In l i n e w i t h past and current work i n these l a b o r a -t o r i e s on the p h y s i c a l and thermodynamic p r o p e r t i e s of the n - a l c o h o l s ( 4 0 - 4 6 ) , i t was decided t h a t the equipment should be designed w i t h a view to making measurements on these substances. Bridgman (33,34) has a l r e a d y made measure-ments on the n - a l c o h o l s from to i n c l u s i v e and observed an i n c r e a s i n g e f f e c t of pressure on the v i s c o s i t y as the l e n g t h of the carbon chain i n c r e a s e s . A d d i t i o n a l data on t h i s e f f e c t would prove very u s e f u l , so i t was decided to t r y to extend the range of Bridgman 1s measurements to higher members of the s e r i e s . P a r a l l e l w i t h the development of the pressure v i s c o -meter, apparatus was r e q u i r e d f o r making accurate measurements at atmospheric pressure on any a l c o h o l s s e l e c t e d f o r i n v e s t i -g a t i o n , and on m a t e r i a l s s e l e c t e d f o r c a l i b r a t i o n of the pressure viscometer. For t h i s purpose, standard Cannon-Fenske c a p i l l a r y viscometers were c a l i b r a t e d according to accepted proceedures. Normal o c t y l a l c o h o l , Gg H-^ OH, was s e l e c t e d as a s u i t a b l e member of the normal a l c o h o l s e r i e s on which to s t a r t making measurements. I t i s a v a i l a b l e i n a f a i r l y pure commercial grade and can be p u r i f i e d to a h i g h degree by f r a c t i o n a l d i s t i l l a t i o n , which i s not p o s s i b l e w i t h n -hexanol or n - heptanol, and being somewhat removed from the C, to C x 5 members, i t would provide p o s s i b l e i n t e r p o l a t i o n s f o r the 15 homologous s e r i e s . A l i t e r a t u r e survey on c e r t a i n of the p h y s i c a l p r o p e r t i e s of n - o c t a n o l i n c l u d i n g the v i s c o s i t y at atmospheric pressure was r e q u i r e d . A l s o , atmospheric pressure measurements on i t s d e n s i t y and v i s c o s i t y , as w e l l as s u f f i c i e n t measurements to provide an estimate of the p u r i t y were necessary. The b a s i s f o r i n v e s t i g a t i o n of the pressure dependence of the v i s c o s i t y of n - o c t a n o l could thus be provided,and i t was a l s o p o s s i b l e to e s t a b l i s h data of i n t e r e s t i n i n v e s t i g a t i n g the v i s c o s i t y of the homologous s e r i e s of normal a l c o h o l s at atmospheric pressure. 16 I I THEORY Al© CORRELATION OP LIQUID VISCOSITIES (a) General Theory The theory of l i q u i d v i s c o s i t i e s i s c o n s i d e r a b l y more i n v o l v e d than that of gases and the l a r g e amount of work which has been published on the subject i n d i c a t e s that agreement w i t h experiment has been g e n e r a l l y poor. A number of good review a r t i c l e s on the subject have been published, which makes i t somewhat e a s i e r to discuss the problem. The reviews by Gemant (47) H i r s c h f e l d e r , C u r t i s s and B i r d (8), Andrade (48) and V o l a r o v i c h (49) cover the f i e l d q u i t e ade-quately up to recent years. L a t e s t developments are considered by Bond! (50). These authors agree that the g e n e r a l l y poor s t a t e of development of the theory i s undoubtedly a s s o c i a t e d w i t h an imperfect knowledge of the l i q u i d state,compared w i t h that of e i t h e r the gaseous or s o l i d s t a t e s . A good working p i c t u r e on which to base a theory of l i q u i d v i s c o s i t i e s i s given by Gemant (47): In the case of gases, the viscous f o r c e i s e q uivalent to a t r a n s f e r of momentum and thus the theory i s based on the k i n e t i c theory . . . . With l i q u i d s , the s i t u a t i o n i s d i f f e r e n t , molecules here are under strong mutual f o r c e s , and thus the p o s s i b i l i t y a r i s e s t h a t i t i s these f o r c e s that are d i r e c t l y connected w i t h the viscous f o r c e . To o b t a i n a rough p i c t u r e , .17 one can imagine t h a t molecules, i n order to be d i s p l a c e d r e l a t i v e to each other, have to overcome t h e i r mutual a t t r a c t i o n . The stronger the l a t t e r , the smaller the flow f o r a given shearing s t r e s s . With i n c r e a s i n g temperature, the randon k i n e t i c energy of the molecules helps to overcome molecular f o r c e s , hence v i s c o s i t y must decrease (contrary to the behavior of gases), a g e n e r a l l y observed f a c t . With i n c r e a s i n g pressure, molecules come nearer and the mutual a t t r a c t i o n becomes stronger, hence v i s c o s i t y i n c r e a s e s , and t h i s , too, i s confirmed by experiment. Two t h e o r i e s of the v i s c o s i t y of l i q u i d s w i l l be mentioned here i n some d e t a i l . These are the t h e o r i e s of Andrade (51,52) and E y r i n g (53,54,55) , which approach the problem from quite d i f f e r e n t aspects, yet a r r i v e at the same form of equation f o r the v a r i a t i o n of v i s c o s i t y w i t h temper-at u r e . Both t h e o r i e s a l s o lead to a r e l a t i o n between the v i s c o s i t y and the a p p l i e d pressure. Other recent t h e o r i e s w i l l be mentioned b r i e f l y f o r the sake of completeness. Andrade's Theory The molecules of the l i q u i d are regarded as v i b r a t i n g w i t h a mean frequency ,y , about some e q u i l i b r i u m p o s i t i o n . On t h i s p i c t u r e , the v i s c o s i t y at the me l t i n g p o i n t , y\ , i s c a l c u l a t e d on the assumption that at the m e l t i n g p o i n t momentum t r a n s f e r takes place at the extremes of an o s c i l l a t i o n , which leads to the r e l a t i o n , (4) 18 .where = fundamental v i b r a t i o n frequency, "W\ = mass of a molecule, 0'i = av volume of l i q u i d per molecule, and C i s a constant near u n i t y r\j 1.33 I n order to o b t a i n an expression f o r -V f o r monatomic l i q u i d s , i t i s assumed f u r t h e r t h a t , since the volume change on m e l t i n g i s s m a l l and t h e r e f o r e the molecular f o r c e s i n the s o l i d and l i q u i d s t a t e s at the m.p. cannot be a p p r e c i a b l y d i f f e r e n t , the frequency of v i b r a t i o n i n the l i q u i d s t a t e at the m.p. i s approximately equal to that i n the s o l i d s t a t e . Hence the formula of L.Indemann (56) f o r the frequency of v i b r a t i o n of the s o l i d can be used f o r V i n equation (4), V = K / (5) where K = 3.1 X 1 0 1 2 , A = atomic weight, V = atomic volume. S u b s t i t u t e d i n t o equation (4), t h i s r e l a t i o n gives S - T ^ o ' ^ A T ^ V ' ^ (6) By c o n s i d e r i n g the experimental values f o r 16 l i q u i d metals and argon, Andrade concludes that the theory i s i n s a t i s f a c t o r y agreement i n absolute magnitude, except f o r c e r t a i n metals which have an anomalous c r y s t a l l i n e s t r u c t u r e . 19 I t i s f u r t h e r shown that the v i s c o s i t y at the me l t i n g p o i n t i s p r o p o r t i o n a l to the ^ /3 r c^' power of the de n s i t y at the m e l t i n g p o i n t , , and t h i s r e l a t i o n i s assumed to hold f o r a l l l i q u i d s . The v a r i a t i o n of w i t h temperature i s derived on the b a s i s that the t r a n s f e r of momentum f o r viscous f l o w i s asso c i a t e d w i t h an energy of a c t i v a t i o n , £ , and according to the Boltzmann theory, where, = v i s c o s i t y at temperature T, E. = a c t i v a t i o n energy, & = Boltzmann's constant, assuming f o r the moment tha t the energy of a c t i v a t i o n i s Independent of temperature. F i n a l l y , the e f f e c t of the v a r i a t i o n of t w i t h temperature i s as s o c i a t e d w i t h the volume change and i t i s assumed th a t E i s i n v e r s e l y p r o p o r t i o n a l to the volume , <\j , by comparison w i t h the v a r i a t i o n of the p o t e n t i a l energy of a molecule as given by the van der Waal's equation. Combination of equations (4) and (8) w i t h t h i s assumption leads t o the equation, * 1 T = C \ r " ' A £ ^ (9) where C and <X are constants, which i s Andrade's b a s i c equation f o r the v a r i a t i o n of v i s c o s i t y w i t h temperature. 20 Equation (9) has been found to give e x c e l l e n t c o r r e l a t i o n of the v a r i a t i o n of v i s c o s i t y w i t h temperature, and Andrade, u s i n g the data of Thorpe and Rodger (11), has found t h a t i t gives b e t t e r agreement over wider temperature ranges than the more commonly used Arrhenius form of the equation, ^ T = A e B / T d o ) where A and B are constants, independent of temperature. To take account of the v a r i a t i o n of v i s c o s i t y of l i q u i d s w i t h pressure, Andrade deri v e s the v i b r a t i o n frequency at h i g h pressures to be given by, -V = < W , / i i < - , / a - (li) where \/ = atomic volume K = a d i a b a t i c c o m p r e s s i b i l i t y and <o i s a constant. Hence, the v a r i a t i o n of v i s c o s i t y w i t h pressure i s given by the r e l a t i o n , \ - f ^ l V ' V S ^ i - 4 . ) as) x where the s u b s c r i p t 1 r e f e r s to atmospheric pressure and to h i g h pressure. Since no data on a d i a b a t i c c o m p r e s s i b i l i t y were a v a i l a b l e , Andrade used the i s o t h e r m a l c o m p r e s s i b i l i t y and the experimental data of Bridgman (17) to t e s t equation (12). 21 For l i q u i d Hg, he found t h a t the equation gave a value of 1,32 f o r at 12,000 Atras. which was e x a c t l y the f i g u r e obtained e x p e r i m e n t a l l y by Bridgman. For other l i q u i d s he found that the theory agreed moderately w e l l w i t h experiment up to a pressure of 2,000 Atm. but above t h i s value gave values of which were too low. The theory of Andrade i s , however, not an absolute theory. I t s t i l l leaves two e m p i r i c a l constants C and t o be adjusted to f i t the experimental data f o r temperature dependence, and no attempt has been made to c o r r e l a t e these w i t h other known p h y s i c a l p r o p e r t i e s of l i q u i d s , except i n the unique case of monatomic molecules at t h e i r m e l t i n g p o i n t . The theory i s r e a l l y too sketchy and vague t o be of much s i g n i f i c a n c e from a fundamental poi n t of view. Many other s e m i t h e o r e t i c a l developments ha.veappeared from time to time w i t h a view to o b t a i n i n g the Arrhenius form of equation f o r the v a r i a t i o n of v i s c o s i t y w i t h temperature. Some which should be mentioned are those of van der Waals J r . (57,58), F r e n k e l (59,60), and MacLeod (61,62), but none of these have a t t a i n e d the prominence of the E r y i n g theory, summarized below. Eyring*s Theory U n l i k e previous t h e o r i e s which had been used t o e x p l a i n the v i s c o s i t y of l i q u i d s , the Ey r i n g theory i s based 22 on a concrete physico-chemical p i c t u r e and a l l the constants can be r e l a t e d to other p r o p e r t i e s of the l i q u i d , i . e . , there are no a r b i t r a r y constants. The theory i s based on an extension of the theory of absolute r e a c t i o n r a t e s (63) i n which the viscous flow process i s t r e a t e d as a f i r s t - o r d e r chemical r e a c t i o n . I n order to a P P l y t h i s theory, the l i q u i d s t r u c t u r e i s described as a mixture of molecules and vacant l a t t i c e s i t e s o:r "ho l e s . " In order to pass i n t o a vacant l a t t i c e s i t e , a molecule must pass through a p o t e n t i a l b a r r i e r which e x i s t s because of the strong molecular f o r c e s between the molecules. I n the absence of any impressed f o r c e , t h i s p o t e n t i a l b a r r i e r i s symmetrical, but on the a p p l i c a t i o n of an e x t e r n a l f o r c e the b a r r i e r i s d i s t o r t e d i n the d i r e c t i o n of the f o r c e . This makes i t e a s i e r f o r molecules to be d i s p l a c e d i n the d i r e c t i o n of the impressed f o r c e than i n the reverse d i r e c t i o n and makes f o r a net t r a n s f e r of molecules. Applying the theory of absolute r e a c t i o n r a t e s to the forward and reverse processes o u t l i n e d above, E r y i n g and h i s a s s o c i a t e s have obtained the f o l l o w i n g equation f o r the v i s c o s i t y of a l i q u i d , 23 r] = EJ> (13) where, |p = impressed shearing f o r c e , fc0 = absolute r e a c t i o n r a t e i n t h e absence of an e x t e r n a l f o r c e , "VI = no. of molecules / u n i t volume, k = soltzmann's constant, T = absolute temperature, and a, S are dimensions r e l a t e d to the l a t t i c e s t r u c t u r e of of the l i q u i d . L 1 W T ~ ^ H * / R T w e e (u) where, in. = Plank's constant, AS = entropy of a c t i v a t i o n , i l H = enthalpy of a c t i v a t i o n . =fc =fc * 4 H — TAS = yAF"f' i s the f r e e energy of a c t i v a t i o n . Thus, s u b s t i t u t i n g i n t o (13), the equation f o r the v i s c o s i t y i s , v\ = E S ( U A ^ R T ( 1 5 ) I n t h i s equation, the v i s c o s i t y i s given .as a f u n c t i o n of the shearing f o r c e , p , and the theory t h e r e f o r e takes non-Newtonian behavior i n t o account. However, when a^/2Snkt i s small compared to u n i t y , the s i n h can be replaced by the f i r s t term of i t s Taylor expansion, and one o b t a i n s , (16) 24 This i s Eyring»s b a s i c equation which gives the v i s c o s i t y , , f o r o r d i n a r y Newtonian l i q u i d s . Although {§£)rik and A F * are i n no sense a r b i t r a r y constants, yet no means i s a v a i l a b l e to evaluate them e x a c t l y i n terms of known p r o p e r t i e s of a l i q u i d . For a rough estimate, i t i s assumed that the dimensions S and a which describe the l a t t i c e s t r u c t u r e are approximately e q u a l i s e that (JVcc*)2" !• Attempts have been made to c o r r e l a t e A F w i t h the thermodynamic p r o p e r t i e s of the l i q u i d , but no r e a l l y good c o r r e l a t i o n has been obtained. E m p i r i c a l l y , E y r i n g found that A P ^ i s most c l o s e l y c o r r e l a t e d w i t h the energy of v a p o r i z a t i o n , AEVo.|3 , per mole , and t h a t f o r many l i q u i d s , most s i g n i f i c a n t d e v i a t i o n s were obtained f o r l i q u i d s , such as the a l c o h o l s , which are a s s o c i a t e d by hydrogen-bonding. On these two assumptions, the approximate equation f o r the v i s c o s i t y of a l i q u i d i s g i v e n as \ = A ( A £ v 4 / 2 . A S R T " ) (18) which i s a u s e f u l equation f o r rough estimates. In developing an equation f o r the e f f e c t of pressure, E y r i n g considers the energy term A F * and notes t h a t i t takes account only of the energy spent i n c r o s s i n g the energy b a r r i e r 25 caused by the a t t r a c t i v e f o r c e s of neighbouring molecules. Since t h i s process i s accompanied by the f o r m a t i o n of a temporary hole, work i s done against the e x t e r n a l pressure, \p , and a d d i t i o n a l energy must be s u p p l i e d f o r t h i s purpose. He d e r i v e s that t h i s energy i s given by the term W /y^ , where ^/v\' i s the volume of hole per modecule. This term modifies the equation f o r the v i s c o s i t y to, 1 = n W e x V ^ V R T (19) U n f o r t u n a t e l y the value of n 1 cannot be deduced on t h e o r e t i c a l grounds. Values of 10 f o r pentane and 8 f o r ether were obtained from the experimental data,which gave f a i r agreement w i t h the theory. Other Theories Panchenkov (64,65) has developed a theory based on the t r a n s f e r of momentum, but t a k i n g i n t o account the bond energy of the molecule i n the l i q u i d . His f i n a l e xpression takes the form. ^ = o . ^ K 5 / ^ 4 / 5 T , / 2 ^ e / R T 0 - - ( 2 0 ) where, <X = 3 j ^ ( ^ Q % N 1 ' 3 (21) T" = r a d i u s of a molecule ? M = mol. wt., 9 = d e n s i t y , & = bond energy of molecule i n the l i q u i d , R. = gas constant , N = Avogadros' No. 26 B"y t a k i n g i n t o account the v a r i a t i o n of and w i t h pressure, s a t i s f a c t o r y agreement w i t h experiments on the e f f e c t of pressure has been r e p o r t e d . More r e c e n t l y , the theory of t r a n s p o r t phenomena i n dense gases and l i q u i d s has been developed by means of a non-e q u i l i b r i u m s t a t i s t i c a l mechanics. The work i n t h i s f i e l d has" been published p a r t i c u l a r l y by Kirkwood (66,67) and by Born and Green (68). B i r d et a l . (8) have pointed out the p o t e n t i a l importance of t h i s approach,and imply t h a t i t i s l i k e l y to giv e r e s u l t s which w i l l agree w e l l w i t h experiment. However, only some approximate c a l c u l a t i o n s have been reported so f a r , and much computation work remains to be done. (b) The Theory of Corresponding States The great success of the use of the theory of corresponding s t a t e s i n i n t e r p r e t i n g the data on compressibi-l i t y and various thermodynamic p r o p e r t i e s of gases and l i q u i d S j h a s lead to a c o n s i d e r a t i o n of the a p p l i c a t i o n of s i m i l a r concepts to c o r r e l a t e the data on t r a n s p o r t p r o p e r i t e s of f l u i d s . The theory f i r s t developed by van der Waals, i s based on the c o n s i d e r a t i o n that the c r i t i c a l p o i n t i s a "point of corresponding s t a t e s " and that t h e r e f o r e , the r e l a t i o n between a p a r t i c u l a r f l u i d property , , should be represen-ted by a unique f u n c t i o n of t h a t property at the c r i t i c a l p o i n t , <j> , f o r a l l substances. Further, t h i s f u n c t i o n i s given i n terms of the reduced temperature and pressure , 27 r > as f o l l o w s , (22) or .g reduced property. (23) This i s the b a s i s f o r the g e n e r a l i z e d charts of Hougen and Watson (69) f o r c o m p r e s s i b i l i t y , s p e c i f i c heat, e t c . , which are very u s e f u l i n engineering c a l c u l a t i o n s . U n f o r t u n a t e l y , the theory i s c e r t a i n l y not of completely general a p p l i c a t i o n , some substances showing considerable d e v i a t i o n from the g e n e r a l i z e d c o r r e l a t i o n . This problem has long been recognized and i n recent years the a d d i t i o n of a t h i r d parameter has been I n v e s t i g a t e d , The most comprehensive work has been done by P i t z e r and co-workers (70), who introduced X as the reduced vapor pressure measured at T r = 0.7; R i e d e l (Ti') who introduced X as the temperature d e r i v a t i v e of the vapor pressure at the c r i t i c a l c r i t i c a l c o m p r e s s i b i l i t y , Z-c , and d i d extensive c o m p i l a t i o n of g e n e r a l i z e d thermodynamic p r o p e r t i e s based thereon. For v i s c o s i t y , the c o r r e l a t i o n used has been of the (24) p o i n t ; and Lydersen, Greenkorn and Hougen (72) who used the form, (25) 28 Hougen and Watson (69) have a l s o prepared a g e n e r a l i z e d v i s c o s i t y chart based on t h i s r e l a t i o n which i s s a i d to be a p p l i c a b l e to both gases and l i q u i d s over wide temperature and pressure ranges. Although t h i s c o r r e l a t i o n i s undoubt-edly v a l u a b l e f o r rough estimates at hig h pressures and temper-atures i n the absence of r e l i a b l e data, i t gives poor accuracy over much of the range of v a r i a b l e s . Grunberg and Nissan (72a) have prepared a nomograph f o r the reduced v i s c o s i t y as a f u n c t i o n of reduced temperature and reduced d e n s i t y . They c l a i m an accuracy of — 10$ f o r ranges of~N- from 0.3 to 15 and <?^_ from 0.3 to 18. X, mentioned above, to such tra n s p o r t p r o p e r t i e s as v i s c o s i t y has not yet been attempted, although general c o r r e l a t i o n to w i t h i n 2 t o 3$ should r e s u l t . They a p p l i e d t h i s r e l a t i o n to gases and found e x c e l l e n t agreement of the values from t h e i r g e n e r a l i z e d charts w i t h experiments. Carr, Parent and Peck (73) have extended the charts of Comings and Elgy to higher pressures, but i t seems that the r e l a t i o n , equation (26) ?has not been t r i e d f o r l i q u i d s . Apparently, the use of some form of t h i r s parameter, 29 More r e c e n t l y , de Boer (74 ) has developed a "quantum mechanical theory of corresponding s t a t e s " i n which the v a r i a b l e s , T and \r are reduced i n terms of quantum mechanical parameters as f o l l o w s ; - W c r * , T * = ^ - (27) where \r and £- are constants i n the molecular p o t e n t i a l f u n c t i o n * C r ) = £ - f ( £ ) (28) Again, t h i s approach has not been considered f o r l i q u i d s . Much c l o s e r c o r r e l a t i o n of v i s c o s i t y data has been obtained by c o n s i d e r i n g a theory of corresponding s t a t e s f o r a s mall group of r e l a t e d compounds, f o r example the members of a s i n g l e homologous s e r i e s . I n p a r t i c u l a r , Smith and Brown (75) obtained good c o r r e l a t i o n w i t h i n a s i n g l e homologous s e r i e s by p l o t t i n g ^/T ' ^ I y-where I i s the Souders c o n s t i t u t i v e f a c t o r ( 7 6 ) . They obtained s i n g l e curves f o r n - P a r a f f i n s , Ethers, a c i d s , n - a l c o h o l s and i s o -a l c o h o l s . * w-A good review of reduced v i s c o s i t y equation i s given by H e l l e r (77) i n a recent a r t i c l e . 30 (c) The E f f e c t of Temperature on the V i s c o s i t y of L i q u i d s The l a r g e decrease i n the v i s c o s i t y of l i q u i d s w i t h r i s e i n temperature has been the subject of extensive r e s e a r c h from the time of P o i s e u i l l e up to the present day. As yet, no s i n g l e r e l a t i o n s h i p between the v i s c o s i t y and the temperature which i s a p p l i c a b l e to a l l l i q u i d s , w i t h i n experimental e r r o r , has been obtained, and the subject i s s t i l l am "open" f i e l d of re s e a r c h . However, there do e x i s t r e l a t i v e l y simple r e l a t i o n s i n v o l v i n g only a few e m p i r i c a l constants which are of q u i t e general a p p l i c a b i l i t y over l i m i t e d temperature range, and others wftich f i t data f o r some compounds very c l o s e l y over extended temperature ranges. In a f i e l d of research i n which there i s such a vast l i t e r a t u r e , i t i s f o r t u n a t e that many review a r t i c l e s e x i s t . P a r t i c u l a r l y complete reviews are given by P a r t i n g t o n ( 7 8 ) , Bowden and Morgan ( 7 9 ) , S h r i n i v a s a n and Prasad (80) and La n d o l t - B o r n s t e i n ( 2 8 ) . P a r t i n g t o n l i s t s approximately 50 formulae which have been published between 1842 and 1947 and the l i s t i s c e r t a i n l y not exhaustive. Many a r t i c l e s have a l s o appeared sin c e 1947 ( 8 1 - 9 3 ) . Among a l l the equations which have been proposed, the simple exponential formula mentioned p r e v i o u s l y , equation (10), has been most wid e l y used and f i t s the m a j o r i t y of data f o r most l i q u i d s b e t t e r than any other s i n g l e 31 formula. This i s o f t e n r e f e r r e d t o as Andrade's formula, but i t seems to have been o r i g i n a l l y proposed by Reynolds'-; (see Bingham (9) page 130). The formula i s p a r t i c u l a r l y a t t r a c t i v e because I t i s i n general agreement w i t h the best accepted t h e o r i e s of v i s c o s i t y ( f o r example, those mentioned p r e v i o u s l y ) . Prom the t h e o r e t i c a l development, which i n d i c a t e s t h a t R i s some form of energy of a c t i v a t i o n , i t i s not t o be expected that 6 w i l l be a true constant, independent of temperature. I t i s a g e n e r a l l y accepted f a c t that such energy f u n c t i o n s change w i t h temperature, and one would expect the energy of a c t i v a t i o n f o r viscous flow to change as w e l l , and t h i s i s borne: out by experiment. I f one w r i t e s the energy, AP^, as a l i n e a r f u n c t i o n of temperature, A F * = £ = - v - o ( T (29) and s u b s t i t u t e s i n t o the Reynolds' formula one ob t a i n s , v] - A e ^ = A e * / R e £ / R T , e / « r Hence, Y| = r\ e (30) which i s of the same form as equation (10). This i m p l i e s that a f i r s t - o r d e r v a r i a t i o n of the energy term i s i m p l i c i t l y i n c l uded i n the bonstant A, which may give some i n d i c a t i o n why the formula works so w e l l f o r considerable temperature ranges. 32 Many attempts have been made to adopt the simple exponential formula to wider temperature ranges by i n c l u d i n g a temperature v a r i a t i o n of e i t h e r E or A, or both. Some of these w i l l be l i s t e d to show the form of the adaptations. i ) Andrade's formula, equation ( 9) ?which has been discussed p r e v i o u s l y i s perhaps the best attempt to f i t the data more c l o s e l y , because i t introduces no new constants, although i t r e q u i r e s d e n s i t y data over the same temperature range. i i ) Hovorka, Lankelma, Stanford (94) proposed, i v \ 4j- ~ •+ B i v f - l - C (31) which i s equivalent to the form *1 = A T <3 (32) suggested by Innes (93) much more recently,and found to give good agreement f o r water, Hg, C^H^g a n < 3 Me OH. over wide temperature ranges up to near the b o i l i n g p o i n t . i i i ) Gutmann and Simmons (84) suggested JU v| = A + B»/CT>0 (33) r | = A e J (34) and obtained b e t t e r agreement f o r a l l l i q u i d s examined i n c l u d i n g a s sociated l i q u i d s , l i q u i d metals and e l e c t r o l y t e s , 33 I v ) G i r i f a l c o (92) c o n s i d e r s t h e v a r i a t i o n o f the a c t i v a t i o n energy by i n t r o d u c i n g a t e r m w h i c h i s q u a d r a t i c i n Vx i n a d d i t i o n t o the l i n e a r t e r m o f t h e b a s i c e q u a t i o n : fi*vv^ = — - + •% ^ ^ (35) An a n a l y s i s of t h e d a t a i n the l i t e r a t u r e showed t h a t the e q u a t i o n c o r r e c t l y r e p r e s e n t s t h e d a t a f o r a l a r g e number of a s s o c i a t e d l i q u i d s , whereas f o r n o n - a s s o c i a t e d l i q u i d s o( = 0 and t h e b a s i c e q u a t i o n s u f f i c e s ; . v) L e d e r e r (95) by a n a l o g y w i t h N e r n s t ' s vapor p r e s s u r e e q u a t i o n d e r i v e d t h e f o r m u l a £ o3» A = s I R T - 2 " T * k 3 „ T + E T + c ( 3 6 ) b u t , Jaeger (58) i n d i c a t e s t h a t the f o r m u l a i s no b e t t e r t h a n t h a t o f Andrade, e q u a t i o n (6). T h i s f o r m u l a has a l s o been r e c e n t l y c o n s i d e r e d by Baum (87). Other f o r m u l a e w h i c h a re based on the e x p o n e n t i a l f o r m u l a a r e , v i ) C o r n e l i s s o n and Waterman (91) U ± = A (37) v i i ) L i t o v i t z (83) a "for* A e ( 3 8 ) f o r a s s o c i a t e d l i q u i d s , e x c l u d i n g a l c o h o l s . 34 v i i i ) B a n e r j i (81) 1 = A - B T (39) i x ) Douglas (95) \ = - r C A e B / T ^ c e V r ) (40) and x) Thomas (96) V 4 - A e ^ ^ c e ^ ( 4 1 ) The l a s t two e q u a t i o n s gave e x c e l l e n t agreement f o r a s s o c i a t e d l i q u i d s . I n summary, the b a s i c e x p o n e n t i a l f o r m a l a e of Reynolds and Andrade g i v e g e n e r a l l y good agreement w i t h e x periment f o r many l i q u i d s over moderate t e m p e r a t u r e ranges, F o r a s s o c i a t e d l i q u i d ' s , where the degree o f a s s o c i a t i o n changes c o n s i d e r a b l y over t h e temp e r a t u r e r a n g e , and f o r many, l i q u i d s o v er w i d e r temperature r a n g e s , the energy of a c t i v a t i o n v a r i e s c o n s i d e r a b l y and a d d i t i o n a l f u n c t i o n s of tempe r a t u r e must be i n t r o d u c e d t o ta k e account o f t h i s v a r i a t i o n a d e q u a t e l y . Bingham ( 9) ?page 132, approaches the problem f r o m a d i f f e r e n t p o i n t o f v i e w . He c o n s i d e r s the v a r i a t i o n o f the f l u i d i t y , <§> ~ 4^, t o be the fu n d a m e n t a l v a r i a b l e , and has found v a r i o u s e q u a t i o n s i n the f o r m , ~T~ = - K 4 0 ( 42) i n p a r t i c u l a r , X = A -v- B>^> c / 4 > (43) and ~T = A •+- &4> -4- C/t4> + £ ) ( 4 4 ) 35 Bingham has a p p l i e d e x t e n s i v e d a t a f i t t i n g t o t h e s e e q u a t i o n s and has found t h a t e q u a t i o n (43) g i v e s agreement c l o s e t o the e x p e r i m e n t a l e r r o r f o r most l i q u i d s , b u t d e v i a t i o n s are c o n s i d e r a b l e f o r t h e n - a l c o h o l s f o r w h i c h e q u a t i o n (44) i s p r e f e r a b l e . T a b l e s are g i v e n f o r the v a l u e s o f A,B,C and D f o r 87 l i q u i d s d e t e r m i n e d by Thorpe and Rodger (11). U n f o r t u n a t e l y , t h i s approach has n e v e r a t t a i n e d the p r o m i -nence of the e x p o n e n t i a l t y p e of f o r m u l a , because i t i s not r e l a t e d t o any c o r r e s p o n d i n g t h e o r y . A l t h o u g h the f i t t i n g o f the d a t a i s good, e q u a t i o n s (43) and (44) a r e p a r t i c u l a r l y d i f f i c u l t t o u s e , because of t h e i r f orm, i n w h i c h T i s the e x p l i c i t v a r i a b l e , r e q u i r i n g a labiorous c a l c u l a t i o n f o r <^> at any p a r t i c u l a r t e m p e r a t u r e . (d) E f f e c t of P r e s s u r e on the V i s c o s i t y of L i q u i d s The l a c k o f p r e s s u r e d a t a on v i s c o s i t y makes i t d i f f i c u l t t o o b t a i n r e l i a b l e e q u a t i o n s t o c o r r e l a t e v i s c o s i t y w i t h p r e s s u r e , and c o m p a r a t i v e l y few c o r r e l a t i o n s have been attem p t e d , w i t h r e l a t i v e l y poor s u c c e s s . As mentioned p r e v i o u s l y , the b a s i c t h e o r i e s of Andrade and E y r i n g have l e d t o r e l a t i o n s h i p s f r o m w h i c h the e f f e c t o f p r e s s u r e can be d e t e r m i n e d . However, the agreement has been o n l y f a i r , p a r t i c u l a r l y at v e r y h i g h p r e s s u r e s . Good Review a r t i c l e s on the e f f e c t o f p r e s s u r e on the v i s c o s i t y o f l i q u i d s have been r e c e n t l y p u b l i s h e d by B l o k (97) and Dow (98). 36 Most l i q u i d s show an i n c r e a s e o f v i s c o s i t y w i t h p r e s s u r e , the r a t e o f change w i t h p r e s s u r e i n c r e a s i n g , t h e h i g h e r the p r e s s u r e . Some e x c e p t i o n s t o t h i s g e n e r a l b e h a v i o r have been r e p o r t e d . Water seems t o be p a r t i c u l a r l y anomalous. Cohen (99) n o t i c e d t h a t a t 25°C the v i s c o s i t y d e c r e a s e d w i t h p r e s s u r e , but the r a t e of d e c r e a s e was s m a l l e r a t h i g h e r p r e s s u r e s , up t o 900 atm. Hauser (100) measured the v i s c o s i t y of water at t e m p e r a t u r e s between 30° and 57°C a t p r e s s u r e s up t o 400 atm. and observed t h a t a t about 32°C t h e e f f e c t of p r e s s u r e was not m e a s u r a b l e . Below t h i s t e m p e r a t u r e the v i s c o s i t y d e c r e a s e d w i t h p r e s s u r e and above t h i s tempera-t u r e i t i n c r e a s e d . Bridgman (35) observed t h a t water behaved n o r m a l l y a t 30° and 75°C, but a t 0° and 10.3°C, the v i s c o s i t y p r e s s u r e c u r v e has a minimum a t a p r e s s u r e o f a p p r o x i m a t e l y 1,000 atm. Suge (101) r e p o r t e d a., d e c r e a s e i n the v i s c o s i t y f o r v e g e t a b l e o i l s w i t h i n c r e a s e d p r e s s u r e . No c o n f i r m a t i o n o f the ancraalous b e h a v i o r f o r v e g e t a b l e o i l s has been r e p o r t e d . I t has a l s o been q u i t e g e n e r a l l y o b s e r v e d , t h a t the e f f e c t of p r e s s u r e i s most pronounced at l o w e r t e m p e r a t u r e s , the p r e s s u r e c o e f f i c i e n t o f v i s c o s i t y d e c r e a s i n g w i t h r i s e I n t e m p e r a t u r e . F i n a l l y , the e f f e c t of p r e s s u r e i s more pronounced f o r l i q u i d s of h i g h m o l e c u l a r w e i g h t t h a n f o r t h o s e o f low m o l e c u l a r w e i g h t such as the common o r g a n i c l i q u i d s . F o r example, Bridgman (35) found t h a t f r o m 1 t o 12,000 atmospheres 37 t h e v i s c o s i t y o f MeOH i n c r e a s e s l o t i m e s , n -Amyl a l c o h o l 7 700 times and eugenol 10 t i m e s , a l l v a l u e s g i v e n a t a. temp e r a t u r e of 30°C. A l i t e r a t u r e s u r v e y was made of the a v a i l a b l e d a t a on the e f f e c t of p r e s s u r e on t h e v i s c o s i t y of l i q u i d s , f r o m the C h e m i c a l A b s t r a c t s o f 1926 t o 1957 and t h e r e f e r e n c e s t o t h i s work a r e g i v e n i n Appendix I . Most o f the a v a i l a b l e d a t a p r i o r t o 1926 i s made r e f e r e n c e t o by l a t e r a u t h o r s (9 ,35 ,78 ,97) . The e f f e c t o f p r e s s u r e on t h e v i s c o s i t y has been a s s o c i a t e d w i t h the change of volume w i t h p r e s s u r e , i n many c o r r e l a t i o n s . The s i m p l e s t and h i s t o r i c a l l y the f i r s t of such c o r r e l a t i o n s i s the renowned e q u a t i o n of B a c h i n s k i i (102) \ = (45) 1 V — W where 1/ i s the s p e c i f i c volume and W and C a r e c o n s t a n t s . W i s c o n s i d e r e d t o be the a c t u a l volume o f m o l e c u l e s , so t h a t (iT - W) r e p r e s e n t s the f r e e volume. Or, as o r i g i n a l l y s t a t e d , t h e f l u i d i t y i s d i r e c t l y p r o p o r t i o n a l t o the f r e e volume. That the volume change i s c e r t a i n l y i m p o r t a n t , i s su p p o r t e d b o t h by t h e o r y and e x p e r i m e n t . I n b o t h t h e t h e o r i e s o f Andrade and E y r i n g , the v a r i a t i o n o f the volume i s c o n s i d e r e d t o be most i m p o r t a n t , and i n the Panchenkov f o r m u l a , e q u a t i o n 0.6), the v a r i a t i o n i s p a r t i a l l y a t t r i b u t e d t o the 38 d e n s i t y . On t h e e x p e r i m e n t a l s i d e , i t has been g e n e r a l l y observed t h a t l i q u i d s w i t h h i g h c o m p r e s s i b i l i t i e s have l a r g e v i s c o s i t y - p r e s s u r e c o e f f i c i e n t s and the r e v e r s e f o r t h o s e w i t h low c o m p r e s s i b i l i t i e s . Mercury, f o r example, has t h e l o w e s t observed v i s c o s i t y - p r e s s u r e c o e f f i c i e n t , i n c r e a s i n g o n l y 33$ f o r a p r e s s u r e r i s e of 12,000 atm. a t 30°C. Bridgman (35) however, has p o i n t e d out t h e i n a d e q u a c i e s o f any t h e o r y w h i c h i s based e n t i r e l y on a c o n s i d e r a t i o n o f t h e volume e f f e c t . I n s p i t e of the s e l i m i t a t i o n s , some r e a s o n a b l y good e m p i r i c a l and s e m i - t h e o r e t i c a l e q u a t i o n s have been proposed on the b a s i s of volume e f f e c t s . Bingham, Adams and M c C o u s l i n (103) found t h a t t h e f l u i d i t y - v o l u m e c u r v e s f o r the n - a l c o h o l s were g i v e n by a p a r a b o l i c e q u a t i o n , s i m i l a r t o t h a t f o r t e m p e r a t u r e , e q u a t i o n (44), V = A 4 > - &/(ct>+-^) C (46) whether the change i n volume was due t o temp e r a t u r e o r p r e s s u r e . They used Bridgman's h i g h p r e s s u r e d a t a t o check t h i s e q u a t i o n f o r p r e s s u r e c o r r e l a t i o n . MacLeod (104) d e r i v e d the g e n e r a l r e l a t i o n s h i p , V - ^ [ ^ / ( v u - u . ) ] e E / R T U 7 ) where V w / (Vu-W) i s the r a t i o of the t o t a l volume t o f r e e space and \f| ^  and are t h e v i s c o s i t i e s of the l i q u i d and vapor r e s p e c t i v e l y . De C a r v a l h o (105) on s e m i t h e o r e t i c a l grounds, d e r i v e d the f o r m u l a ^ T ^ ' Vo ; (48) where V|o i s t h e v i s c o s i t y a t a t m o s p h e r i c p r e s s u r e and ^ a and ^ a r e the d e n s i t i e s a t at m o s p h e r i c and under h i g h p r e s s u r e r e s p e c t i v e l y . He found t h a t handbook d a t a f o r CS2 and MeOH agree w i t h t h i s f o r m u l a . The f o l l o w i n g a re some o t h e r c o r r e l a t i o n s w h i c h have been used f o r p r e s s u r e - v i s c o s i t y d a t a . i ) Warburg and Sachs (106) proposed a s i m p l e l i n e a r r e l a t i o n s h i p , > = y\e(\ + OLV) (49) and found good agreement f o r w a t e r , CO z , e t h e r and benzene up t o 150 atm. i i O Bridgman (17) has a p p l i e d a s i m p l e e x p o n e n t i a l f o r m u l a , ^ = Ae P (50) t o h i s e x t e n s i v e d a t a on o r g a n i c l i q u i d s , b u t o b t a i n e d approximate c o r r e l a t i o n o n l y up t o moderate p r e s s u r e s . Kuss (107) a l s o used the f o r m u l a , i n the f o r m ^ = y\0e*k 5 ^ - c t -V-VD ( 5 i ) 40 and has l i s t e d v a l u e s of at , C and b f o r s e v e r a l l i q u i d s a t 25°C,up t o a p r e s s u r e o f 2000 atm. i i i ) I r a n y (108) had d e s c r i p e d an e m p i r i c a l c o r r e l a t i o n w h i c h would r e l a t e a l l v i s c o s i t y - p r e s s u r e f u n c t i o n s of l i q u i d s by a g e n e r a l law c a l l e d t h e 'Tf - f u n c t i o n . Dow (98) has p o i n t e d out t h a t the c o r r e l a t i o n i s of l i m i t e d a p p l i c a -b i l i t y because a l l e x p e r i m e n t a l e v i d e n c e i s c o n t r a r y t o a u n i q u e , e x p l i c i t , v i s c o s i t y - p r e s s u r e f u n c t i o n . T h i s o b s e r v a t i o n a p p l i e s e q u a l l y t o the e x p o n e n t i a l f o r m u l a e above. i n p a r t i c u l a r l u b r i c a n t s , has been t h e s u b j e c t of much r e s e a r c h s i n c e the f i r s t measurements i n 1916 by Hersey and Shore (20) w i t h the r o l l i n g - b a l l v i s c o m e t e r . A c o n s i d e r a b l e degree of agreement between experiment and e m p i r i c a l c o r r e l a t i o n has been a c h i e v e d . The s u b j e c t has been w e l l r e c e i v e d by Hersey and Hopkins (109) and by Dow (98). The a p p l i c a b i l i t y of the ASTM v i s c o s i t y - t e m p e r a t u r e c h a r t D341-39 f o r i n t e r p o l a t i n g h i g h p r e s s u r e d a t a has been shown by Dow (98). Sanderson (110) and l a t e r C l a r k (111) have extended the use of the ASTM c h a r t by n o t i n g t h a t t e m p e r a t u r e and p r e s s u r e have an e q u i v a l e n t e f f e c t on t h e v i s c o s i t y , w h i c h i s e x p r e s s e d by the e m p i r i c a l r e l a t i o n , The e f f e c t o f p r e s s u r e on the v i s c o s i t y o f o i l s , and (52) .41 o where P i s i n p s i . and T i n R . C l a r k p o i n t e d out t h a t t h e c o r r e l a t i o n i s good up t o moderate p r e s s u r e s , but d e v i a t i o n s up t o 100$ were n o t e d f o r some o i l s a t h i g h p r e s s u r e s . I t i s c o n c l u d e d t h a t - the s e a r c h f o r c o r r e l a t i o n o f v i s c o s i t y - p r e s s u r e d a t a w i t h o t h e r p h y s i c a l p r o p e r t i e s has not been s u c c e s s f u l and much e x p e r i m e n t a l and t h e o r e t i c a l work remains t o be done. 4 2 (e) Theory i n R e l a t i o n t o the n - a l c o h o l s The above c o n s i d e r a t i o n s on the t h e o r y o f t h e v i s c o s i t y o f l i q u i d s w i t h p a r t i c u l a r r e f e r e n c e t o the e f f e c t o f t emperature and p r e s s u r e have i n d i c a t e d t h a t a s s o c i a t e d l i q u i d s i n g e n e r a l are more d i f f i c u l t t o f i t t o a c c e p t e d t h e o r i e s and c o r r e l a t i o n s t h a n n o n - a s s o c i a t e d l i q u i d s . I n p a r t i c u l a r , the n - a l c o h o l s show c o n s i d e r a b l e d e v i a t i o n s from the normal b e h a v i o r o f the l a r g e m a j o r i t y of u n a s s o c i a t e d compounds. T h i s p a r a l l e l s the n o n - i d e a l b e h a v i o r of the n - a l c o h o l s f o r o t h e r p h y s i c a l p r o p e r t i e s of l i q u i d s . I n e s s e n c e , we are d e a l i n g w i t h a b i n a r y m i x t u r e o f a s s o c i a t e d and u n a s s o c i a t e d s p e c i e s and over much of the range, the degree of a s s o c i a t i o n i s c h a n g i n g r a p i d l y . I t i s not s u r p r i s i n g t h e n t h a t anomalous b e h a v i o r i s observed i n p r o p e r t i e s of the l i q u i d s t a t e , such as v i s c o s i t y , where the s i z e of the m o l e c u l e s and the magnitude of t h e m o l e c u l a r f o r c e s are of such obv i o u s i m p o r t a n c e . The b e h a v i o r of the n - a l c o h o l s i n r e l a t i o n t o t h e o r i e s o f the l i q u i d s t a t e and o f v i s c o s i t y i n p a r t i c u l a r , has a t t r a c t e d a c e r t a i n amount of p r a c t i c a l and t h e o r e t i c a l r e s e a r c h . The r e l a t i o n of the v i s c o s i t y v a r i a t i o n o f the members w i t h i n the s e r i e s t o m o l e c u l a r s t r u c t u r e i s a l s o o f g r e a t i n t e r e s t . F o r t u n a t e l y , the e f f e c t o f t e m p e r a t u r e and p r e s s u r e have been s t u d i e d f o r the f i r s t f i v e members, n o t a b l y by Thorpe and Rodger (11) and by Bridgman (17,33-35) 43 . ( p r e s s u r e ) . The purpose of the p r e s e n t work has been t o attempt t o extend the range t o h i g h e r members of the s e r i e s and t h i s has been a c h i e v e d f o r the e f f e c t o f t e m p e r a t u r e on . the v i s c o s i t y of n - o c t a n o l . Thole (112) t r i e d t o o b t a i n a c o r r e l a t i o n by p l o t t i n g t h e l o g v i s c o s i t y of the n - a l c o h o l s a t p a r t i c u l a r t e m p e r a t u r e s a g a i n s t the number of c a r b o n atoms i n the m o l e c u l e and found a s t r a i g h t - l i n e r e l a t i o n s h i p f o r the C and h i g h e r members a t each t e m p e r a t u r e . M e t h a n o l and e t h a n o l were anomalous i n t h i s r e s p e c t . Thorpe and Rodger suggested t h a t c omparison s h o u l d be made a t t e m p e r a t u r e s f o r w h i c h the t e m p e r a t u r e c o e f f i c i e n t , 5— , was the same, i m p l y i n g t h a t d such t e m p e r a t u r e s were some f o r m o f " c o r r e s p o n d i n g t e m p e r a t u r e s , " b u t no improvement i n the c o r r e l a t i o n was o b t a i n e d . o f c o r r e s p o n d i n g s t a t e s a p p l i e s t o the n - a l c o h o l s and o b t a i n e d a s i n g l e c u r v e f o r a l l t h e members a t v a r i o u s Senders c o n s t i t u t i v e f a c t o r mentioned p r e v i o u s l y (76)• They a l s o o b t a i n e d good c o r r e l a t i o n f o r the s a t u r a t e d l i q u i d s and v a p o r s by p l o t t i n g Thorpe and Rodger (11) and Dunstan,,Benson and S m i t h and Brown (75) f o u n d t h a t a s p e c i f i c t h e o r y t e m p e r a t u r e s by p l o t t i n g vs.TV, where I i s the c r i t i c a l p r e s s u r e of EtOH it •it 44 a g a i n s t the reduced t e m p e r a t u r e , T . A g a i n a s i n g l e c u r v e was o b t a i n e d . The method i s l i m i t e d i n a p p l i c a b i l i t y because of the l a c k of c r i t i c a l t e m p e r a t u r e and p r e s s u r e d a t a . G o l i k , R a v i k o v i c h and O r i s h c h e n k o (113) have made a d e t a i l e d s t u d y of the v i s c o s i t y of n - a l c o h o l s and m i x t u r e s i n r e l a t i o n t o m o l e c u l a r s t r u c t u r e . They a n a l y s e d t h e i r measurements by the s i m p l e e x p o n e n t i a l f o r m u l a , e q u a t i o n (10), and found t h a t t h e a c t i v a t i o n energy i n c r e a s e s and t h e p r e -e x p o n e n t i a l f a c t o r d e c r e a s e s w i t h i n c r e a s e of t h e c r i t i c a l t e m p e r a t u r e of the a l c o h o l , i . e . , w i t h i n c r e a s i n g m o l e c u l a r w e i g h t , w h i c h , t h e y n o t e , i s i n complete agreement w i t h t h e shape of t h e p o t e n t i a l e n e rgy c u r v e s f o r t h e s e s u b s t a n c e s . Andrade (51) has c a l c u l a t e d t h e v a l u e s of C and i n h i s r e l a t i o n f o r the e f f e c t o f t e m p e r a t u r e on v i s c o s i t y , e q u a t i o n (9), f o r t h e a l c o h o l s f r o m C]_ t o C^. The i n c r e a s e of o< and d e c r e a s e of C w i t h i n c r e a s e of m o l e c u l a r wt. i s i n concordance w i t h the o b s e r v a t i o n s o f G o l i k , R a v i k o v i c h and O r i s h c h e n k o , mentioned above. J a e g e r (58) has noted t h a t the p l o t o f l o g Y| v s . J/-f f o r EtOH and n—PrlOH tends t o a s t r a i g h t l i n e a t h i g h temper-a t u r e s , but shows obvi o u s c u r v a t u r e a t low t e m p e r a t u r e s . He assumes t h a t the degree o f a s s o c i a t i o n g r a d u a l l y d e c r e a s e s w i t h i n c r e a s i n g t e m p e r a t u r e and t h a t a t h i g h t e m p e r a t u r e a t t a i n s a f i x e d v a l u e i n d i c a t e d by a c o n s t a n t v a l u e of the 45 energy of a c t i v a t i o n (or t h e s l o p e of t h e l o g v j \/^- p l o t . J o b l i n g and Lawrence (114) have r e c e n t l y examined the e x i s t i n g v i s c o s i t y - p r e s s u r e and v o l u m e - p r e s s u r e d a t a o f the normal a l c o h o l s t o and i s o b u t a n o l and have o b t a i n e d good c o r r e l a t i o n o f the d a t a . They show t h a t a t c o n s t a n t t e m p e r a t u r e , t h e v i s c o s i t y - v o l u m e d a t a l i e on a smooth c u r v e . F u r t h e r , a p l o t of l o g a g a i n s t gave s t . l i n e s , a t c o n s t a n t volume. From t h i s p l o t , t h e y o b t a i n e d t h e i s o c h o r i c energy a c t i v a t i o n , E^, as a f u n c t i o n o f the volume f r o m atmo-s p h e r i c p r e s s u r e t o v e r y h i g h p r e s s u r e s . U n f o r t u n a t e l y , t h e te m p e r a t u r e d a t a i s l i m i t e d t o o n l y t h r e e o r f o u r t e m p e r a t u r e s and f o r some i s o c h o r e s o n l y two t e m p e r a t u r e s . A g r a p h showing t h e r e l a t i o n s h i p between E and V f o r the f o u r a l c o h o l s i s v g i v e n and i n d i c a t e s t h a t the energy of a c t i v a t i o n i n c r e a s e s c o n t i n u o u s l y as the volume d e c r e a s e s ( w i t h i n c r e a s e of p r e s s -u r e ) . E t h y l a l c o h o l shows an a p p a r e n t l y anomalous b e h a v i o u r , i n h a v i n g a minimum a c t i v a t i o n energy a t a r e l a t i v e volume o f about 0 . 9 5 . The a u t h o r s n o t e t h a t t h i s may be p a r t l y due t o e x p e r i m e n t a l e r r o r I n the d a t a , b u t t h a t the d e p t h of the minimum seems t o o l a r g e t o be accounted f o r e n t i r e l y by e x p e r i m e n t a l e r r o r . The b e h a v i o r i s p a r t i c u l a r l y anomalous s i n c e MeOH shows no such b e h a v i o r . (The f i r s t two members of a homologous s e r i e s o f t e n show anomalies i n p h y s i c a l p r o p e r t i e s ) . T h i s approach has p r o v i d e d a v e r y s i g n i f i c a n t advance i n t h e c o r r e l a t i o n o f p r e s s u r e d a t a f o r a l c o h o l s . 46 I t would u n d o u b t e d l y be most r e w a r d i n g t o extend p r e s s u r e measurements t o o t h e r t e m p e r a t u r e s , and t o h i g h e r members of the s e r i e s w i t h a view t o c o n f i r m i n g t h i s c o r r e l a t i o n and p o s s i b l y p r e d i c t i n g the g e n e r a l v i s c o s i t y - t e m p e r a t u r e -p r e s s u r e b e h a v i o r o f t h e n - a l c o h o l s . B o n d i (50) c o n c l u d e s t h a t , i n a q u a n t i t a t i v e way, the v i s c o s i t y r e f l e c t s the s t r e n g t h o f the hydrogen bonds i n l i q u i d s w i t h c o n t i n u o u s a s s o c i a t i o n and s u b s t a n t i a t e s t h i s by showing the h i g h degree of c o r r e l a t i o n between the I s o c h o r i c energy o f a c t i v a t i o n f o r the v i s c o s i t y and t h e excess energy of v a p o r i z a t i o n TdS v, where, A S V i s t h e e n t r v o f v a p o r i z a t i o n . 47 APPARATUS AND PROCEDURE (a) C a p i l l a r y Viscometers I) D e s c r i p t i o n and Operation. F i v e c a p i l l a r y viscometers were used i n t h i s r e s e a r c h ; these were r o u t i n e Cannon-Fenske viscometers of the type recommended by the ASTM f o r t e s t i n g petroleum products, which i s described by Cannon and Fenske (14) and i n the ASTM p u b l i c a t i o n s (25). Two of these (Nos. A54 and A91) were s i z e 50, two (Nos, B78 and B82) were s i z e 100 and one (N0.C8) was s i z e 200. A diagram of one of these viscometers, i s given i n f i g u r e I . The s p e c i f i c a t i o n s f o r the three s i z e s used are as f o l l o w s : S i z e I.D. of tube C,m.m. I.D. of tube F,m.m. Rang; ;e, CS. 50 2 .6 - 3.4 0.42 - 0.02 0.8 - 3.2 100 2.8 - 3 .6 0 .63 - 0.02 3 - 12 200 2.8 - 3 . 6 1.02 - 0.02 20 - 80 Other important dimensions, which are standard f o r a l l s i z e s , are shown i n f i g u r e I . Viscometer no. B78 was obtained w i t h a c a l i b r a t i o n c e r t i f i c a t e from the Cannon Instrument Co., State C o l l e g e , Pa. A copy of the c a l i b r a t i o n c e r t i f i c a t e i s reproduced i n Appendix I I . 3?o f o l l o w page F i g u r e 1. Cannon-Fenske V i s c o m e t e r 48 The O p e r a t i o n o f t h e s e v i s c o m e t e r s was e s s e n t i a l l y the same as t h a t recommended by the ASTM ( 2 5 ) . The v i s c o -meter was f i r s t f i l l e d by i n v e r t i n g , p l a c i n g t h e o p e n i n g o f l i m b C under the l i q u i d b e i n g t e s t e d , and a p p l y i n g s u c t i o n a t arm A t o draw l i q u i d up i n t o b u l b s D and E. T h i s f i l l i n g p r o c e e d u r e was done a t room t e m p e r a t u r e . The l i q u i d was drawn up as f a r as the et c h e d mark ,H, on the c a p i l l a r y t u b e , F. The v i s c o m e t e r was t h e n q u i c k l y w i t h d r a w n f r o m t h e l i q u i d and i n v e r t e d . Any l i q u i d c l i n g i n g t o the o u t s i d e o f tube C was t h e n wiped o f f w i t h f i l t e r p aper, and the v i s c o m e t e r p l a c e d i n a c o n s t a n t t e m p e r a t u r e b a t h , m a i n t a i n e d a t the a p p r o p r i a t e t e s t t e m p e r a t u r e . By t h i s f i l l i n g p r o c e e d u r e , a c o n s t a n t volume was I n t r o d u c e d i n t o the v i s c o m e t e r a t each f i l l i n g , thus e n s u r i n g a c o n s t a n t f l u i d d r i v i n g head f o r each d e t e r m i n a t i o n . A note was made of the room tem p e r a t u r e a t the t i m e o f f i l l i n g , i n case i t was n e c e s s a r y t o c o r r e c t f o r the same f i l l i n g t e m perature f o r each r u n . However, i t w i l l be shown t h a t t h i s c o r r e c t i o n i s n e g l i g i b l e f o r changes of up t o 5°C i n room t e m p e r a t u r e . F o r a l l the d e t e r m i n a t i o n s on the a l c o h o l s , p r e c a u t i o n s were t a k e n t o ensure t h a t m o i s t u r e d i d not come i n t o c o n t a c t w i t h the l i q u i d f o r more t h a n a few m i n u t e s . T h i s was n e c e s s a r y because t h e n - a l c o h o l s a r e somewhat h y g r o s c o p i c and absorb a c o n s i d e r a b l e amount o f m o i s t u r e i f exposed f o r l o n g p e r i o d s t o m o i s t a i r . The d r y i n g system i l l u s t r a t e d i n f i g u r e 2 was a t t a c h e d t o t h e v i s c o m e t e r s as soon as t h e y were p l a c e d i n the c o n s t a n t t e m p e r a t u r e b a t h . To f o l l o w page 48 TO ATMOSPHERE TO SUCTION SILICA-GEL DRYING TUBE t n>4-C HX1-D TO LOWER RESERVOIR TO EFFLUX BULB F i g u r e 2. D r y i n g System f o r C a p i l l a r y V i s c o m e t e r 49 I n o r d e r t o a p p l y s u c t i o n t o the e f f l u x b u l b v a l v e B was c l o s e d , v a l v e A opened and s u c t i o n a p p l i e d . When the l i q u i d s passed etched mark, G, f i g u r e 1, v a l v e A was c l o s e d , v a l v e B opened and the e f f l u x t i m e t a k e n as d e s c r i b e d p r e v i o u s l y . One or o t h e r v i s c o m e t e r c o u l d be s e l e c t e d by c l o s i n g the a p p r o p r i a t e v a l v e C or D or t h e y c o u l d be f i l l e d s i m u l t a n e o u s l y by l e a v i n g b o t h v a l v e s open. Between r u n s , v a l v e A was always kept c l o s e d so t h a t the system was o n l y open t o t h e atmosphere t h r o u g h the d r y i n g t u b e . S u c t i o n f o r the f i l l i n g and o p e r a t i o n was s u p p l i e d b y a s t a n d a r d r u b b e r s u c t i o n b u l b . The c o n s t a n t t e m p e r a t u r e b a t h used f o r t h e s e d e t e r m i -n a t i o n s was a g l a s s c y l i n d r i c a l b a t h 12" d i a . by 12" h i g h . I t was s u p p l i e d w i t h two h e a t e r s of 250 w a t t s each, One o f the h e a t e r s b e i n g c o n t r o l l e d by a t h e r m o r e g u l a t o r an e l e c t -r o n i c r e l a y f o r o n - o f f c o n t r o l and the o t h e r b e i n g permanent-l y on. B o t h the h e a t i n p u t s c o u l d be v a r i e d c o n t i n u o u s l y f r o m z e r o t o f u l l l o a d t h r o u g h V a r i a c a u t o - t r a n s f o r m e r s . The t h e r m o r e g u l a t o r was a H g - l n - g l a s s t y p e ( P r e c i s i o n S c i e n t i f i c , M i c r o s e t d i f f e r e n t i a l r a nge) w i t h v a r i a b l e c o n t a c t a l l o w i n g f o r c o n t r o l a t any temperature w i t h i n a 45°C range w i t h o u t c h a n g i n g t h e amount of Hg i n the b u l b . The e l e c t r o n i c r e l a y was s u p p l i e d by P r e c i s i o n S c i e n t i f i c Co., ( C a t . No. 6535, S e r i a l No. C-10). The b a t h was i n s u l a t e d w i t h a few l a y e r s of a s b e s t o s paper, uncovered p o r t i o n s b e i n g l e f t i n the f r o n t and t h e back of t h e b a t h , i n o r d e r t o view the p o s i t i o n o f 5,0 the l i q u i d i n the viscometers. A small (5 - watt) l i g h t bulb was shone through the back of the bath to help i n viewing the viscometers c l e a r l y . Pour v e r t i c a l l i n e s about 2" apart were marked on the outside of the bath t o help i n a d j u s t i n g the viscometers to a v e r t i c a l p o s i t i o n before each run. I n order to make t h i s adjustment the centre l i n e through C,D,E and B was made to c o i n c i d e w i t h at l e a s t two of these v e r t i c a l l i n e s . The bath was equipped w i t h a c o o l i n g c o i l which could be suppli e d w i t h c o l d tap water. The bath medium used was tap water. The oper a t i o n of t h i s constant-temperature bath was found to be very s a t i s f a c t o r y , any temperature between 15° and 90°C, being maintained c o n v e n i e n t l y at - i 0.02°C. The temperature was. read from Hg-thermometers graduated in^-°C, and equipped w i t h thermo-meter l e n s , enabled readings to the nearest 0.01°C. Thermometers No.821 (0 - 60°C) and No.3502 (50- 110°C) were used, both having been c a l i b r a t e d against a Platinum Resistance thermometer w i t h an N.B.S. c e r t i f i c a t e . The d e t a i l s of the c a l i b r a t i o n of these thermometers are given i n Appendix I I I . I t i s f e l t t hat these c a l i b r a t i o n s were accurate to the nearest 0.02°C and that t h e r e f o r e the temper-ature of the v i s c o s i t y determinations were known to the nearest 0.04°C. Care was taken to ensure that the same Immersion used i n the c a l i b r a t i o n was maintained d u r i n g a l l the determinations so that no c o r r e c t i o n f o r the emergent stem was necessary (assuming constant room temperature). 51 I n o r d e r t o determine the e f f l u x t i m e , s u c t i o n was a p p l i e d a t C, a f t e r s u f f i c i e n t time had e l a p s e d t o ensure t h a t the l i q u i d i n the v i s c o m e t e r had a t t a i n e d t h e tempera-t u r e o f the b a t h , and l i q u i d was drawn f r o m b u l b B i n t o b u l b E and about 1 cm. p a s t t h e e t c h e d mark G. The time was t a k e n f o r the l i q u i d s u r f a c e t o move fr o m etched mark G t o e t c h e d mark H. F o r most o f t h i s work a s t o p - w a t c h g r a d u a t e d i n t e n t h s o f a second was used f o r t i m i n g the j s f f l u x o f the l i q u i d . F o r the c a l i b r a t i o n r u n s i n w h i c h t h e time o f e f f l u x o f the same l i q u i d i n v i s c o m e t e r B78 and o t h e r s were compared, i t was u n n e c e s s a r y t o have the s t o p - w a t c h c a l i b r a t e d . However, f o r the c a l i b r a t i o n r u n s w i t h d i s t i l l e d w a t e r , and o t h e r a b s o l u t e d e t e r m i n a t i o n s , i t was n e c e s s a r y t o know the e x a c t times a b s o l u t e l y . T h i s s t o p - w a t c h was t h e r e f o r e c a l i b r a t e d , by comparison w i t h an e l e c t r i c l a b o r a t o r y t i m e r w h i c h was r u n by a synchronous motor, and g r a d u a t e d i n s e e s . A c c o r d i n g t o t h e B r i t i s h Columbia E l e c t r i c Co. L t d . (115), the f r e q u e n c y of e l e c t r i c power i n Vancouver was m a i n t a i n e d c o n s t a n t t o w i t h i n 0.05 c y c l e a t a l l times e x c e p t "peak" p e r i o d s d u r i n g w h i c h the v a r i a t i o n would n o t exceed 0.1 c y c l e . A e h a r t f o r v a r i a t i o n of t h e f r e q u e n c y over an average day i n d i c a t e d the t i m e s o f t h e "peak" p e r i o d s , and showed t h a t t h e v a r i a t i o n s were r o u g h l y o s c i l l a t o r y , and t h a t over a p e r i o d o f one hour, the average v a r i a t i o n would 5 2 be much smaller than 0.05 c y c l e . This corresponds to the synchrons t i m i n g device having an accuracy c o n s i d e r a b l y greater than 0.1$ f o r periods of about one hour. The f o l l o w i n g comparison was obtained, Synchronous Stopwatch, % D i f f . Timer,mins. Seconds slow  45 4.3 0.159 60 6.0 0.167 45 4.2 0.156 Mean d e v i a t i o n = 0.16$ slow. At the end of a l l c a l i b r a t i o n runs, the watch was readjusted u n t i l no appreciable d i f f e r e n c e was obtained between i t s time and those of the synchronous timer. A f t e r the l a s t adjustment, the f o l l o w i n g comparison was obtained, Synchronous Stopwatch $ D i f f . Timer 45 mins. +0.2 sec. +0.008 45 mins. - 0.5 sec. -0.018 45 mins. 0.0 sec. 0.0 Mean d e v i a t i o n = 0.01$ slow. F i n a l l y , the stop-watch was compared w i t h the timer used i n con j u n c t i o n w i t h the pressure viscometer (see below), This m a g n e t i a l l y operated timer was guaranteed by the 53 m a n u f a c t u r e r s t o have an a b s o l u t e p r e c i s i o n o f i - j ^ second i n f o u r m i n u t e s , o r about — 0 . 0 4 % Oomparison o f t h e s t o p -w a t c h w i t h t h e t i m e r over s e v e r a l p e r i o d s o f about t h i r t y m i n u t e s , show no s i g n i f i c a n t d e v i a t i o n I n the t i m e s r e a d by b o t h i n s t r u m e n t s . D u r i n g the l a t t e r p a r t o f t h i s work, and i n p a r t i c u l a r t h e d e t e r m i n a t i o n s on n - a l c o h o l , b o t h the stop-., watch and the m a g n e t i c a l l y o p e r a t e d t i m e r were used t o deter m i n e the e f f l u x times i n t h e c a p i l l a r y v i s c o m e t e r s . D u r i n g a l l the c a l i b r a t i o n r u n s i n w h i c h v i s c o m e t e r B78 was compared w i t h o t h e r ' v i s c o m e t e r ^ t h e two w e r e . f i l l e d w i t h i n , m i n u t e s , p l a c e d i n t h e b a t h t o g e t h e r , and the e f f l u x t i m e s t a k e n i m m e d i a t e l y f o l l o w i n g one a n o t h e r . T h i s proceedure ensured t h a t d u r i n g c a l i b r a t i o n r u n s no c o r r e c t i o n was n e c e s s a r y f o r v a r i a t i o n i n e i t h e r f i l l i n g t e m p e r a t u r e o r b a t h t e m p e r a t u r e . There was a l s o no e r r o r due t o i n a c c u r a c y i n t he t i m i n g d e v i c e , i f i t I s assumed t h a t the s t o p - w a t c h o p e r a t e d c o n s i s t e n t l y d u r i n g the c o m p a r a t i v e c a l i b r a t i o n s . The e f f l u x t i m e s f o r each r u n were r e p e a t e d a t l e a s t t h r e e times,and the mean o f the t h r e e v a l u e s was t a k e n as t h e c o r r e c t time t o be used t o de t e r m i n e t h e k i n e m a t i c v i s c o s i t y . R e p r o d u c i b i l i t y o f e f f l u x t imes was u s u a l l y w i t h i n 0.1% and i n even extreme c a s e s , never exceeded 0 . 2 $ . A l l t he a b s o l u t e d e t e r m i n a t i o n s were made i n d u p l i c a t e w i t h two d i f f e r e n t v i s c o m e t e r s kept i n t h e b a t h a t the same t i m e , and the average o f t h e two v i s c o s i t i e s 54 ^ o b t a i n e d i s r e p o r t e d as t h e v i s c o s i t y o f the l i q u i d . These do n ot s e r v e as two independent d e t e r m i n a t i o n s , s i n c e t h e two v i s c o m e t e r s have been c a l i b r a t e d a g a i n s t t h e same s t a n d a r d , and e r r o r s i n t h e c o n s t a n t o f t h i s v i s c o m e t e r would be p r e s e n t i n the c o n s t a n t s o f t h e o t h e r s . However, t h i s p r o c e e d u r e does h e l p t o re d u c e e r r o r s due t o a l i g n m e n t out of t he v e r t i c a l and d i f f e r e n c e s i n the volume o f sample t a k e n A f i l l i n g . I t a l s o s e r v e s t o b r i n g out i r r e g u l a r b e h a v i o r w h i c h may a r i s e out o f d u s t e n t e r i n g the v i s c o m e t e r and grease c l i n g i n g t o the c a p i l l a r y . When a d e t e r m i n a t i o n was complete, the v i s c o m e t e r s were washed w i t h s o l v e n t . F o r d e t e r m i n a t i o n s on o i l s , t h e y were washed t w i c e w i t h benzene, and t w i c e w i t h a c e t o n e , and f o r o t h e r d e t r m i n a t i o n s , t h r e e washings w i t h acetone were u s e d . F i n a l l y t he v i s c o m e t e r s were d r i e d by p a s s i n g a i r t h r o u g h them. The a i r was c o n t i n u o u s l y p u r i f i e d and d r i e d i n a t r a i n c o n s i s t i n g o f cone. NaOH s o l r i , d i s t i l l e d w a t e r and s i l i c a g e l s u p p o r t e d between two l a y e r s of c o t t o n - w o o l . T h i s ensured t h a t no d u s t e n t e r e d the v i s c o m e t e r s d u r i n g d r y i n g . When out o f u s e , t h e y were s t o r e d i n a c l e a n d r y c a b i n e t i n an i n v e r t e d p o s i t i o n , t h e open ends r e s t i n g on a f l a t g l a s s p l a t e . From t i m e t o t i m e , i t was n o t i c e d t h a t one o r o t h e r of the v i s c o m e t e r s began t o g i v e i r r e g u l a r times and when t h i s o c c u r r e d t h e v i s c o m e t e r was c l e a n e d i n h o t chromic a c i d , 55 washed s u c c e s s i v e l y i n r u n n i n g t a p water and w i t h d i s t i l l e d w a t e r , and d r i e d . T h i s would i n v a r i a b l y c u r e the e r a t i c b e h a v i o r w h i c h was p r o b a b l y due t o g r e a s e or d u s t i n the c a p i l l a r y , i i ) Theory o f and C o r r e c t i o n s f o r Cannon-Fenske  V i s c o m e t e r s . An e x c e l l e n t summary of the t h e o r y o f c a p i l l a r y v i s c o m e t e r s , w i t h p a r t i c u l a r r e f e r e n c e t o the Cannon-Fenske m o d i f i e d Ostwald v i s c o m e t e r , i s g i v e n by Cannon (116), I t makes r e f e r e n c e t o i m p o r t a n t work on the magnitude o f the k i n e t i c e n e rgy c o r r e c t i o n w h i c h was n o t a v a i l a b l e i n an e a r l i e r a r t i c l e by Cannon and Fenske (14). f l u i d i n a c a p i l l a r y o f f i n i t e l e n g t h i s g i v e n i n terms o f the d r i v i n g head as f o l l o w s : " The f i r s t term r e p r e s e n t s the f r a c t i o n of the d r i v i n g head w h i c h goes t o overcome the v i s c o u s f o r c e i n the l e n g t h L of c a p i l l a r y , as g i v e n by P o i s e u i l l e 1 s l a w . The second t e r m I s the f r a c t i o n o f the d r i v i n g head w h i c h i s used t o overcome the i n e r t i a l e f f e c t s a t the e n t r a n c e and e x i t of the c a p i l l a r y . S o l v i n g f o r t h e k i n e m a t i c v i s c o s i t y , — , one o b t a i n s the b a s i c v i s c o s i t y e q u a t i o n a s , The b a s i c e q u a t i o n g o v e r n i n g the v i s c o u s f l o w o f a (53) The meaning of a l l symb.ols used here and else w h e r e i n t h i s r e p o r t a r e c o n t a i n e d under "Nomenclature" i n t h e p r e l i m i n a r y pages o f the r e p o r t . . 56 V - i = - ^ ^ ( K . - V X ) - ( 5 4 ) ? 8 U V V 8 ITU-T V = C t - J f c / t " (55) where, \/ (56) 6 U V 1 I n t h e s e e q u a t i o n s , i f c.g.s. u n i t s a r e used t h r o u g h o u t , "Y|_ i s i n p o i s e s and V i n s t o k e s . K i n e t i c Energy C o r r e c t i o n The term B/ t i s the k i n e t i c energy c o r r e c t i o n . U n f o r t u n a t e l y , B i s not a c o n s t a n t because m i s a f u n c t i o n o f the Reynolds:;; Ho, and w i l l t h e r e f o r e v a r y w i t h t h e e f f l u x t i m e . B a r r (4) has i n d i c a t e d t h a t v a l u e s of m f r o m 0 t o 1.12 have been r e p o r t e d ^ a n d Cannon (116) quotes e x p e r i m e n t a l v a l u e s w h i c h show t h a t even f o r the same v a l u e o f Re, m v a r i e s f r o m one i n s t r u m e n t t o another, depending on the shape of the e n t r a n c e and e x i t of the c a p i l l a r y . The g e n e r a l c o n c l u s i o n s drawn a r e t h a t m approaches z e r o a t v e r y low v a l u e s of Re and i n c r e a s e s w i t h i n c r e a s i n g Re up t o a v a l u e of about u n i t y ; a l s o , square-ended c a p i l l a r i e s show a l a r g e r v a l u e of m t h a n do those w i t h g r a d u a l l y t a p e r e d or trumpet-shaped ends. Prom the f i g u r e s g i v e n by Cannon, i t can be c o n c l u d e d t h a t m w i l l not exceed 0 .4 i n an i n s t r u m e n t w i t h g r a d u a l l y t a p e r e d e n t r a n c e and e x i t (as i n the Cannon-Penske v i s c o m e t e r ) , p r o v i d i n g the Reynolds No. does not exceed 100 57 r On s u b s t i t u t i n g f o r m, V and L i n the e x p r e s s i o n f o r B/j., i t i s found that the c o r r e c t i o n w i l l be l e s s than, 0.4 x 3.15 1 = 5.3 x 10" 3 3 t o k e 8 Tf x 9.5 t t As a percentage of the approximate v i s c o s i t y Ct, the c o r r e c t i o n i s l e s s than, 53- ^ c e n t i s t o k e , % where C i s i n /sec. On t h i s b a s i s , the minimum value of t f o r a maximum allowable k i n e t i c energy c o r r e c t i o n has been c a l c u l a t e d f o r the three s i z e s of viscometer, as f o l l o w s : -Size Approx Value of Minimum Value of t f o r max. e r r o r constant C. 0.1$ 0.2$ 0.3$ 50 0.0025 460 325 265 100 0.012 210 150 120 200 0.10 70 50 40 The corresponding values of the Reynolds No. are approximately as f o l l o w s • Corresponding Re at max. e r r o r of Size 0.1$ 0.2$ • 0.3$ 50 18 29 55 . ' 100 12 23 37 200 8 15 22 Since these values of Re are w e l l below 100, the r e l e v a n t value of m i s l i k e l y to be l e s s than 0.4 and hence 58 the minimum times given are conservative estimates. Surface Tension On the assumption t h a t , f o r the purposes of surface t e n s i o n c o r r e c t i o n , the viscometer behaves as a u-tube w i t h the arms having d i f f e r e n t , constant, r a d i i T; and N~2 at the exposed surface, the e f f e c t i v e d i f f e r e n c e i n d r i v i n g head, A H S T , f o r two l i q u i d s of d i f f e r e n t surface t e n s i o n , i s given by, I n f a c t , the r a d i u s of the e f f l u x bulb,'C, and the lower r e s e v o i r ^ b o t h change at the f r e e surface of the l i q u i d , so that equation (57) i s not exact. An accurate method of c a l c u l a t i o n which in c l u d e s the changing diameter at the f r e e surface has been developed by Barr(117) and Sugden (118). Gannon, however, has shown th a t the e f f e c t i s small and that the use of equation (57) w i l l give s u f f i c i e n t l y accurate r e s u l t s f o r the c o r r e c t i o n . I t i s i n t e r e s t i n g to consider the magnitude of t h i s e f f e c t f o r various l i q u i d s . S u b s t i t u t i n g the appropriate values f o r t , , -Cx and H i n t o equation (5T) g i v e s , or ArU-r r v. Or- /o - - ' ' 0 1 H = 0 0 1 0 6 (.T. - T,) ( 5 8 ) 5-9 The v a l u e o f V, , w h i c h has been s u b s t i t u t e d i s 0 . 8 ( TJ ) max., where ( ) max = 1 .5 cm. Hence, i n o r d e r t o keep the c o r r e c t i o n l e s s t h a n 0 . 1 $ , the change i n (^~) must be l e s s t h a n about 11 u n i t s . V a l u e s o f (-^  ) were c a l c u l a t e d f rom the d a t a i n Timmermans (29) and are r e p r o d u c e d i n t a b l e 1 f o r a v a r i e t y of l i q u i d s . Prom the t a b l e , i t can be seen t h a t a t 20°C, t h e v a l u e o f f o r a r o m a t i c s , p a r a f f i n s and a l c o h o l s v a r i e s f r o m 28 t o 35 and f o r " o t h e r s " f rom 26 t o 4 3 . F u r t h e r m o r e , a 60° r i s e i n t e m p e r a t u r e causes a r e d u c t i o n ^ a b o u t 7 u n i t s . T h i s shows t h a t the s u r f a c e t e n s i o n c o r r e c t i o n f o r measurements on o r g a n i c l i q u i d s i s q u i t e s m a l l , i f the c a l i b r a t i o n has been done w i t h o r g a n i c l i q u i d s o r i s r e f e r r e d t o a v a l u e o f (^) o f about 33 u n i t s . The c o r r e c t i o n f o r water compared w i t h o r g a n i c l i q u i d s i s q u i t e i m p o r t a n t . P e r r y (119) g i v e s t h e s u r f a c e t e n s i o n o f water as 7 2 . 8 dynes per cm^ a t 20°C w h i c h g i v e s a v a l u e of (—) c l o s e t o 73 u n i t e s whence A ( - ^ ) r^j 40 u n i t s and the c o r r e c t i o n i s about 0 . 4 $ a t 20°C. T h i s c o r r e c t i o n must be a p p l i e d when c a l i b r a t i o n s a r e b e i n g done w i t h w a t e r . V a r i a t i o n i n F i l l i n g Temperature and T e s t Temperature. T h i s causes a change i n the t o t a l volume o f l i q u i d i n the v i s c o m e t e r and c o n s e q u e n t l y changes the d r i v i n g head, H. F o r o i l s , Cannon and Fenske (1 ) recommend u s i n g a l i n e a r i n t e r p o l a t i o n based on 0 . 5 $ d i f f e r e n c e f o r 60°C change i n TABLE I APPROXIMATE VALUES OF (|r) FOR COMMON 60 ORGANIC LIQUIDS L i q u i d A r o m a t i c s .Benzene Toluene E t h y l Benzene O-xylene D e c a l i n P a r a f f i n s n-C 8 3-MeHeptane n-C„ n-C 14 Temperature, C 20 60 20 30 20 20 20 20 85 20 50 20 85 20 r v dynes/cm*  ^ * gma/cirr A l c o h o l s °i °2 n-C~ i - c | °4 C8 " O t h e r s " EtOAc Acetophenone P h e n o l A n i l i n e 20 30 20 30 20 30 20 30 20 30 20 30 50 20 80 33 27.5 33 32 33.5 34.5 35 31" 24.5 30 27 32 24" 34.5 28.5 28. 28.5 27.5 29.5 27.5 30.0 30.5 26.5 25.5 38 38 34 42.5 38 61 temperature. However, t h i s i s not very accurate and f o r an exact c a l c u l a t i o n the f o l l o w i n g formula was developed, C r ^ C x L , V-- V' (59) where and C-^  are the c a l i b r a t i o n constants and and V-^  the volume of l i q u i d at the two temperatures, r e s p e c t i v e -l y . S u b s t i t u t i n g f o r H and d one obtains % p = 1.46 ( Vz- V, ) = 1.46 V, (<?•/?,- \ ) and since V^ = 7 c c s . AC % ~c = 10.5 I ) (60) This c a l i b r a t i o n can be used f o r c a l c u l a t i n g the temperature c o r r e c t i o n q u i t e a c c u r a t e l y . The c o r r e c t i o n Is u s u a l l y l e s s than 0.1$ f o r a 10°C change, and I n general the magnitude of the c o r r e c t i o n depends on the l i q u i d being t e s t e d . V a r i a t i o n i n Bath Temperature. The e r r o r s due to v a r i a t i o n In bath temperature during a run and inaccuracy i n the reported t e s t temperature, are c l e a r l y not a f u n c t i o n of the viscometer. These e r r o r s can be estimated from a knowledge of the approximate r^ — T data f o r the l i q u i d being t e s t e d . Assuming a l i n e a r 62 v a r i a t i o n of l o g a g a i n s t ]/y , one can w r i t e \ - ^ or l o g Y| = l o g A + -=^. D i f f e r e n t i a t i n g t h i s r e l a t i o n Prom a knowledge o f the v a l u e o f oL y t h e e r r o r c a n be c a l c u l a t e d . F o r n-PrOH a t 30°C, a change i n temp e r a t u r e o f 0.05°C l e a d s t o a v a l u e o f =£j r^j 0.05$. At low t e m p e r a t u r e s , the e f f e c t i s - o b v i o u s l y more i m p o r t a n t t h a n a t h i g h e r t e m p e r a t u r e s . " O v e r s h o o t i n g " the f i l l i n g mark. T h i s c o r r e c t i o n i s s i m i l a r t o t h a t f o r v a r i a t i o n i n f i l l i n g t e m p e r a t u r e . The c o r r e c t i o n i s g i v e n i n terms o f the e f f e c t i v e change of head due t o the volume o f the o v e r s h o o t . I t can be r e a d i l y shown t h a t f o r the s e r i e s 200 v i s c o m e t e r s a l o a d i n g e r r o r of 0.1$ w i l l o n l y a r i s e i f the f i l l i n g mark i s o v e r s h o t by about 10 cms. The c o r r e c t i o n w i l l c l e a r l y be l e s s f o r t h e s e r i e s 100 and 50, so i t i s u n i m p o r t a n t . A l i g n m e n t E r r o r The Cannon-Penske V i s c o m e t e r s a re d e s i g n e d w i t h t h e e f f l u x b u l b d i r e c t l y above the lo w e r r e s e r v o i r , and w i t h t h i s d e s i g n the minimum d e v i a t i o n i s o b t a i n e d f o r •."alignment e r r o r s . 63 An e r r o r of 0.1$ w i l l o n l y a r i s e i f the a l i g n m e n t i s out b y as much as 2 ^° w h i c h i s v e r y e a s i l y a v o i d e d . i l l ) C a l i b r a t i o n of C a p i l l a r y V i s c o m e t e r s . The proceedure f o r the c a l i b r a t i o n o f c a p i l l a r y v i s c o m e t e r s i s g i v e n i n d e t a i l i n the ASTM "T e s t f o r K i n e m a t i c V i s c o s i t y " (D445-53T) (25). The method i s based on the use o f "Master V i s c o m e t e r s " as p r i m a r y s t a n d a r d s . These v i s c o m e t e r s have been d e s c r i b e d by Cannon (23) and a n a l y s e d as a b s o l u t e i n s t r u m e n t s by S w i n d e l l s , Hardy and C o t t i n g t o n (24) a t t h e N a t i o n a l Bureau of S t a n d a r d s , who found t h a t c a l i b r a t e d w i t h f r e s h l y d i s t i l l e d w a t e r , A a r e v e r y a c c u r a t e p r i m a r y s t a n d a r d s • I n the "Master V i s c o m e t e r s , " t h e d r i v i n g head, H, i s about 47 cms. w h i c h i s about 5 t i m e s t h e d r i v i n g head f o r t h e r o u t i n e v i s c o m e t e r s . S i n c e the o t h e r d i m e n s i o n s a r e a p p r o x i m a t e l y the same as i n t h e r o u t i n e i n s t r u m e n t s , t h i s means t h a t the c o r r e c t i o n s a r e a p p r o x i m a t e l y 1/5 o f t h o s e f o r t h e r o u t i n e v i s c o m e t e r s . S w i n d e l l s , Hardy and C o t t i n g t o n (74) found t h a t the t o t a l of a l l t h e c o r r e c t i o n s amounted t o o n l y 0.13$ i n extreme cases and t h a t the c o r r e c t i o n s c o u l d be a p p l i e d v e r y a c c u r a t e l y . The ASTM recommends u s i n g M a s t e r v i s c o m e t e r s w h i c h have been c a l i b r a t e d w i t h w a t e r , t o d e t e r m i n e the v i s c o s i t y of a s e r i e s of h y d r o c a r b o n l i q u i d s and d e s c r i b e a " s t e p - u p " proceedure by w h i c h t h i s can be done f o r a wide range of 64 v i s c o s i t i e s w i t h a minimum e r r o r . E i t h e r o f two p r o c e e d u r e s a r e recommended f o r c a l i b r a t i n g r o u t i n e v i s c o m e t e r s of the t y p e used i n t h i s work; (1) c a l i b r a t i c h d i r e c t l y w i t h o i l s w h i c h have been de t e r m i n e d i n "Master V i s c o m e t e r s " or (2) by means of I n s t r u m e n t S t a n d a r d s , i . e . d i r e c t c o m p a r i s o n o f u n c a l i b r a t e d r o u t i n e v i s c o m e t e r s w i t h those c a l i b r a t e d by method (1), above. I n t h i s work, v i s c o m e t e r B 7 8 w h i c h was c a l i b r a t e d by the Cannon I n s t r u m e n t Co. i s such ana I n s t r u -ment S t a n d a r d . I n b o t h methods (1) and (2), above,the ASTM recommends c a l i b r a t i o n o f each v i s c o m e t e r w i t h a t l e a s t two l i q u i d s of d i f f e r e n t v i s c o s i t y . The c a l i b r a t i o n p r o c e e d u r e o u t l i n e d above ensures t h a t the c a l i b r a t i o n ! o f a r o u t i n e v i s c o m e t e r i s a c c u r a t e l y done r e l a t i v e t o w a t e r . I n o r d e r t o measure v i s c o i t i e s a c c u r a t e l y on an a b s o l u t e b a s i s , i t i s n e c e s s a r y t o know t h e v a l u e of t h e v i s c o s i t y of water on an a b s o l u t e b a s i s . U n t i l q u i t e r e c e n t l y , the v i s c o s i t y of w a t e r was n o t a c c u r a t e l y known* I n 1952, S w i n d e l l s , Coe and G o d f r e y (22) p u b l i s h e d r e s u l t s based on v e r y a c c u r a t e e x p e r i m e n t s f r o m w h i c h t h e y determined the v i s c o s i t y of w a t e r a t 20°C as 1.0019 - 0.0003 c e n t i p o i s e . They recommend t h a t a v a l u e of 1.002 cp. be used as the s t a n d a r d f o r V i s c o s i t y measurements. S w i n d e l l s , Hardy and C o t t i n g t o n (24) have r e p o r t e d t h a t the l e a d i n g p h y s i c a l l a b o r a t o r i e s i n Europe have agreed t o concur i n t h i s recommendation w i t h t h e i r A merican c o u n t e r p a r t s . P r e v i o u s t o 1952, t h e v a l u e a c c e p t e d by t h e N a t i o n a l Bureau of S t a n d a r d s 65 and the ASTM was 1.005 cp. However, other reputable sources have given values which do not agree w e l l w i t h t h i s f i g u r e . The I n t e r n a t i o n a l C r i t i c a l Table (26) f o r example gives the f i g u r e of 1.0087. L a n d o l t - B o r n s t e i n , 5 T H E d i t i o n (27) l i s t s the values obtained by w e l l known experimenters, and these range from 0.9978 to 1.007 cp. This u n c e r t a i n t y i n the value of v i s c o s i t y of water at some standard temperature makes i t very d i f f i c u l t to compare v i s c o i t y measurements before 1952 from d i f f e r e n t sources. I t would be a r e l a t i v e l y simple matter to c o r r e c t previous measurements i n accordance w i t h the value of 1.002 cp. at 20°C i f the standard being used was quoted, but, u n f o r t u n a t e l y , t h i s i n f o r m a t i o n i s seldom given. In t h i s work, the c a l i b r a t i o n constants f o r v i s c o -meters A54, A91 and B82 were obtained by d i r e c t comparison of the e f f l u x times of three l i q u i d s i n these viscometers and viscometer B78. The kinematic v i s c o s i t i e s of these l i q u i d s v a r i e d from about 2 to 8 c e n t i s t o k e s . A f o u r t h comparison was made between B78 and B82 w i t h an o i l w i t h kinematic v i s c o s i t y of about 10 c e n t i s t o k e s . The c a l i b r a t i o n constant of viscometer C8 was determined approximately by a s i n g l e comparison w i t h B78>using an o i l w i t h kinematic v i s c o s i t y of about 35 c e n t i s t o k e s . No f u r t h e r measurements were made w i t h C8 during the course of t h i s work. As a f i n a l check, runs w i t h f r e s h l y d i s t i l l e d water were c a r r i e d out w i t h the s e r i e s 50 viscometers (A54 and A91) and the values of the c a l i b r a t i o n 66 c o n s t a n t s compared w i t h t h o s e p r e v i o u s l y o b t a i n e d . The l i q u i d s used f o r these c a l i b r a t i o n s were d e c a l i n , n - p r o p a n o l and 3 p e t r o l e u m o i l s , d e s i g n a t e d o i l s A, B and C, w h i c h were p r e p a r e d by m i x i n g v a r i o u s p r o p o r t i o n s o f SAE 10 and k e r o s e n e ; o i l C was u n d i l u t e d SAE 10. The samples of d e c a l i n and n - p r o p a n o l were C P . grades used w i t h o u t f u r t h e r p u r i f i c a t i o n , because of the c o m p a r a t i v e n a t u r e o f the d e t e r m i n a t i o n s . A l l t h e l i q u i d s used were f i l t e r e d i n t o c l e a n , d r y f l a s k s w h i c h were p r o v i d e d w i t h g r o u n d - g l a s s s t o p p e r s . The d i s t i l l e d w a t e r used f o r ..the check c a l i b r a t i o n s was f r e s h l y d i s t i l l e d i n a s t a n d a r d l a b o r a t o r y s t i l l . The work of S w i n d e l l s , Coe and G o d f r e y (22) has shown t h a t r e s u l t s o b t a i n e d w i t h water produced by a s i m p l e d i s t i l l a t i o n , s u c h as i s a c c o m p l i s h e d by a commercial l a b o r a t o r y s t i l l , p r o d u c e s w a ter o f a s u f f i c i e n t l y u n i f o r m c o m p o s i t i o n . Hence, no o t h e r f o r m of p u r i f i c a t i o n , n or a second d i s t i l l a t i o n was r e q u i r e d . (b) The P r e s s u r e V i s c o m e t e r i ) H i s t o r i c a l The r o l l i n g b a l l v i s c o m e t e r c o n s i s t s e s s e n t i a l l y o f an i n c l i n e d tube of u n i f o r m d i a m e t e r down w h i c h a b a l l of s m a l l e r d i a m e t e r r o l l s under the i n f l u e n c e o f g r a v i t y . The a n g l e of r o l l i s u s u a l l y between 4 5 ° t o 5 ° f r o m the h o r i z o n t a l . The m o t i o n o f the b a l l i s r e s i s t e d by the f l u i d , and hence the time of r o l l f o r a f i x e d d i s t a n c e i s a f u n c t i o n of the v i s c o s i t y of the f l u i d . There i s no \ 6? fundamental d i f f e r e n c e between t h i s instrument and the f a l l i n g - b a l l viscometer a t t r i b u t e d to Hoppler (18) i n which the angle of the i n c l i n e d tube i s kept c l o s e to the v e r t i c a l . The instrument was f i r s t developed i n 1914 by Flowers (19), who used i t f o r atmospheric pressure measure-ments. He discussed i n great d e t a i l the theory of the instrument and the co r r e c t i o n s which must be a p p l i e d . Flowers a l s o l i s t e d the many advantages of the instrument and suggested i t s adaptation to h i g h pressure work, where i t would have many advantages over the c a p i l l a r y viscometer. Hersey and Shore (120) i n 1916 published the f i r s t r e s u l t s obtained w i t h t h i s instrument under pressure up to 7,000 p s i . L a t e r developments (121,122,20) l e d to the design of a pressure instrument which could be used f o r measurements up to 60,000 p s i . and temperatures up to 14-0°C, i n the v i s c o s i t y range from 0.004 t o 300 p o i s e s . The instrument has since been used e x t e n s i v e l y f o r h i g h pressure measurements of the v i s c o s i t y of l i q u i d s over wide ranges of pressure and temperature. Hocott and Buckley (123) have developed the instrument f o r r o u t i n e t e s t s on subsurface o i l samples 1and m o d i f i c a t i o n s are now a v a i l a b l e commercially. Sage and as s o c i a t e s (36,38,39) have made extensive measurements on both gases and l i q u i d s and have 68 d i s c u s s e d t h e t h e o r y o f t h e i n s t r u m e n t . More r e c e n t l y , measurements w i t h the r o l l i n g - b a l l v i s c o m e t e r have been r e p o r t e d by E x l i n e and En Dean (124) Mason, W i l c o x and Sage (37) M a k i t a (125,126) and Lundberg (107). The t h e o r y of the i n s t r u m e n t was i m p e r f e c t l y known u n t i l 1943,when Hubbard and Brown (128) p u b l i s h e d a t h e o r y based on d i m e n s i o n a l a n a l y s i s of the r e l e v a n t v a r i a b l e s and checked by l i t e r a t u r e d a t a and many measurements of t h e i r own. T h i s t h e o r y e n a b l e s measurements t o be put on a sound b a s i s and makes f o r a much more c e r t a i n e v a l u a t i o n o f t h e v a r i o u s e r r o r s and c o r r e c t i o n s . Lewis (129) has r e c e n t l y a n a l y s e d t h e i n s t r u m e n t i n terms of the hydrodynamics of v i s c o u s f l u i d s and found good agreement w i t h Hubbard and Brown. i i ) D e s c r i p t i o n and O p e r a t i o n . The f o r m of R o l l i n g -b a l l v i s c o m e t e r used i n t h i s r e s e a r c h was e s s e n t i a l l y t h a t d e s c r i b e d by Hoc.ott and B u c k l e y (123) f o r m e a s u r i n g the v i s c o s i t y o f s u b - s u r f a c e samples of o i l . The d e s c r i p t i o n and o p e r a t i n g i n s t r u c t i o n s f o r t h e o r i g i n a l d e s i g n a r e r e p r o d u c e d i n Appendix IV fr-om the o r i g i n a l m a n u f a c t u r e r s s h e e t s . A d e t a i l e d s e c t i o n e d d r a w i n g of the v i s c o m e t e r has a l s o been r e p r o d u c e d and i s shown i n f i g u r e 3« M o d i f i c a t i o n s have been made, p a r t i c u l a r l y i n the t i m i n g system, w i t h a view t o i m p r o v i n g the a c c u r a c y of the i n s t r u m e n t . 69 P l a c i n g the v i s c o m e t e r tube i n the l a t h e i n d i c a t e d t h a t i t was not p e r f e c t l y s t r a i g h t a l o n g i t s l e n g t h . T h i s meant t h a t , s i n c e no p r o v i s i o n was made f o r o r i e n t i n g t h e b a r r e l i n a c o n s t a n t p o s i t i o n r e l a t i v e t o the v i s c o m e t e r body, t h e p a t h f o l l o w e d by t h e b a l l was not t h e same f o r each d e t e r m i n a t i o n . The f i r s t two s e t s o f c a l i b r a t i o n r u n s (see below) g a v e - i n c o n s i s t e n t r e s u l t s , i n d i c a t i n g t h a t t h i s e f f e c t was i m p o r t a n t so p r o v i s i o n was made t o m a i n t a i n the tube , I n the same r e l a t i v e p o s i t i o n f o r each r u n . I n t h i s way, a l t h o u g h the b a l l d i d not t r a v e l a l o n g a f i x e d s l o p e f o r the whole l e n g t h o f the tub e , i r r e g u l a r i t i e s i n t h e tube would not a f f e c t the c o n s i s t e n c y o f the i n s t r u m e n t . I n o r d e r t o m a i n t a i n t h e b a r r e l i n a f i x e d p o s i t i o n , t h e r o l l - t u b e was keyed t o the l o c k - n u t w h i c h i s used t o keep the b a r r e l i n p l a c e . S i n c e the l o c k - n u t was screwed t i g h t l y i n t o the b a r r e l and was t h e r e f o r e i n a f i x e d p o s i t i o n , the tube was a l s o main-t a i n e d i n a f i x e d p o s i t i o n r e l a t i v e t o the b a r r e l . A f t k e r t h i s was done, f u r t h e r c a l i b r a t i o n r u n s i n d i c a t e d t h a t the i n s t r u m e n t o p e r a t e d c o n s i s t e n t l y . The d i a m e t e r o f the b a r r e l was de t e r m i n e d w i t h a t r a v e l l i n g m i c r o s c o p e . S e v e r a l t r a v e r s e s were made a c r o s s d i f f e r e n t d i a m e t e r s and the mean o f a l l t h e v a l u e s t a k e n as the t r u e d i a m e t e r . A s i n g l e b a l l was used t h r o u g h o u t t h i s work. I t was a s t a i n l e s s s t e e l b a l l f r o m a l o t of 12 w h i c h was o b t a i n e d f r o m a b a l l - b e a r i n g m a n u f a c t u r e r , and had a r a t e d d i a m e t e r of 0.2500 ± 0.0005 i n . Each o f the 12 b a l l s 70 were weighed and found to have weights v a r y i n g from 1.0261 to 1.0315 gflis., w i t h a mean weight of 1.0285 grm. I t was assumed that the v a r i a t i o n i n weight was due t o v a r i a t i o n i n the diameter and not the d e n s i t y of the m a t e r i a l , ' and the d e n s i t y was c a l c u l a t e d from the mean weight and the ra t e d diameter. The f o l l o w i n g i s a summary of these measure-ments, Tube d i a . (measured) = 0.2583 - 0.0008 i n s . B a l l d i a . (manufacturer) = 0.2500 i 0.0005 I n s . B a l l wt. (measured) = 1.0261 gms. B a l l d e n s i t y ( c a l c u l a t e d ) = 7.671^ gms/cm3 on the ba s i s of mean wt. of 12 b a l l s . The i n s u l a t e d contact at the bottom of the b a r r e l which i n d i c a t e s the i n s t a n t at which the b a l l reaches the end of i t s r o l l was al s o modified s l i g h t l y . A short copper contact was provided i n the o r i g i n a l design, and t h i s was replaced by a nichrome contact about 2 cms. lo n g . This means that the e f f e c t i v e l e n g t h of the viscometer tube was reduced from about 20 to 18 cms. l " A f l a t s p i r a l s p r i n g was made from the g s t a i n l e s s s t e e l t u bing which was used i n the pressure system,and connected to the body connector w i t h the s p r i n g i n a v e r t i c a l plane, and i n such a way that the t e n s i o n of the s p r i n g kept the viscometer body f i r m l y down on the f i x e d stop. Another m o d i f i c a t i o n which was made to the instrument was to 71 incorporate a back stop, s i m i l a r to the f i x e d stop mentioned i n the o p e r a t i n g i n s t r u c t i o n s . Most extensive m o d i f i c a t i o n s were made to the o r i g i n a l , manually operated, system used f o r t i m i n g the t r a v e r s e of the b a l l . A new t i m i n g system was designed to r e g i s t e r a u t o m a t i c a l l y the time of r o l l , as shown i n f i g u r e 4. A prime c o n s i d e r a t i o n i n t h i s design was to m a i n t a i n as small a current as p o s s i b l e through the b a l l and the i n s u l a t e d contact at the bottom of the viscometer tube. I n order to a t t a i n this,, a s e n s i t i v e e l e c t r o n i c r e l a y (Cenco E l e c t r o n i c Relay, Cat. No. F3961, S e r i a l No. 113) was used. Designed f o r on-off c o n t r o l of heating systems,110V a.c. was provided at the t e r m i n a l s , J , but f o r the present purpose i t was modified by i s o l a t i n g the power r e l a y c o n t a c t s , D. A current of about 10 microA. i s s u f f i c i e n t to operate t h i s r e l a y . The timer used f o r most of t h i s work was a Jacquet l a b o r a t o r y stop-watch, c a t . No. 308d (130) which i s graduated i n sec. and i s provided w i t h an " i n p u l s e " electromagnet f o r s t a r t i n g and stopping. I n t h i s design, the watch i s s t a r t e d or stopped by c l o s i n g the magnet c i r c u t , and opening the c i r c u i t merely de-energizes the magnet and r e l e a s e s the s t a r t - s t o p plunger, making the watch ready f o r another c y c l e of o p e r a t i o n . To f o l l o w page 71 VISCO-METER MERCURY SWITCH TIMER 110 V ru F i g u r e 4. T i m i n g System f o r P r e s s u r e V i s c o m e t e r 7 2 Another t i m e r was deve l o p e d d u r i n g the c o u r s e o f t h i s work, but i t was not used f o r any measurements r e p o r t e d h e r e , a l t h o u g h i t was found t o o p e r a t e s a t i s f a c t o r i l y . I t i s d e s c r i b e d i n Appendix V. A g l a s s e n c l o s e d mercury s w i t c h , A, was clamped t o the o u t s i d e o f the v i s c o m e t e r body and p a r a l l e l t o i t , i n such a way t h a t the s w i t c h was open when t h e body was i n the p o s i t i o n w i t h the i n s u l a t e d c o n t a c t up,and c l o s e d when the body was i n i t s normal p o s i t i o n a g a i n s t the f i x e d - s t o p . The mercury s w i t c h t e r m i n a l s were connected i n p a r a l l e l w i t h the I n s u l a t e d c o n t a c t , C, and a t t a c h e d t o the "T" t e r m i n a l s o f the e l e c t r o n i c r e l a y . A m a n u a l l y o p e r a t e d s w i t c h B was connected i n s e r i e s w i t h the mercury s w i t c h , as shown. The r e l a y c o n t a c t s , D, were connected d i r e c t l y t o the o n - o f f t e r m i n a l s , F^of the magnet o f t h e t i m e r . F i n a l l y power was s u p p l i e d t o the e l e c t r o n i c r e l a y and the t i m e r a t E and G, r e s p e c t i v e l y . The body o f the v i s c o m e t e r was "grounded" t o the frame w h i c h s u p p o r t e d the c o n s t a n t t e m p e r a t u r e b a t h i n w h i c h the v i s c o m e t e r was immersed d u r i n g d e t e r m i n a t i o n s . The c o n s t a n t temperature b a t h was 27" x 14" s e c t i o n and 19" h i g h , made fr o m 1/4" sheet a l u m i n i u m and alu m i n i u m w elded; i t was equipped w i t h a d r a i n f o r c l e a n i n g out p u r p o s e s . The b a t h was s u p p o r t e d on a s o l i d D e x i o n frame w i t h the bottom h o r i z o n t a l a c c o r d i n g t o a s p i r i t l e v e l . 73 I t was I n s u l a t e d w i t h 2" o f l o o s e r o c k wool and the bottom was s u p p o r t e d on 2" i n s u l a t i n g b r i c k s , t h e spaces between the b r i c k s b e i n g f i l l e d i n w i t h r o c k w o o l . The t o p was c o v e r e d w i t h 1/2" plywood on w h i c h t h e h e a t e r s and thermo-r e g u l a t o r were mounted, as w e l l as t e r m i n a l s f o r t h e e l e c t r i c a l c o n n e c t i o n s t o the v i s c o m e t e r . The b a t h medium was Chevron No. 9 White O i l w i t h a v i s c o s i t y of 190 s a y b o l t s e e s , a t 100°P and a f l a s h p o i n t o f 350°F. The b a t h was s t i r r e d by a ! / l 6 H.P. E a s t e r n E l e c t r i c v a r i a b l e speed ( r h e o s t a t c o n t r o l l e d ) s t i r r e r . Two 500 w a t t C a l r o d h e a t e r s w i t h s t a i n l e s s s t e e l s h e aths were u s e d , one b e i n g connected d i r e c t l y t o the mains w i t h a s w i t c h and 5&mp. f u s e i n s e r i e s , and the o t h e r t o an e l e c t r o n i c r e l a y f o r 5n-o f f c o n t r o l . The r e l a y was a Cenco R e l a y C o n t r o l U n i t , Cat, No. 60940,.which was, v e r y s i m i l a r t o the one used f o r the t i m i n g system. The t h e r m o r e g u l a t o r was a m e r c u r y - i n - g l a s s t y p e w i t h b o t h l a r g e s u r f a c e and l a r g e volume. The o n - o f f h e a t e r was hooked up i n such a way t h a t n o r m a l l y p a r t of t h e l o a d was p e r m a n e n t l y on and p a r t was on o n - o f f c o n t r o l , and a s w i t c h was p r o v i d e d w h i c h c o u l d b r i n g a l l o f the l o a d t o on-o f f c o n t r o l . The power s u p p l i e d was c o n t r o l l e d by r h e o s t a t s , and ammeters were p r o v i d e d t o i n d i c a t e the heat i n p u t . S w i t c h e s , r e h e o s t a t s , ammeters and p i l o t l i g h t s were mounted on a p a n e l f o r c o n v e n i e n c e . 74 The temperature was measured by a C e n t r i g r a d e M e r c u r y thermometer No. 6343 w i t h 0.1°C g r a d u a t i o n s and range 0 — 110°C w h i c h had been p r e v i o u s l y c a l i b r a t e d a g a i n s t a p l a t i n u m r e s i s t a n c e thermometer c e r t i f i e d by t h e N.B.S. (see Appendix I I I f o r c a l i b r a t i o n ) . Care was t a k e n t o m a i n t a i n t h e immersion t h e same as t h a t used i n t h e c a l i b r a -t i o n so t h a t no c o r r e c t i o n f o r the emergent stem was r e q u i r e d . A f t e r the d e t e r m i n a t i o n on each o i l , t h e v i s c o m e t e r was emptied and d i s m a n t l e d , and a l l t h e p a r t s were t h o r o u g h l y c l e a n e d . The c l e a n i n g p r o c e e d u r e i n v o l v e d two or t h r e e washings w i t h benzene, and a s i m i l a r number w i t h acetone and f i n a l l y d r y i n g w i t h a i r f o r one h o u r . The v i s c o m e t e r . t u b e was t h e n r e p l a c e d i n the body and-a new c a l i b r a t i n g l i q u i d was poured i n w i t h the body s u p p o r t e d i n a v e r t i c a l p o s i t i o n . L i q u i d was i n t r o d u c e d up t o a few m.m. above the s h o u l d e r w h i c h s u p p o r t s the body c l o s u r e , and t h e n the b a l l w a s , ; i n t r d -duped. I n f a l l i n g down the tube, the b a l l d i s p l a c e d any a i r b u b b l e s w h i c h may have been t r a p p e d i n the tube and f o r c e d ' th e s e t h r o u g h the s l o t s on the o u t s i d e of the t u b e . The c l o s u r e was t h e n r e p l a c e d , w i t h the p l u n g e r c o m p l e t e l y w i t h -drawn, and t i g h t e n e d down f i r m l y . I n i t a l l y , l i q u i d was d i s p l a c e d between the body and the c l o s u r e and t h r o u g h the t u b i n g a t t a c h e d t o the body c o n n e c t o r , e n s u r i n g t h a t no a i r was t r a p p e d i n the v i s c o m e t e r . F i n a l l y , t h e v i s c o m e t e r was p l a c e d i n the c o n s t a n t t e m p e r a t u r e b a t h and the a p p r o p r i a t e e l e c t r i c a l and t u b i n g c o n n e c t i o n s were made. 75 S e v e r a l hours were a l l o w e d f o r t h e v i s c o m e t e r t o r e a c h t e m p e r a t u r e e q u i l i b r i u m . A f t e r about 2-3 h r s ; , t h e v i s c o m e t e r was r o t a t e d t o the r e v e r s e p o s i t i o n and t h e b a l l a l l o w e d t o r o l l out i n t o the upper chamber. Then t h e v i s c o -meter was r o t a t e d back t o the v e r t i c a l p o s i t i o n and the b a l l e n t e r e d t h e tube a g a i n , d i s p l a c i n g the l i q u i d i n t h e tube i n t o t h e upper chamber v i a the s l o t s . T h i s m i x i n g p r o c e e d u r e was r e p e a t e d s e v e r a l t i m e s t o ensure u n i f o r m t e m p e r a t u r e e q u i l i b r i u m between t h e v i s c o m e t e r and i t s c o n t e n t s , and the b a t h o i l . F i n a l l y t he f r o n t and back f i x e d s t o p s were put i n p l a c e , and the p l u n g e r screwed down t i g h t l y f i x i n g the tube f i r m l y a g a i n s t the b a r r e l g a s k e t and c l o s i n g o f f the upper end of the t u b e . I n o r d e r t o dete r m i n e the time o f r o l l , t he v i s c o -meter body was r o t a t e d a g a i n s t the t e n s i o n o f the s p r i n g , and kept i n t h e r e v e r s e p o s i t i o n / w i t h the i n s u l a t e d c o n t a c t up, u n t i l s u f f i c i e n t t i m e had e l a p s e d t o ensure t h a t the b a l l had r e t u r n e d t o the t o p of the tube and r e s t e d on the end o f the p l u n g e r . When s u f f i c i e n t time had e l a p s e d , the body was h e l d a g a i n s t the b a c k - s t o p and t h e n s u d d e n l y r e l e a s e d w i t h s w i t c h B i n the c l o s e d p o s i t i o n . As the body r o t a t e d by t h e a c t i o n o f t h e s p r i n g , the merc u r y s w i t c h was a u t o m a t i c a l l y c l o s e d and the e l e c t r o n i c r e l a y a c t i v a t e d . T h i s c l o s e d t h e r e l a y c o n t a c t s D, w h i c h e n e r g i z e d t h e e l e c t r o - m a g n e t and s t a r t e d the t i m e r . The e l e c t r o - m a g n e t was d e - e n e r g i z e d and made r e a d y f o r the s t o p p i n g o p e r a t i o n by opening t h e manual s w i t c h , B , At the end •76 of the r o l l , when the b a l l touched the i n s u l a t e d contact, C, the e l e c t r o n i c r e l a y was again a c t i v a t e d and stopped the timer. In t h i s way the time of r o l l was obtained automatic-a l l y and was read to the nearest sec. At the end of one determination, the body was again r o t a t e d to the reverse p o s i t i o n and the b a l l allowed to r o l l back to the i n i t i a l p o s i t i o n . As the b a l l l e f t the i n s u l a t e d contact, the r e l a y c i r c u i t was broken and the electromagnet again de-energized. Between 5 and 20 successive determinations were made on each l i q u i d at each temperature and the mean of these was taken as the c o r r e c t time of r o l l . H i ) Theory and E r r o r s . The b a s i c equation d e s c r i b -i n g the r e l a t i o n s h i p between the v a r i a b l e s i n the r o l l i n g -b a l l viscometer, as derived by Hubbard and Brown (128), i s , ri = H aCt>4-d) (62) where, K i s the c o r r e l a t i o n f a c t o r and i s a f u n c t i o n of the diameter r a t i o ( /D) only. According to t h i s equation, when a s i n g l e b a l l and tube are being considered, so that d and D are constant, and when the angle from the h o r i z o n t a l , 0 , i s constant, the v i s c o s i t y i s given by the r e l a t i o n , ^ = C ' J L ^ L s C ' F E _ ? ) T ( 6 3 ) or ri = C ( f t - ? ) - t (64) Prom t h i s equation, G i s the c a l i b r a t i o n constant, and i f i t i s known, the v i s c o s i t y of any l i q u i d can be determined from 77 t h e time o f r o l l , -fc; , and t h e d e n s i t y d i f f e r e n c e Prom the Hubbard and Brown e q u a t i o n , t h e c a l i b r a t i o n c o n s t a n t i s g i v e n by, c = W a ( t > + < 9 (65 E q u a t i o n (65) i s the b a s i s f r o m w h i c h the v a r i a t i o n o f the c a l i b r a t i o n w i t h v a r i o u s e f f e c t s can be d e t e r m i n e d . The c o r r e l a t i o n f a c t o r , K, i s d e f i n e d by a f r i c t i o n f a c t o r Reynold^:.: No. e q u a t i o n , & = _ L 1 (66) where R i s t h e r e s i s t a n c e of the f l u i d t o m o t i o n o f the b a l l . E q u a t i o n . (Gt>) o n l y h o l d s from low v a l u e s o f Re up t o the c r i t i c a l v a l u e R e c , i . e . , i n the v i s c o u s regime of f l o w . Above the c r i t i c a l R e y n o l d ^ ; No., the f r i c t i o n f a c t o r i s not l i n e a r i n Re. Hubbard and Brown, f r o m an a n a l y s i s of the l i t e r a t u r e d a t a and f r o m s u p p l e m e n t a r y e x p e r i m e n t s o f t h e i r own, have o b t a i n e d c o r r e l a t i o n s f o r R e c and K as a f u n c t i o n o f the d i a m e t e r r a t i o d/D. These c o r r e l a t i o n s a r e g i v e n i n f i g u r e s 5 and 6. The f o r m e r i s v e r y u s e f u l i n d e t e r m i n i n g the minimum t i m e s of r o l l w h i c h must be used i n o r d e r t o r e m a i n below t h e c r i t i c a l Reynold^;.; No. , the l a t t e r f o r o b t a i n i n g an e s t i m a t e o f the c a l i b r a t i o n c o n s t a n t , C, f r o m e q u a t i o n (&;5),' and i n c a l c u l a t i n g t h e magnitude of c e r t a i n e r r o r s . 4 5 4 0 3 5 O UJ cr 3 0 cc o 5 0 I 1 1 1 1 0 . 8 4 0 . 8 8 0 . 9 2 0.96 1.00 D I A M E T E R RATIO — <*/D F i g u r e 5 . - C r i t i c a l Reynolds-: No. f o r R o l l i n g - B a l l V i s c o m e t e r ?8 U n f o r t u n a t e l y , t h e s e c o r r e l a t i o n s a r e not known a c c u r a t e l y enough t o c a l c u l a t e t h e c a l i b r a t i o n c o n s t a n t t o c l o s e r t h a n about i 10%. Hence, the i n s t r u m e n t ' m u s t be c a l i b r a t e d u s i n g f l u i d s o f known v i s c o s i t y and d e n s i t y , and from t h e times of r o l l o b t a i n i n g t h e b e s t s t r a i g h t l i n e c o r r e l a t i o n between and ( ^ - ? ) t # E q u a t i o n (3) i s the same as the e q u a t i o n proposed o r i g i n a l l y by F l o w e r s (19) t o c o r r e l a t e t h e v i s c o s i t y w i t h the time o f r o l l , and i t has been used c o n s i s t e n t l y e v er s i n c e t o c o r r e l a t e the measurements o f r o l l i n g - b a l l and f a l l i n g - b a l l v i s c o m e t e r s . F l o w e r s d i d n o t d e r i v e an e x p r e s s i o n f o r the a b s o l u t e v a l u e of C s i m i l a r t o e q u a t i o n (65). He based h i s a n a l y s i s on t h e Stokes e q u a t i o n f o r f r e e f a l l o f a sphere, -t = (67) 4Z<3 (<?*-?> and assumed f o r the r o l l i n g - b a l l v i s c o m e t e r , an e q u a t i o n c o u l d be w r i t t e n i n t h e form, - t = W ^ 4 (68) where W i s a c o r r e c t i o n f a c t o r f o r the " w a l l - e f f e c t , and hence, ' C = - d j _ (69) 18W T h i s type of approach, i n w h i c h the Stokes law e q u a t i o n i s m o d i f i e d t o accomodate w a l l - e f f e c t s , has s i n c e been used by IS F r a n c i s (131) and Bacon (132) but no c o n s i s t a n t c o r r e l a t i o n has been obtained, except f o r values of d/D which are much smaller than u n i t y . The approach of Hubbard and Brown (128) and of Lewis (129) Is'- more fundamental and seems to be much c l o s e r to the tru e p i c t u r e . However, there s t i l l seems to be some doubt about the v a l i d i t y of equation (&,5) which gives the absolute value of the constant ,C, In p a r t i c u l a r , i t seems that the sine f u n c t i o n does not apply except at reasonably small angles from the h o r i z o n t a l and t h i s has been s u b s t a n t i -ated by the work of Block (133) and Young ( 1 3 4 ) . The l a t t e r a t t r i b u t e s the d e v i a t i o n from the sine f u n c t i o n at higher angles of slope to a combination of r o l l i n g and s l i d i n g . From a p r a c t i c a l p o i n t of view, the f u n c t i o n a l r e l a t i o n between G and the diameter r a t i o , /^E>, i s much more import-ant, and i t seems that the Hubbard and Brown equation gives t h i s c l o s e l y enough to enable one to c a l c u l a t e the c o r r e c t -ions to be a p p l i e d f o r temperature and pressure v a r i a t i o n s . E r r o r s and Co r r e c t i o n s In general, there are many c o r r e c t i o n s to be a p p l i e d to the time of r o l l , t , and the c a l i b r a t i o n constant ,C, before the v i s c o s i t y can be evaluated a c c u r a t e l y from equation ( 6 4 ) . Under many c o n d i t i o n s , however, the c o r r e c t i o n s are zero or small so that they do not apply. 80 1) Timing c o r r e c t i o n s . There may be a time l a g i n the measuring system, i n other words, the true time of r o l l may d i f f e r from the observed time by a constant f a c t o r due to f i n i t e time lags i n the r e l a y s operating the t i m i n g c i r c u i t . This may show up i n the c a l i b r a t i o n of the i n s t r u -ment by g i v i n g a f i n i t e i n t e r c e p t on the curve of t Vs . ^v^— This time l a g can be determined from the c a l i b r a t i o n and app l i e d to subsequent measurements, since i t i s independent of the v i s c o s i t y being determined, 2) A c c e l e r a t i o n e f f e c t . The b a l l s t a r t s i t s r o l l from r e s t , and t h i s means that i t takes a f i n i t e time to a t t a i n i t s t e r m i n a l v e l o c i t y ; t h i s should a l s o be a p p l i e d as a c o r r e c t i o n to the observed time. An estimate of the e f f e c t can be obtained by s o l v i n g the d i f f e r e n t i a l equation r e l a t i n g to the motion of the b a l l from r e s t up to the time i t a t t a i n s i t s t e r m i n a l v e l o c i t y , — k g | = P _ p V (70) where P = S ' g S i n 6 IL^l ( f t - ? ) (71) and P = 17 (-^—) ( 7 2 ) The general s o l u t i o n of equation (70) i s r e a d i l y obtained as, V = Ae ^ + J L (73) and from the i n i t i a l c o n d i t i o n , t = 0, V = 0,one obtains 81 (74) o r , t h e time t a k e n t o a t t a i n a v e l o c i t y V i s g i v e n by, t = f J U ( l - v £ ) (75) T h i s e q u a t i o n g i v e s the t i m e t o a t t a i n t h e t e r m i n a l v e l o c i t y , w h i c h i s P/^ , as i n f i n i t e . However, a v e r y c l o s e e s t i m a t e of t h e c o r r e c t i o n n e c e s s a r y f o r the a c c e l e r a t i o n e f f e c t i s o b t a i n e d by d e t e r m i n i n g t h e time t o r e a c h , say, 99% o f t h e t e r m i n a l v e l o c i t y . The a p p r o p r i a t e v a l u e s o f F and p c a n be c a l c u l a t e d f r om the d i m e n s i o n s o f the a p p a r a t u s and t h e Hubbard and Brown c o r r e l a t i o n f o r K. 3) E f f e c t o f p r e s s u r e . I f t h e l i q u i d i s under h i g h p r e s s u r e , the tube may i n c r e a s e i n d i a m e t e r , thus c h a n g i n g t h e v a l u e of ^/B from t h a t a t a t m o s p h e r i c p r e s s u r e , a n d t h e e f f e c t i v e v a l u e of the c a l i b r a t i o n c o n s t a n t . Some i n s t r u m e n t s , l i k e the one used i n t h i s work, a r e d e s i g n e d so t h a t the f l u i d b e i n g t e s t e d i s under the same p r e s s u r e i n s i d e and o u t s i d e the r o l l - t u b e . I n such a c a s e , no p r e s s u r e c o r r e c t i o n i s n e c e s s a r y . The magnitude of t h e c o r r e c t i o n can be d e t e r m i n e d by c a l c u l a t i n g the i n c r e a s e i n d i a m e t e r and a p p l y i n g the f o r m u l a Sc. o f d / \ e = J(VDy "6> The f o r m of -~r- w i l l be d e v e l o p e d i n the f o l l o w i n g - s e c t i o n 4Ca/D) on the e f f e c t of t e m p e r a t u r e . 82 4) E f f e c t of Temperature. This i s somewhat more complicated than the e f f e c t of pressure, because temperature may have an important e f f e c t on tube diameter, tube l e n g t h , b a l l diameter and b a l l d e n s i t y . R e w r i t i n g equation (65) one obtains, or o = g < 3 S - e < K i ) ^ - r <vs) Considering the small change g> C f o r small changes i n * V d , d an L , by t a k i n g logs and d i f f e r e n t i a t i n g , one o b t a i n s , | = i i _ S U (79) ° 4> di t_ The f i r s t termvcan be put e x p l i c i t y i n terms of a change of d/D, i n the form, Prom a knowledge of the c o e f f i c i e n t of expansion of the b a l l and the tube ? the value of £ (^/P), £d and £L can be obtained and s u b s t i t u t e d i n t o equation (79) and (80) i n order to o b t a i n the r e q u i r e d c o r r e c t i o n . I n p a r t i c u l a r , to evaluate • &$> » o n e must w r i t e , 4> = k ( 4 + 0 ( 8 1 ) (82) 83 The v a l u e s o f K and • — — can be o b t a i n e d f r o m t h e d(d/o) c o r r e l a t i o n of Hubbard and Brown. I f t h e tube and t h e b a l l a r e b o t h made f r o m t h e same m a t e r i a l so t h a t the c o e f f i c i e n t o f t h e r m a l e x p a n s i o n i s t h e same f o r b o t h , (^/D) i s z e r o and e q u a t i o n C79) r e d u c e s t o , £ = 2 ^ _ ? t (83) P o r a change i n t e m p e r a t u r e , and ^£ a r e e q u a l and a r e g i v e n c l o s e l y b y the p r o d u c t o f the mean v a l u e of the c o e f f i c i e n t o f l i n e a r e x p a n s i o n , , i n t h e te m p e r a t u r e r a n g e , and the t e m p e r a t u r e d i f f e r e n c e , A t ? % = oCXt (84) F i n a l l y , a c o r r e c t i o n s h o u l d be a p p l i e d t o the d e n s i t y o f the b a l l . I t can be e a s i l y shown t h a t t h i s c o r r e c t i o n i s g i v e n c l o s e l y b y, i j r = - 3 ° t A t ( 8 5 ) w h i c h i s t h r e e t i m e s the c o r r e c t i o n t o the c a l i b r a t i o n c o n s t a n t i n the s p e c i a l case when S(^/D) i s z e r o . I n t h i s case the t o t a l c o r r e c t i o n t o t h e v i s c o s i t y c a l c u l a t e d f r o m the c a l i b r a t i o n c o n s t a n t and b a l l d e n s i t y a t the c a l i b r a t i o n t e mperature i s g i v e n a p p r o x i m a t e l y by A t , w h e r e o< i s t h e c o e f f i c i e n t o f t h e r m a l e x p a n s i o n of the b a l l (and the tube) and A t i s the d i f f e r e n c e i n t e m p e r a t u r e . I — E X — H 4 H— t X t " K B t> 1/81 -CXr l a O - X H l b 1/8" 1/4" 0 84 i v ) C a l i b r a t i o n . The pressure viscometer was c a l i b r a t e d at atmospheric pressure using three petroleum o i l s ( O i l s D, E and P) at temperatures of 30°, 4 5 ° and 60°C. A c a l c u l a t i o n based on equations(23) and ( 3 4 ) showed th a t the c o r r e c t i o n f o r temperature i n t h i s range was very s m a l l (see below) and i t was t h e r e f o r e unnecessary to c a l i b r a t e at a s i n g l e temperature. C a l i b r a t i o n s were made at two slopes, approximately 11° and 23° from the h o r i z o n t a l , the three o i l s being used at 11° and two ( O i l s D and E) at 23°, so tha t nine and s i x p o i n t s , r e s p e c t i v e l y , were obtained f o r the two s l o p e s . The range of v i s c o s i t i e s covered was from about 1 . 5 to 10 c e n t i p o i s e s . The petroleum o i l s were blended from SAE 10 and kerosene and were f i l t e r e d i n t o c l e a n g l a s s stoppered f l a s k s . The o i l s were introduced i n t o the viscometer and the viscometer brought up to the t e s t temperature by the proceedure o u t l i n e d p r e v i o u s l y . The times of r o l l at any p a r t i c u l a r temperature were determined f o r the two slopes before moving on to a new temperature. U s u a l l y , determinations were made at 30°C f i r s t , l a t e r 4 5 ° and 60°C, and i n some cases the temperture was again lowered to 30°C and a few runs made to check the consista n c y of ope r a t i o n . I t was found that good agreement was obtained between the two sets at 30°C and t h i s check was omitted i n l a t e r determinations. The kinematic v i s c o s i t y and d e n s i t y of the o i l s were determined by the methods o u t l i n e d above,and from these the absolute v i s c o s i t y was c a l c u l a t e d . The v i s c o s i t y , d e n s i t y and ,85 time of r o l l f o r each o i l a t each t e m p e r a t u r e were c o r r e l a t e d i n o r d e r t o o b t a i n the c a l i b r a t i o n c o n s t a n t f o r the two s l o p e s . At the end o f the d e t e r m i n a t i o n s on each o i l , the v i s c o m e t e r was removed f r o m t h e the c o n s t a n t temperature bath^and the o u t s i d e n e a r the c l o s u r e was c l e a n e d and d r i e d . The c l o s u r e was t h e n opened and a sample o f the o i l p i p e t t e d out f o r a check d e t e r m i n a t i o n on the k i n e m a t i c v i s c o s i t y . I n t h i s way, any c o n t a m i n a t i o n of the c a l i b r a t i n g l i q u i d by b a t h o i l o r by o t h e r means c o u l d be r e a d i l y checked and a t t e n d e d t o . (c) D e n s i t y D e t e r m i n a t i o n s D e n s i t y d e t e r m i n a t i o n s were c a r r i e d o u t i n d u p l i c a t e i n two s p e c i f i c g r a v i t y b o t t l e s o f a p p r o x i m a t e l y 25 m l . volume. The pyknometers were s t a n d a r d V i c t o r Meyer t y p e and were p r o v i d e d w i t h g r o u n d - g l a s s caps t o p r e v e n t e v a p o r a t i o n f r o m the l i q u i d s u r f a c e . The pr o c e e d u r e used f o r f i l l i n g and w e i g h i n g the pyknometers was e x a c t l y as o u t l i n e d by Bauer (135). The pyknometers were f i r s t washed two or t h r e e t i m e s w i t h a c e t o n e , d r i e d i n an oven a t 250°P f o r a few h o u r s , c o o l e d i n a d e s i c c a t o r , and, a f t e r w i p i n g w i t h a m o i s t chamois c l o t h , were p l a c e d I n the b a l a n c e c a s e . A f t e r about o n e - h a l f hour, the b o t t l e s were weighed to the n e a r e s t ^rz m i l l i g r a m on a M e t t l e r G r a m a t l c A n a l y t i c a l 86 Balance, the weighings being repeated u n t i l constant reading was obtained. The pyknometers were c a l i b r a t e d at 30°, 4-5° a n ^ 60°C w i t h f r e s h l y d i s t i l l e d water which had a measured r e s i s t i v i t y of 800,000 ohm cm. and which was b o i l e d j u s t p r i o r to use to remove d i s s o l v e d a i r . Thermostatting at 30°C was c a r r i e d out i n the same constant temperature bath used f o r the v i s c o s i t y determinations i n the c a p i l l a r y v i s c o -meters, and about 20 mins. were allowed t o a t t a i n temperature e q u i l i b r i u m . The pyknometers were next removed from the bath, wiped f r e e of any c l i n g i n g water w i t h f i l t e r paper and f i n a l l y w i t h a moist chamois c l o t h , and placed i n the balance case. Weighings of the f u l l pyknometerswere done as above. This proceedure was repeated f o r 45°C and 60°G, and. then the pyknometers were washed, d r i e d and weighed again to check the empty weight. The volumes of the pyknometers were c a l c u l a t e d at each temperature by d i v i d i n g the weight of water by the d e n s i t y of water at the appropriate temperature (136). I n c a l c u l a t i n g the weight of water, a c o r r e c t i o n f o r the weight of a i r i n the empty b o t t l e was a p p l i e d . The same proceedure f o r o b t a i n i n g the true weight of l i q u i d i n the pyknometer was used f o r the absolute measurements. The d e n s i t y was c a l c u l a t e d by d i v i d i n g the weight of l i q u i d by the volume of the pyknometer at the 87 p a r t i c u l a r t e m p e r a t u r e . D u p l i c a t e d e n s i t y d e t e r m i n a t i o n s were made a t 30°, 45° and 60°G on the t h r e e o i l s used i n c a l i b r a t i n g the p r e s s u r e v i s c o m e t e r and on n - o c t a n o l a t 25°, 30°, 45° and 60°C. The d e n s i t i e s a r e r e p o r t e d a s , d^, gma/ml. (d) P r e s s u r e Equipment The p r e s s u r e system was d e s i g n e d and assembled f o r a maximum w o r k i n g p r e s s u r e o f 10,000 p s i . An assembly d r a w i n g o f the system i s g i v e n i n f i g u r e 7. A l l the components except the t r a n s f e r bomb, B, a r e s t a n d a r d c a t a l o g i tems and were" o b t a i n e d f r o m the m a n u f a c t u r e r s . The system c o n s i s t s e s s e n t i a l l y o f the v i s c o m e t e r , A , w h i c h has been d e s c r i b e d above, c o n t a i n i n g the l i q u i d t o be measured, the t r a n s f e r bomb,B, i n w h i c h a mercury l e v e l i s m a i n t a i n e d , and the p r e s s u r e g e n e r a t o r , C , w h i c h i s ke p t f u l l o f mercury and i s used f o r p r e s s u r i z i n g the system by p o s i t i v e d i s p l a c e m e n t . A p r e s s u r e gauge,D, i s connected by a tee a t K t o measure t h e p r e s s u r e i n the system. A g l a s s mercury r e s e r v o i r , E , i s connected t o the p r e s s u r e system t h r o u g h the Kovar g l a s s - m e t a l j o i n t , H, and i s used f o r d i s -placement when the system i s not under p r e s s u r e . The mercury r e s e r v o i r , p r e s s u r e g e n e r a t o r and t r a n s f e r bomb a r e j o i n e d a t the double-stem two-way v a l v e , I . Ano t h e r v a l v e , 2, i s p r o v i d e d i n the l i n e t o the t r a n s f e r bomb, so t h a t any two 88 or a l l of these components can be interconnected. The t r a n s f e r bomb i s connected near i t s c l o s u r e to the glass t r a n s f e r apparatus, f i g u r e 9. (see below) v i a another Kovar glass-metal j o i n t , J , Valves, 3 and 4, are provided between the t r a n s f e r bomb and the glass t r a n s f e r apparatus and the pressure gauge, r e s p e c t i v e l y . A bleed l i n e to atmosphere i s provided at the pressure gauge and can be closed by valve 5. The main components and valves are interconnected by standard pressure tubing and f i t t i n g s , as shown. The viscometer, A, i s described i n d e t a i l above. P r e c i s e i n f o r m a t i o n was not a v a i l a b l e on the pressure and temperature to which t h i s instrument had been t e s t e d . I m p e r i a l O i l L t d . , have i n d i c a t e d (137) t h a t i t has been used at pressures up to 7,500 p s i , and that t h i s makeof. * viscometer i s u s u a l l y designed f o r a maximum working pressure of 10,000 p s i , but could not provide i n f o r m a t i o n on the exact temperature and pressure to which i t was t e s t e d . A c a l c u l a -t i o n based on the minimum diameter r a t i o i s given i n Appendix VI,oh the recommendations of the A.S.M.S. (138) f o r the design of pressure v e s s e l s . At 10,000 p s i . , there i s a s a f e t y f a c t o r of about 5 or 6 on the u l t i m a t e s t r e n g t h which i s w i t h i n the recommendations of the A.S.M.E. Catalog data on pressure bombs (139) shows that a temperature i n c r e a s e from 70° to 500°P corresponds to approximately 10$ decrease i n maximum working pressure, which s t i l l leaves an accepta-b l e f a c t o r of s a f e t y . The viscometer was tes t e d t o 89 pressure up to 11,000 p s i at room temperature, and was found to be safe and pressure t i g h t under these c o n d i t i o n s . The t r a n s f e r bomb ,B, shown i n f i g u r e 8 was designed and machined i n these l a b o r a t o r i e s from 3" bar stock 316 s t a i n l e s s s t e e l . The o v e r a l l dimensions are 10" h i g h , 3"O.D. and 1^/4" I.D., g i v i n g a diameter r a t i o of 1.72 and a working volume of 300 ccs . The pressure design on t h i s bomb i s given i n Appendix VI along w i t h the viscometer. The enclosure i s a s e l f - s e a l i n g type described by Comings (140),and i s provided w i t h a tapered t e f l o n gasket , Q, I n i t i a l l y pressure i s ap p l i e d to the gasket by t i g h t e n i n g the screws ,P, against the s t e e l washer ,0, and thus r a i s i n g the in n e r core ,L. A 12 gauge nichrome wire ,T, enters the bomb through the e l e c t r i c a l connector and i s i n s u l a t e d by ceramics. Three designs of e l e c t r i c a l connector were t r i e d , but a l l f a i l e d under pressure of about 10,000 p s i . The type shown was a commercial design (139) which c o n s i s t s of a double-ended soapstone cone ,S, to which pressure i s a p p l i e d by t i g h t e n -i n g the nut ,R, on to the s t e e l f o l l o w e r ,TJ. I t i s thought that t h i s f a i l e d because the cone f i t t e d too l o o s e l y i n i t s r e c e p t a c l e , and t h e r e f o r e i n s u f f i c i e n t pressure was a p p l i e d to the wire by t i g h t e n i n g the nut. A l e n g t h ,V, of 0.003" s t a i n l e s s s t e e l wire connects the nichrome wir e , T, and a 1" small s t a i n l e s s s t e e l p l a t e ,X, which i s supported on two.g-s t a i n l e s s s t e l l rods , W, the wire being kept t i g h t by the a c t i o n of two sm a l l h e l i c a l springs ,Y, made from 0.02" qo nichrome w i r e . I t i s necessary to know the l e v e l of mercury i n the t r a n s f e r bomb to get an I n d i c a t i o n of the r e l a t i v e amount of l i q u i d i n the viscometer. This i s done by measuring the r e s i s t a n c e of the exposed p o r t i o n of r e s i s t a n c e w i r e , i . e . , the r e s i s t a n c e between the nichrome wire ,T, and the body of the bomb. This bomb can be r e a d i l y adapted f o r l i q u i d c o m p r e s s i b i l i t y measurements i f an accurate r e s i s t a n c e bridge i s used to measure the r e s i s t a n c e of exposed w i r e . The Pressure Generator ,C, i s a High Pressure Instrument Co., Model 50-3, designed f o r a working pressure of 15,000 p s i . P o s i t i v e displacement of 10 c c s . i s provided, w i t h a stoke of 3". The Pressure Gauge i s a 16" d i a l , Heiss-Bourdon type reading from 0 to 15,000 p s i i n 20 p s i i n t e r v a l s . A c a l i b r a t i o n c e r t i f i c a t e i s provided by the manufacturers, and the instrument i s guaranteed to read c o r r e c t l y to the nearest 15 p s i . Other s p e c i a l f e a t u r e s of the gauge i n c l u d e the p r o v i s i o n of an e x t e r n a l bleeder, and automatic temperature compensation f o r temperatures up to 100°P. A l l f i t t i n g s and pressure tubing are standard items r a t e d f o r pressures up to 15,000 p s i i n the manufacturers' 1" catalogs (139,141). Most of the l i n e s were ^ O.D. by 0.043 I.D. tubing but V 4 " O.D. by 5/32" I.D. was used i n c e r t a i n 91 l o c a t i o n s , i n d i c a t e d i n f i g u r e 7. V4-" to - tub i n g adaptors were machined i n these l a b o r a t o r i e s according to standard design (141). (e) Transfer Apparatus The t r a n s f e r apparatus i s used to introduce the sample being t e s t e d , from the f l a s k i n which i t i s c o l l e c t e d i n p u r i f i c a t i o n to the t r a n s f e r bomb and f i n a l l y i n t o the viscometer. The design of the glassware i s based on the work of Kay and Donham (142). A sketch of the equipment i s shown i n f i g u r e 9« The system was assembled and vacuum t e s t e d and found to hold a vacuum of 0.01 m.m. of mercury f o r a per i o d of about 24 hours, without appreciable change. Vacuum was provided by a Cenco Megavac Pump w i t h 1/2 H.P. motor and was measured by a standard McLeod gauge. The system c o n s i s t s of a 500 ml. f l a s k , a, i n which the Sample i s stored a f t e r p u r i f i c a t i o n , and two c y l i n d r i c a l v e s s e l s b and c, of approximately 300 ml. c a p i c i t y . Standard ground-glass j o i n t s and high vacuum stop-cocks are provided where i n d i c a t e d . The stop-cock 10 and ground j o i n t d have mercury seals which enable a high vacuum t o be a t t a i n e d without greasing. Stop-cocks 6 and 7 and the ground j o i n t of the cold-trap ,e, were greased w i t h h i g h vacuum rubber-base grease and stop-cocks 8 and 9 w i t h h i g h vacuum s i l i c o n e grease. Other j o i n t s and stop-cocks were not greased. TO TRANSFER BOMB TO VACUUM 10 H± 4 8 12 tin 9 1 ' TO MC LEOD GUAGE e 4 o l-b •o 0 0 F i g u r e 9 . T r a n s f e r Apparatus 0 92 ( f ) P r o c e e d u r e f o r I n t r o d u c t i o n of Sample and Pressurizing-;:-1. F i l l i n g w i t h M e r c u r y . The mercury r e s e r v o i r ,E, i s f i l l e d , and the two-way s t o p - c o c k ,6, c l o s e d . V a l v e s l b and 4 a r e t h e n c l o s e d and a l l o t h e r p r e s s u r e v a l v e s l e f t open. Vacuum i s a p p l i e d t h r o u g h t h e g l a s s equipment, e v a c u a t i n g the t r a n s f e r bomb and the p r e s s u r e g e n e r a t o r , a l o n g w i t h a l l the c o n n e c t i n g l i n e s . A f t e r about an hour, v a l v e l b i s opened s l i g h t l y so t h a t mercury e n t e r s the p r e s s u r e equipment and r i s e s i n the bomb ,B, up t o about h a l f - w a y . Next the r e s e r v o i r ,E, i s evacuated, d r a w i n g mercury back. T h i s p r o c e e d u r e i s r e p e a t e d , i n much the same way as e v a c u a t i n g a McLeod gauge, u n t i l vacuum e x i s t s i n the bomb ,B, and t h e r e s e r v o i r , E, The vacuum i s r e l e a s e d i n the same way as a McLeod gauge by s u c c e s s i v e l y c r a c k i n g v a l v e 3 and s t o p - c o c k 6 t o atmosphere. 2. I n t r o d u c t i o n o f Sample t o T r a n s f e r Bomb. The sample i s i n t r o d u c e d by vacuum d i s t i l l a t i o n . F i r s t the e n t i r e system i s e v a c u a t e d , c a r e b e i n g t a k e n t o m a i n t a i n t h e c o r r e c t l e v e l s o f mercury i n B and E d u r i n g t h e o p e r a t i o n . Stop-rcock 7, w h i c h i s a t t a c h e d t o low p r e s s u r e n i t r o g e n , i s t h e n opened s l o w l y , l e t t i n g n i t r o g e n i n t o the system and c a r e i s a g a i n t a k e n t o ensure m a i n t a i n i n g the c o r r e c t mercury l e v e l s by s i m u l t a n e o u s l y l e t t i n g a i r i n t o t h e mercury r e s e r v o i r E. See f i g u r e s 7 and 9 . 93 When the e n t i r e system i s under an atmosphere of n i t r o g e n , v e s s e l a c o n t a i n i n g the sample, a l s o under an atmosphere of n i t r o g e n , i s attached to the system and about 300 c c s . of sample are n i t r o g e n d i s p l a c e d i n t o v e s s e l b by opening stop-cock 11 and a p p l y i n g n i t r o g e n pressure at 12. Valve 11 i s then c l o s e d , the sample f o r z e n i n b and the e n t i r e system evacuated as b e f o r e . Next valve 3 i s closed and the sample i s vacuum d i s t i l l e d i n t o the v e s s e l c, the f i r s t 50 ccs. being c o l l e c t e d i n the c o l d - t r a p ,e, and the f i n a l 50 c c s . remaining i n b. When approximately 200 ccs. have been c o l l e d t e d i n c,stop-cock 10 i s c l o s e d , v a l v e 3 opened and the e n t i r e system again evacuated,while the pure sample i s kept f r o z e n i n v e s s e l c. The l i n e s are then purged by thawing s l i g h t l y and a l l o w i n g a l i t t l e vapor to enter the pressure system. This may be repeated a few times, as i t serves to remove f i n a l t r a c e s of a i r i n the pressure system. F i n a l l y , the whole 200 c c s . of sample are vacuum d i s t i l l e d from c i n t o the t r a n s f e r bomb ,B, and v a l v e 3 i s c l o s e d . 3. I n t r o d u c t i o n of Sample to Viscometer. The sample i s allowed to thaw and a t t a i n v a p o r - l i q u i d e q u i l i b r i u m i n the t r a n s f e r bomb, the viscometer and the connecting l i n e s . A i r i s then allowed to enter v e s s e l , E , pushing mercury i n t o the t r a n s f e r bomb,and when atmospheric pressure i s a t t a i n e d , valve l a i s c l o s e d . Q4 4 . P r e s s u r i z i n g . The system i s p r e s s u r i z e d by p r o v i d i n g p o s i t i v e d i s p l a c e m e n t a t the p r e s s u r e g e n e r a t o r a f t e r t h e sample has r e a c h e d t e m p e r a t u r e e q u i l i b r i u m i n the v i s c o m e t e r . I t i s recommended t h a t measurements be made a t c o n s t a n t temperature over the whole p r e s s u r e range f r o m 0 t o 1 0 , 0 0 0 p s i b e f o r e moving on t o a new t e m p e r a t u r e . 95 NORMAL OCTANOL ~ PURIFICATION AND CHARACTERIZATION A F i s h e r C e r t i f i e d Reagent grade of n - O c t a n o l was p u r i f i e d f o r use i n t h i s r e s e a r c h . L o t p r o p e r t i e s were g i v e n a s , B o i l i n g range 194.3° - 195.3°C N o n - v o l a t i l e m a t t e r 0.008 % F r e e a c i d 0.005 % D e t e r m i n a t i o n s were made on t h e d e n s i t y and v i s c o s i t y a t 30°C and t h e tfefractive i n d e x a t 20°C f o r samples t a k e n f r o m the b o t t l e , and the f o l l o w i n g r e s u l t s were o b t a i n e d . D e n s i t y a t 30°C, d^°, 0.8187 V i s c o s i t y a t 30°C 6.390 c.p. R e f r a c t i v e Index a t 20°C 1.4294^ The l i q u i d was p u r i f i e d by a s i n g l e f r a c t i o n a t i o n i n a Todd P r e c i s e F r a c t i o n a t i o n Assembly, w i t h a 25 m.m. column packed w i t h 4 m.m. g l a s s h e l i c e s , g i v i n g a p p r o x i m a t e l y 60 t h e o r e t i c a l p l a t e s . Seven hundred and f i f t y m i s . were charged t o t h e s t i l l - p o t and d i s t i l l e d a t a r e f l u x r a t i o o f 50: 1, t h e f i r s t and l a s t 200 m i s . b e i n g r e j e c t e d . The m i d d l e c u t of 350 m i s . was c o l l e c t e d a t an overhead t e m p e r a t u r e o f 194.4°C (751 m.m.) w h i c h remained c o n s t a n t t o w i t h i n ^Q°C t h r o u g h t o u t th e c o l l e c t i o n o f the m i d d l e c u t . The p u r i f i e d o c t a n o l was c o l l e c t e d and s t o r e d i n a w e l l stopped 500 m l . g r o u n d - g l a s s f l a s k . 96 The c o r r e s p o n d i n g p r o p e r t i e s o b t a i n e d a f t e r p u r i f i c a t i o n were, D e n s i t y , 30°C, d 3 ° O.8I84 V i s c o s i t y a t 30°C 6.396 cp. R e f r a c t i v e Index, 20°C 1.4294 2 The d a t a from the l i t e r a t u r e of t h e p h y s i c a l p r o p e r t i e s o f n - o c t a n o l shows l a r g e i n c o n s i s t e n c i e s . T a b l e 2 g i v e s the r e s u l t s of the l i t e r a t u r e s e a r c h i n c h r o n o l o g i c a l o r d e r f r o m 1884 on, i n c l u d i n g the r e s u l t s o f t h i s work. The o n l y p o i n t s of r e a s o n a b l e agreement i n the d a t a a re the d e n s i t y a t 25°C, and t h e r e f r a c t i v e i n d e x a t 20°C. Many a u t h o r s r e p o r t v a l u e s of the f o r m e r c l o s e t o 0.8221 and o f the l a t t e r between 1.4291 and 1.4296 and the v a l u e s o b t a i n e d i n t h i s work c o r r e s p o n d c l o s e l y w i t h t h e s e . The d e n s i t y d a t a of Smythe and Stoops (143) from 0 t o 60°C compare v e r y c l o s e l y w i t h the v a l u e s o b t a i n e d i n t h i s work, and these d a t a were i n t e r p o l a t e d and e x t r a p o l a t e d up t o 90°C and t h e v a l u e s used t o c a l c u l a t e t he a b s o l u t e v i s c o s i t y f r o m the k i n e m a t i c v i s c o -s i t y o b t a i n e d i n t h e c a p i l l a r y v i s c o m e t e r s (see b e l o w ) . E r r o r s g r e a t e r t h a n 0.05$ were c e r t a i n l y n o t i n t r o d u c e d by t h i s - . p r o c e e d u r e . There i s g r e a t e r disagreement i n t h e d a t a f o r the v i s c o s i t y a t v a r i o u s t e m p e r a t u r e s . I n p a r t i c u l a r , the r e p o r t e d v a l u e s f o r 20°C d i f f e r by as much as 8$. I n some cases the r e p o r t e d d e n s i t i e s d i f f e r g r e a t l y f rom those mentioned above, and t h e r e f o r e the p u r i t y o f the m a t e r i a l i s i n doubt, and i n 97 o t h e r cases no d e n s i t y measurements nor any c r i t e r i a o f p u r i t y a re r e p o r t e d and i t i s t h e r e f o r e i m p o s s i b l e t o a s s e s s t h e degree of p u r i t y . C l o s e agreement on v i s c o s i t y v a l u e s have been o b t a i n e d i n t h i s work w i t h the d a t a o f Bingham and D a r a l l (144) and Mumford and P h i l l i p s (145). TABLE 2 97a PHYSICAL PROPERTIES OP N-OCTANOL PROM THE LITERATURE Author Date b.p.°C. Temp. n P e r k i n (146) I884 195-6 Zander Garten-meister Dunstan et a l Lowry Behal (147) I884 — (148) 1890 (149) 1914 (150) 1914 — (151) 1919 194-6 Verkade and Coops (152) 1927 Smythe and Stoops(143) 1929 Bingham 1930 and D a r a l l ( 1 4 4 ) D e f f e t (153) 1931 E l l i s and Reid (154) 1932 Bu t l e r et a l (155) 1933 194.5 N e v j i and Jatkar (156) 1934 15 25 20 25 50 90 20 20 20.5 34.6 0 10 20 30 40 50 60 0 10 20 30,. 40 60 80 100 0 15 30 0 25 20 25 30 1.43035 1.4274 1.42937 1.4256 t Visco-d s l t y 4 cp. 0.82935, 0.82249 ] 0.8359 0.8264 8.925 7.22 3.22 1.21 0.8270 0.8342 0.8146 0.8391 0.8322 0.8253 0.8186 0.8115 0.8042 0.7970 20.82' 13.45 9.066 6.357 4.589 2.600 1.608 1.069 0.84216 0.83202 0.82192 0.83848 0.82137 0.82238 0.8256 IO.64 6.125 97b Table 2. continued P h y s i c a l P r o p e r t i e s of n-octanol from the L i t e r a t u r e . Author Date b.p.C Temp. a Visco-s i t y cp. B u t l e r ;:(.I57) et a l 1935:; 194.5 O l i v e r (158) Komarews ky(15 9) and Coley Dorough (160) et a l . M u l l e r (161) Jones e t a l ( l 6 2 ) Dreisbach (163) and M a r t i n Mumford & (145) P h i l l i p s Van E r i c h s e n (I64) This work 20 25 1.42957 1937 195.1-4 20 (764.6m.m.) 1941 194-5 25 1941 195.0 1942 — 1948 — 1949 195.28 1950 194.6 1952 — 0 25 20 25 20 25 20 25 20 15 20 25 30 45 50 60 75 90 0.82322 0.8249 1.4296 0.8394 1.4275 0.8224 0.8221 1.42913 0.82555 1.42749 0.82209 1.4292 0.8254 1.4294 0.8219 0.8184 0.8079 0.7972 8.420 7.33 1.4287 0.8265 9.13 0.82332 7.55 11.05 9.123 7.626 6.396 3.965 3.420 2.600 1.796 1.296 I . C a l c u l a t e d from d. 2. C a l c u l a t e d from f l u i d i t y . §8 RESULTS (a) V i s c o s i t i e s a t At m o s p h e r i c P r e s s u r e i ) C a l i b r a t i o n o f C a p i l l a r y V i s c o m e t e r s . The r e s u l t s o f the c a l i b r a t i o n of the c a p i l l a r y v i s c o m e t e r s a re g i v e n i n t a b l e 3 . The t e s t t emperature g i v e n i s the te m p e r a t u r e a f t e r c o r r e c t i o n s were a p p l i e d a c c o r d i n g A t h e c a l i b r a t i o n o f t h e thermometer. The k i n e m a t i c v i s c o s i t y l i s t e d was c a l c u l a t e d f r o m the e f f l u x t i m e i n BY8 and the c a l i b r a t i o n c o n s t a n t a t 37.78°C ( 1 0 0 . 0 0°F). F o r t h e r u n s a t 2 0 . 0 0°C, t h e r e i s a s l i g h t t e mperature c o r r e c t i o n t o be a p p l i e d t o t h e s e valueSj but t h i s was not a p p l i e d . The v a l u e of t h i s c o r r e c t i o n , a c c o r d i n g t o Cannon's a p p r o x i m a t i o n mentioned above, was about + 0 . 1 $ . Nor was the c o r r e c t i o n f o r the c a l i b r a t i o n o f the st o p - w a t c h a p p l i e d t o t h e s e v a l u e s . The f i g u r e s a r e g i v e n as an i n d i c a t i o n of the range o f k i n e m a t i c v i s c o s i t y c o v e r e d i n the c a l i b r a t i o n s . The c a l i b r a t i o n c o n s t a n t was c a l c u l a t e d f r o m the f o r m u l a , C = 0 . 0 1 2 4 5 l i - (86) where t . was t h e e f f l u x t i m e i n B78 and t„ t h a t i n the i 2 u n c a l i b r a t e d v i s c o m e t e r . T h i s e q u a t i o n g i v e s t h e c a l i b r a t i o n c o n s t a n t a t 37 .78°C s i n c e t h e v a l u e of the constant,-:- 0 . 0 1 2 4 5 , f o r B78 was determined a t t h i s t e m p e r a t u r e . Assuming t h a t the tempe r a t u r e c o r r e c t i o n i s t h e same f o r a l l the v i s c o m e t e r s , and 99 the theory above i n d i c a t e s t h a t t h i s i s c l o s e l y so, then, there i s no e r r o r introduced by c a l i b r a t i o n at a d i f f e r e n t temperature and c a l c u l a t i n g the constant at 37.78°C. At the bottom of t a b l e 3 are given the mean values of the c a l i b r a t i o n constant f o r each viscometer c a l c u l a t e d from the values of the l a s t column. The r e s u l t s of the c a l i b r a t i o n s w i t h d i s t i l l e d water are given i n t a b l e 4» The approximate c a l i b r a t i o n constant i s c a l c u l a t e d from the formula, C = 1.0038 ( 8 ? ) t where, 1.0038 i s the value of the kinematic v i s c o s i t y of water i n CS. at 20°C c a l c u l a t e d from an absolute v i s c o s i t y of 1.002 cp. and a d e n s i t y of 0.9982 gms/cm.3. The t i m i n g c o r r e c t i o n was determined from the c a l i b r a t i o n of the stop-watch mentioned above. The k i n e t i c energy c o r r e c t i o n was c a l c u l a t e d as ^/0t^f u s i n g the approximate c a l i b r a t i o n constant and the e f f l u x time. The surface t e n s i o n c o r r e c t i o n was a p p l i e d u s i n g equation (58) 'V (water). with a value of 33 for ( /f) and a value of 72.8 for (V?) The values of C c a l c u l a t e d on t h i s b a s i s are approxi-mately 0.15 and 0.20 % lower than those obtained i n the comparative c a l i b r a t i o n s . 100 i l ) V i s c o s i t i e s o f O i l s . These a r e g i v e n i n t a b l e 5 t o g e t h e r w i t h the d e n s i t y and the c o r r e c t i o n s f o r change o f c a l i b r a t i o n c o n s t a n t w i t h t e m p e r a t u r e . The mean k i n e m a t i c v i s c o s i t y was c a l c u l a t e d f r o m d u p l i c a t e r u n s made i n two v i s c o m e t e r s p l a c e d i n the c o n s t a n t t e m p e r a t u r e b a t h a t the same t i m e , f r o m 3 bo 6 d e t e r m i n a t i o n s o f the e f f l u x t i m e b e i n g made f o r each v i s c o m e t e r . R e p r o d u c i b i l i t y o f e f f l u x t i m e s was u s u a l l y w i t h i n 0.1$, but i n extreme cases amounted t o about 0.2$. The o n l y c o r r e c t i o n w h i c h was a p p l i e d t o the k i n e m a t i c v i s c o s i t y was t h a t due t o the change i n v i s c o m e t e r c o n s t a n t w i t h t e m p e r a t u r e . The a b s o l u t e v i s c o s i t y was c a l c u l a t e d f r o m the c o r r e c t e d k i n e m a t i c v i s c o s i t y and the d e n s i t y . H I ) V i s c o s i t y of Normal O c t a n o l a t V a r i o u s Temperatures. The v i s c o s i t y o f n - o c t a n o l a t t e m p e r a t u r e s f r o m 1 5 ° t o 90°C i s g i v e n i n t a b l e 6. The same comments as above on t h e a p p l i c a t i o n of c o r r e c t i o n s a p p l y t o t h i s d a t a . F o r some o f the t e m p e r a t u r e s , the d e n s i t y d a t a o f Smythe and Stoops (143) were u s e d ; t h e a c c u r a c y of t h e s e d a t a have been d i s c u s s e d above. The d a t a a re a l s o p r e s e n t e d g r a p h i c a l l y i n f i g u r e 10, a l o n g w i t h the v a l u e s f r o m t h e l i t e r a t u r e w h i c h were g i v e n i n t a b l e 2 above. The v i s c o s i t y was c o r r e l a t e d w i t h t e m p e r a t u r e on the b a s i s o f some of the e q u a t i o n s s u g g e s t e d i n the l i t e r a t u r e w h i c h have been d i s c u s s e d under t h e s e c t i o n on Theory. I n a l l 8 10 11 ABSOLUTE VISCOSITY, CENTI POISE 101 c a s e s , the b e s t f i t f o r the d a t a was o b t a i n e d by t h e method of l e a s t s q u a r e s . F o r the t w o - c o n s t a n t e q u a t i o n s , t h e c a l c u l a t i o n s were performed on a manual machine. F o r t h e th r e e - a n d f o u r - c o n s t a n t e q u a t i o n s t h e r e g r e s s i o n c o e f f i c i e n t s were o b t a i n e d on th e TJ.B.C. e l e c t r o n i c d i g i t a l computer, Alwac I I I E. The use of R o u t i n e S-3 (165) f o r c o r r e l a t i o n and r e g r e s s i o n made i t u n n e c e s s a r y t o do any s p e c i a l p r o g r a m i n g . I n a l l c a s e s , s u f f i c i e n t s i g n i f i c a n t f i g u r e s were c a r r i e d t h r o u g h the c a l c u l a t i o n s so t h a t e r r o r s g r e a t e r t h a n 0.05$ were n ot i n t r o d u c e d . The f o l l o w i n g c o r r e l a t i o n s were o b t a i n e d : -I n ^ = -8.0503 + 3.006 - | - (88) I n n = -5.8205 + 2871.8 — (89) • Tv I n Y[ = -14.8932 + 4100,5 — + 0.010631 T (90) I n *\ = -4.5553 + 761.50 + 3.5820 - i « (91) I n Y> = - 56.6584 + 5357.0 — + 7.3227 I n T (92) v . - T l n v | = -44.1010 + 5077.4 - | - + 0.0023920 T + 5.6847 I n T (93) The v a l u e s o f C a l c u l a t e d f r o m t h e s e e q u a t i o n s a r e g i v e n f o r each t e m p e r a t u r e i n t a b l e 7, a l o n g w i t h t h e average % d e t e r m i n a t i o n f rom t h e e x p e r i m e n t a l v a l u e s . 102 (b) D e n s i t y D e t e r m i n a t i o n s The c a l i b r a t i o n of the pyknometers w i t h d i s t i l l e d w a t er a t 30, 45 and 60°C i s g i v e n i n t a b l e 8 . The d e n s i t i e s o f O i l s D, E and P and of n - o c t a n o l a r e g i v e n i n t a b l e s 5 and 6 r e s p e c t i v e l y , a l o n g w i t h t h e v i s c o s i t y measurements. (c) C a l i b r a t i o n o f R o l l i n g B a l l V i s c o m e t e r The d a t a o b t a i n e d f o r the c a l i b r a t i o n of t h e r o l l i n g b a l l v i s c o m e t e r a r e p r e s e n t e d i n t a b l e 9. The a c t u a l t i m e s o f r o l l w i t h the average d e v i a t i o n ; f r o m the mean i s g i v e n f o r each s e r i e s a t each t e m p e r a t u r e and s l o p e . The d e n s i t y d i f f e r -ence was c a l c u l a t e d f r o m t h e b a l l d e n s i t y , 7.672 g m s / c . c , and the d e n s i t y o f each o i l . The d e n s i t i e s and v i s c o s i t i e s of t h e o i l s were re p r o d u c e d f r o m t a b l e 5 . and t ( ) were c o r r e l a t e d by a r e g r e s s i o n a n a l y s i s i n ac c o r d a n c e w i t h an e q u a t i o n o f t h e form, y[ = a + b C t ( ^ ~ f ) ] (94) The b e s t v a l u e f o r a and b f o r t h e two s l o p e s were found t o be, 11° s l o p e , *\ = 0.082 + 5.139 x 10~ 3 t (fc - ? )(95) 23° s l o p e , rj = 0.037 + 9.197 x l o " 3 t )(96) For t h e s e c o r r e l a t i o n s , o n l y t h e d a t a o f s e r i e s 3, 4 and 5 were u s e d . The o m i s s i o n o f the d a t a f r o m s e r i e s 1 and 2 w i l l be d i s c u s s e d l a t e r . The e x p e r i m e n t a l and the 103 c a l c u l a t e d v i s c o s i t i e s , t o g e t h e r w i t h the p e r c e n t a g e d e v i a t i o n s a r e g i v e n i n t a b l e 10. The c a l i b r a t i o n i s a l s o p r e s e n t e d i n f i g u r e 11. TABLE 3 CALIBRATION OP CAPILLARY VISCOMETERS BY COMPARISON C a l i b r a t i o n Test L i q u i d Temp.°C Kinematic Viscometer Mean E f f l u x Time,Sees. Const, at V i s c o s i t y No. B78 Test Viscometer 37.78°C n-PrOH 20.00 2.72 B82 A54 A91 218.6(5)** 218.6(5) 218.6(5) 222.7(4) 1092.7(3) 1137.05(2) 0.012221 0.0024907 0.0023936 D e c a l i n 20.00 2.83 B82 A54 A91 226.8(2) 226.8(2) 226.8(2) 231.15(2) 1134.0(2) 1179.65(2) 0.012216 0.0024900 0.0023936 O i l A 20.00 7.05 B82 A54 A91 565.5(3) 565.5(3) 565.5(3) 57§.9(3) 2828.8(3) 2942.6(3) 0.012226 0.0024897 0.0023926 O i l B 37.78 (100°F) 8.24 B82 661 .7(2) 674.05(2) 0.012222 O i l C 37.78 36.6 08 2941.3(5) 337.3(6) 0.10856 «• ( ) r e f e r s to number of nuns averaged. MEAN VALUES OF CALIBRATION CONSTANT Viscometer No. B78 B82 A54 " . A91 C8 Mean Value of Constant at 37.78°C 0.01245 0.01222 0.002490 0.002393 0.1086 (Cannon Instrument Co.) TABLE 4 105 CALIBRATION OP CAPILLARY VISCOMETERS WITH DISTILLED WATER AT 20°C Mean Observed Approximate Viscometer No. E f f l u x time,Sees. C a l i b r a t i o n constant A54 4 0 5 . 4 (16)"* 0 . 0 0 2 4 7 6 1 A91 421.95(16) 0 . 0 0 2 3 7 9 0 C o r r e c t i o n s t o be a p p l i e d , % K i n e t i c Surface Timing Energy Tension A54 -0.16 +0.13 +0.42 A91 -0.16 +0.12 +0.42 Corrected ToJbal C o r r e c t i o n s , % C a l i b r a t i o n constant A54 +0.39 0.002486 A91 +0.38 0.002388 Vt ( ) r e f e r s t o number of runs averaged TABLE 5 106 VISCOSITIES AND DENSITIES OF OILS D,E AND P Mean K i n e m a t i c V i s c o s i t y Temperature, °C O i l D O i l E O i l F 30 45 60 3.272 2.441 1.903 6.350 4.366 3.207 11.59 7.483 5.143 D e n s i t y , 30 45 60 0.8264 0.8365 O.8464 0.8119 0.8263 0.8369 0.8014 0.8162 0.8271 Temperature  C o r r e c t i o n  t o V i s c o s i t y 30 45 60 +0.003 -0.002 -0.005 +0.006 -0.004 -0.008 +0.007 -0.004 - 0 . 0 0 9 C o r r e c t e d K i n e m a t i c V i s c o s i t y , c s . A b s o l u t e V i s c o s i t y , cp. 30 45 60 30 45 60 3.275 2.439 1.898 2.706 1.980 1.521 6.356 4.362 3.119 5.307 3.615 2.624 11.60 7.479 5.134 9.869 6.259 4.246 TABLE 6 VISCOSITY AND DENSITY OP N-OCTANOL AT VARIOUS TEMPERATURES 107 Temp. c o r r . Corrected Absolute To V i s c o s i t y Kinematic V i s c o . % V i s c o s i t y cp. A Mean Den s i t y Temp.°C Kinematic d t V i s c o s i t y 4 15 13.310 0.8288* 20 11.035 0.8253* 25 9.268 0.8219 30 7.807> 0.8184 45 4.9H 0.8079 50 4.258 0.8042*" 60 3.268 0.7972 75 2.293 0.7862* 90 1.679 0.7754* Smythe and Stoops (143) +0.21 13.348 11.054 +0.17 11.054 9.123 +0.12 9.279 7.626 +0.08 7.815 6.396 - 0 . 0 7 4.908 3.965 -0.11 4.253 3.420 - 0 . 2 0 3.261 2.600 -0.34 2.285 1.796 - 0 . 4 8 1.671 1.296 TABLE 7 CORRELATION OF VISCOSITY-TEMPERATURE DATA FOR N-OCTANOL  Temp.°C E x p t . Eqn.(88) Eqn.(89) Eqn.(90) Eqn.(91) Eqn.(92) Eqn.(95) 15 11.05 10.80 10.775 11.03 11.04 10.99 10.98 20 9.123 9.052 9.024 9.121 9.128 9.146 9.139 25 7.626 7.613 7.600 7.592 7.596 7.600 7.597 30 6.396 6.451 6.459 6.396 6.387 6.400 6.399 45 3.965 4.042 4.058 3.965 3.963 3.963 3.963 50 3.420 3.490 3.480 3.425 3.425 3.422 3.422 60 2.600 2.641 2.652 2.603 2.606 2.602 2.602 75 1.796 1.791 1.793 1.796 1.798 1.796 1.796 90 1.296 1.254 1.254 1.295 1.294 1.295 1.295 Mean % I .46 1.56 0.11 0.16 0.17 0.16 D e v i a t i o n TABLE 8 CALIBRATION OP PYKNOMETERS Temperature, C 30 45 60 D e n s i t y of 0.99567 0.99025 0.98324 w a t e r , d^ ' 4 Pyknometer No. 147 124 . 147 124 147 124 Wt. of Water 24.9536 24.7586 24.8223 24.6259 24.6502 24.4566 and A i r Approx. Volume 25.0621 24.8663 25.0667 24.8684 25.0704 24.8735 Buoyancy 0.0301 0.0298 0.0301 0.0298 0.0301 0.0298 C o r r e c t i o n Wt. o f Water 24.9837 24.7884 24.8524 24.6557 24.6803 24.4864 Pyknometer 25.0924 24.8962 25.0971 24.8985 25.1010 24.9038 Volume m l . H o U5 110 TABLE 9 CALIBRATION OP PRESSURE VISCOMETER Temp.°C Sl o p e D e n s i t y Mean Time, D i f f e r e n c e Sees. V i s c o s i t y t ( p s - p S e r i e s 1 _ O i l D, V i s c o m e t e r tube not keyed. 30 11° 6.846 70.81 ± 0.04 2.706 484.8 45 11° 6.860 52.37 - 0.05 1.980 359.3 60 11° 6.871 40.41 ± 0.06 1.521 277.7 S e r i e s 2 — O i l E, V i s c o m e t e r tube n o t keyed. 30 11° 6.835 145.43 ± 0.14 5.307 994.0 45 11° 6.846 98.61 ± 0.14 3.615 675.1 60 11° 6.856 72.20 + 0.04 2.624 488.1 S e r i e s 3 — O i l E, V i s c o m e t e r tube not keyed, b u t i n f i x e d p o s i t i o n . 30 11° 6.835 147.07+ 0.16 5.307 1005.2 45 11° 6.846 99.52 + 0.06 3.615 681.3 60 11° 6.856 71.96 ± 0.06 2.624 493.4 S e r i e s 4 — O i l P - tube keyed 30 11° 6.826 279.62 i 0.44 9.869 1908.5 2 3 ° 157.00 ± 0.08 1071.7 45 11° 6.835 175.06 ± 0.16 6.259 1203.3 2 3 ° 98.85 ± 0.08 .675.6 60 11° 6.845 119.09 ± 0.14 4.246 • 815.2 2 3 ° 66.84 - 0.07 457.5 S e r i e s 5 _ O i l D, tube keyed 30 11° 6.846 73.84 - 0.06 2.706 505.5 2 3 ° 41.55 ± 0.03 284.2 45 11° 6.860 54.63 ± 0.04 1.980 374.8 2 3 ° 30.88 1 0.02 211.8 60 11° 6.871 41.94 ± 0.06 1.521 288.2 2 3 ° 23.94 ± 0.01 164.5 I l l TABLE 10 CORRELATION FOR PRESSURE VISCOMETERS Slope ( e x p t . ) ( c a l c . ) $ D e v i a t i o n 1 1 ° 5.307 5.250 +1.07 3.615 3.583 +0.89 2.624 2.618 +0.23 9.869 0.896 -0.21 6.259 6.266 -0.11 4.242 4.271 - 0 . 6 8 2.706 2.679 +0.68 1.980 2.008 -1.41 1.521 1.563 -2.76 Mean d e v i a t i o n = 0.93$ 23° 9.869 6.259 4.242 2.706 1.980 1.521 9.893 6.250 4.245 2.653 1.985 1.550 -O.24 +0.14 +0.07 +1.96 -0.25 -1.91 Mean d e v i a t i o n = 0.76$ DISCUSSION 112 (2) The P r e s s u r e Apparatus 1) P r e s s u r e V i s c o m e t e r . I n t h e c a l i b r a t i o n of the \ \ p r e s s u r e v i s c o m e t e r a t a t m o s p h e r i c p r e s s u r e , t h e f i r s t two s e r i e s o f r u n s were I n c o n s i s t e n t . Two s t r a i g h t l i n e s c o u l d be drawn t h r o u g h the p o i n t s f o r O i l D and O i l E, b u t the v i s c o s i t i e s c a l c u l a t e d f r o m t h e s e two l i n e s d i f f e r e d by about 5 p e r c e n t whereas the s c a t t e r o f p o i n t s on each l i n e was l e s s t h a n h a l f a p er c e n t . T h i s was a t t r i b u t e d t o a bend i n the v i s c o m e t e r tube, and r e p e a t r u n s w i t h O i l E ( s e r i e s 3) w i t h t h e tube i n a known d i f f e r e n t p o s i t i o n gave s i g n i f i c a n t l y d i f f e r e n t v a l u e s a g a i n o f the time o f r o l l , i n d i c a t i n g t h a t the e f f e c t was i m p o r t a n t . L a t e r , the tube was keyed i n t h e same p o s i t i o n as f o r S e r i e s 3 and new measurements made w i t h O i l P and O i l D. The r o l l t i m e s f o r O i l D were a l s o s i g n i f i c a n t l y d i f f e r e n t f r o m the p r e v i o u s r u n s ( s e r i e s 1.) The f i n a l c o r r e l a t i o n d i s c u s s e d above i s based on t h e l a s t t h r e e s e r i e s , w i t h t h e tube i n a c o n s t a n t p o s i t i o n . The average d e v i a t i o n o f the e x p e r i m e n t a l v i s c o s i t i e s f r o m t h o s e c a l c u l a t e d f r o m the c a l i b r a t i o n e q u a t i o n i s s t i l l l a r g e r t h a n the average d e v i a t i o n f o r any one s e r i e s , as i s shown by the t r e n d s of the d e v i a t i o n s ( t a b l e 10). C o n s i d e r i n g the c a l i b r a -t i o n f o r a s l o p e o f 11°, much c l o s e r agreement i s o b t a i n e d by o m i t t i n g the runs o f s e r i e s 5 } w i t h O i l D ( t h e most f l u i d o i l ) , w h i c h s u g g e s t s t h a t i n e r t i a l e f f e c t s may have been i m p o r t a n t 113 a t low v i s c o s i t i e s . An a n a l y s i s based on t h e t h e o r y o f the Ins t r u m e n t can i n d i c a t e whether t h e s e e f f e c t s a r e r e l e v a n t . The approximate v a l u e o f t h e d i a m e t e r r a t i o f o r the b a l l and tube used i n t h i s work i s 0 . 9 6 9 , w h i c h g i v e s a c r i t i c a l RenyoldSr. No. o f about 18.5 and a c o r r e l a t i o n f a c t o r of about 1.5 x 1 0 ~ 5 ( F i g u r e s 5 and 6 ) . The Reynold§J NO. i s g i v e n by t h e e x p r e s s i o n , Re = ^ hgL ( ^ \ (97) \ n or Re = J L . ^ (98) I n t h i s c a s e , L = 18 cms. , d = 0.2500 cm, D = 0.2583 cm. .-. Re = l a | S ' (99) v t Hence, the s m a l l e s t v a l u e s o f Re were a p p r o x i m a t e l y 8.6 f o r t h e 11° s l o p e , and 13.5 f o r t h e 23° s l o p e . These v a l u e s a r e below the c r i t i c a l v a l u e (18.5), a c c o r d i n g t o the c o r r e l a t i o n of Hubbard and Brown, and t h e r e f o r e a l l measurements were made w e l l w i t h i n the l a m i n a r regime of f l o w , ^ i n e r t i a l e f f e c t s c o u l d not have been i m p o r t a n t . The importance o f the a c c e l e r a t i o n e f f e c t a t the s t a r t of r o l l can be r e a d i l y d e t e r m i n e d f r o m e q u a t i o n (T5). F o r a t y p i c a l r u n w i t h a t i m e of 70 s e e s , and a v i s c o s i t y of 2.6 c p . ( s e r i e s 3, 60°C), ^  = 540 g m . / s e c , F = 123 gm.cm./ p s e c . and m = 1.03 gm., whence, - 114 where, V = t e r m i n a l v e l o c i t y , t Hence, the ti m e r e q u i r e d t o a t t a i n 99$ of t h e t e r m i n a l v e l o c i t y i s about 0 . 0 0 9 s e c . and t o a t t a i n 9 9 . 9 $ I s about 0 . 0 1 3 s e c . T h i s e f f e c t was c l e a r l y not i m p o r t a n t f o r any o f the r u n s i n t h i s work. The e f f e c t o f te m p e r a t u r e must a l s o be c o n s i d e r e d . S i n c e b o t h the b a l l and the tube were o f s t a i n l e s s s t e e l , e q u a t i o n (84) i s a p p l i c a b l e and the c o r r e c t i o n f o r C i s g i v e n by 2"OCAT. The v a l u e of o< f o r s t a i n l e s s s t e e l i s about 1 .4 x 1 0 °C7 w h i c h g i v e s a c o r r e c t i o n o f a p p r o x i m a t e l y 0 . 1 4 $ f o r a temp e r a t u r e range o f 5 0 ° C . T h i s i s q u i t e s m a l l i n comparison w i t h the d e v i a t i o n s o b t a i n e d . No complete e x p l a n a t i o n o f the l a r g e r d e v i a t i o n s a t low v a l u e s o f v i s c o s i t y i s a p p a r e n t , b u t i t may be c o n c l u d e d t h a t measurement o f v i s c o s i t i e s g r e a t e r t h a n 3 c p . can be o b t a i n e d w i t h t h e p r e s e n t c a l i b r a t i o n t o b e t t e r t h a n 1 . 0 $ , w h i c h compares f a v o u r a b l y even w i t h t h e a c c u r a t e work of Hubbard and Brown ( 1 2 8 ) . B e f o r e making measurements under p r e s s u r e , i t w i l l be n e c e s s a r y t o e s t i m a t e the d e n s i t y v a r i a t i o n w i t h p r e s s u r e , s i n c e e x p e r i m e n t a l d a t a a re not a v a i l a b l e . B r i d g m a n (35) has d e s c r i b e d a method of c a l c u l a t i o n by w h i c h t h e d e n s i t y a t any temper a t u r e can be e s t i m a t e d f r o m the d e n s i t y a t a t m o s p h e r i c p r e s s u r e and the c o m p r e s s i b i l i t y d a t a o f a c h e m i c a l l y s i m i l a r 115 compound. I n the case of n - o c t a n o l , a lo w e r member o f t h e homologous s e r i e s o f n - a l c o h o l s would be us e d . S i n c e the v i s c o s i t y c a l c u l a t e d f r o m the c a l i b r a t i o n e q u a t i o n i s not s t r o n g l y dependent on the f l u i d d e n s i t y , s u f f i c i e n t l y c l o s e v a l u e s s h o u l d be o b t a i n e d by t h i s method, and i f more a c c u r a t e v a l u e s are r e q u i r e d , t h e t r a n s f e r bomb can be adapted f o r c o m p r e s s i b i l i t y measurements. i i ) A u x i l i a r y P r e s s u r e Equipment. The p r e s s u r e system proved c o n v e n i e n t t o o p e r a t e and s a t i s f a c t o r y under p r e s s u r e , w i t h the e x c e p t i o n o f the e l e c t r i c a l c o n n e c t i o n i n the t r a n s f e r bomb, w h i c h f a i l e d under 10,000 p s i p r e s s u r e . The double-ended soapstone cone s e a l w h i c h was used i s d e s c r i b e d by the m a n u f a c t u r e r s and Comings (140) as s a t i s f a c t o r y f o r p r e s s u r e s up t o 20,000 p s i , and i t i s p r o b a b l e t h a t f a i l u r e was due t o poor d e s i g n and m a c h i n i n g o f the r e c e p t a c l e f o r the cone. A d v i c e s h o u l d be sought f r o m the m a n u f a c t u r e r s on l i m i t s o f t o l e r a n c e and m a c h i n i n g t e c h n i q u e s . B e f o r e the ap p a r a t u s i s o p e r a t e d under p r e s s u r e , the whole system s h o u l d be r e t e s t e d a t one and a h a l f t i m e s t h e maximum w o r k i n g p r e s s u r e w i t h t h e v i s c o m e t e r a t t h e maximum ; t e s t t e m p e r a t u r e . (b) V i s c o s i t y Measurements a t Atmo s p h e r i c P r e s s u r e E r r o r s i n the v i s c o s i t y measurements i n the Cannon-Fenske v i s c o m e t e r s have a r i s e n f r o m two s o u r c e s , (1) e r r o r s i n the c a l i b r a t i o n c o n s t a n t and (2) e x p e r i m e n t a l e r r o r s d u r i n g 116 c a l i b r a t i o n . The e r r o r i n the c a l i b r a t i o n c o n s t a n t f o r the i n s t r u m e n t s t a n d a r d , v i s c o m e t e r B78, w h i c h was c a l i b r a t e d by the Cannon In s t r u m e n t Co. i s n o t known; however i t i s p r o b a b l y about 0.1 t o 0.2$. I t i s f e l t t h a t e r r o r s g r e a t e r t h a n 0.1$ were not i n t r o d u c e d i n the c a l i b r a t i o n of t h e o t h e r v i s c o m e t e r s by comparison w i t h B78, s i n c e t h e c o n s t a n t o b t a i n e d w i t h s e v e r a l l i q u i d s i n a wide range o f v i s c o s i t i e s a l l gave the same v a l u e s w i t h i n 0.1$. The e r r o r i n the c o n s t a n t f o r the o t h e r v i s c o m e t e r s was t h e r e f o r e a maximum of 0.2 t o 0.3$. The s l i g h t d i sagreement between the c a l i b r a t i o n c o n s t a n t by comparison and w i t h d i s t i l l e d water i s not s u r p r i s i n g . R o u t i n e v i s c o m e t e r s are not d e s i g n e d f o r c a l i b r a -t i o n w i t h w a t e r , s i n c e the magnitude of the c o r r e c t i o n s t o be a p p l i e d a re q u i t e l a r g e , and t h e method o f c a l c u l a t i n g them i s n o t e x a c t . The s m a l l e r .value o f the c o n s t a n t may mean l a r g e r c o r r e c t i o n s were n e c e s s a r y f o r t h e k i n e t i c energy or-the s u r f a c e t e n s i o n . However, the d i f f e r e n c e i s s m a l l , and the r u n s w i t h d i s t i l l e d water have s e r v e d as a u s e f u l check. The a b s o l u t e d e t e r m i n a t i o n s were n e c e s s a r i l y s u b j e c t t o g r e a t e r e r r o r s . Here e r r o r due t o i n a c c u r a c y , i n the t e s t t e mperature come i n t o p l a y . T h i s amounted to about 0.1$, because o f the p o s s i b i l i t y o f e r r o r i n the t e s t t e m p e r a t u r e o f about 0.04°C The d i f f e r e n c e between the c a l c u l a t e d k i n e m a t i c 117 v i s c o s i t y f o r the two v i s c o m e t e r s used f o r each d e t e r m i n a t i o n was u s u a l l y w i t h i n 0,1$, i n d i c a t i n g t h a t e r r o r s due t o a l i g n m e n t and t i m i n g were s m a l l . The te m p e r a t u r e c o r r e c t i o n t o the c a l i b r a t i o n c o n s t a n t c o u l d be a c c u r a t e l y c a l c u l a t e d and no e r r o r s were i n t r o d u c e d i n a p p l y i n g t h i s c o r r e c t i o n . The s u r f a c e t e n s i o n c o r r e c t i o n was not known, b u t , as mentioned above, was n e g l i g i b l e . F i n a l l y , t he k i n e t i c energy c o r r e c t i o n was kept below 0.1$ i n most c a s e s , by u s i n g s u f f i c i e n t l y l o n g e f f l u x t i m e s , b u t f o r t h e d e t e r m i n a t i o n on n - o c t a n o l a t 90°C i t was about 0.2$. The maximum e r r o r i n the a b s o l u t e v i s c o s i t y d e t e r m i n a t i o n s was t h e r e f o r e about 0.5 t o 0.6$. (c) The P u r i t y o f n - O c t a n o l A good check on the c o n s i s t e n c y of the a b s o l u t e v i s c o s i t y measurements i s accorded by the c l o s e f i t of the d a t a on n - o c t a n o l t o a smooth curve,and the s m a l l p e r cen t d e v i a t i o n s f o r the t h r e e and f o u r c o n s t a n t v i s c o s i t y - t e m p e r -a t u r e e q u a t i o n s . - T h i s i n s h a r p c o n t r a s t t o the poor a g r e e -ment between the v a l u e s f r o m d i f f e r e n t s o u r c e s i n the l i t e r a t u r e ( f i g u r e 10), w h i c h i s due i n p a r t t o d i f f e r e n c e s i n the a b s o l u t e v i s c o s i t y s t a n d a r d used, b u t m a i n l y t o d i f f e r e n c e i n degree of p u r i t y . A l t h o u g h no q u a n t i t a t i v e e s t i m a t e was made of the degree o f p u r i t y o f the n - o c t a n o l used i n t h i s r e s e a r c h , the c l o s e agreement of the d e n s i t y a t 25°C and the r e f r a c t i v e i n d e x a t 20°G w i t h v a l u e s a s s e s s e d f r o m the l i t e r a t u r e , i n d i c a t e s t h a t the m a t e r i a l was o f a h i g h p u r i t y . 118 Large disagreement on the v i s c o s i t y at v a r i o u s temperatures was obtained between the present work and that of previous i n v e s t i g a t o r s . I n most cases, i t was impossible to assess the r e l i a b i l i t y of the previous V i s c o s i t y data because of no i n d i c a t i o n of the degree of p u r i t y . I n other cases, the d e n s i t y and /ov r e f r a c t i v e index give c l e a r i n d i c a t i o n of unacceptable p u r i t y . No weight can be put to the agreement of t h i s work w i t h the data of Bingham and D a r a l l (144) and Mumford and P h i l l i p s (145), as no d e n s i t y data are a v a i l a b l e f o r the foraier^and the d e n s i t y data of the l a t t e r d i f f e r i n the t h i r d s i g n i f i c a n t f i g u r e from the values recommended above. (d) V i s c o s i t y of n-Octanol A three-constant equation i s r e q u i r e d to f i t the v i s c o s i t y - t e m p e r a t u r e data f o r n-octanol. The simple exponential formula, equation (10), and the Andrade theory, equation (9), give almost i d e n t i c a l r e p r e s e n t a t i o n of the data w i t h a maximum spread of 5$ and an average d e v i a t i o n of 1.5$ ( t a b l e 7 ) . The very c l o s e f i t of the data to a l l the three and f o u r constant equations (maximum spread 0.7$, average d e v i a t i o n 0.15$) i n d i c a t e s that over the range of temperatures covered, the v a r i a t i o n i n the a c t i v a t i o n energy i s s u f f i c i e n t l y s mall to be represented by any a d d i t i o n a l term. These forms of equation must be t e s t e d over more extended ranges of temperature to show any s i g n i f i c a n t d i f f e r e n c e . 119 Equation (88) can be converted to the exponential form to ob t a i n the pre-exponential f a c t o r and the energy of a c t i v a t i o n , -4 5 970 = 3.19 x 10 exp( — ) , c e n t i p o i s e . This value of the energy of a c t i v a t i o n (5,970 cal./mole) compares fa v o u r a b l y w i t h the value of 6,290 cals./mole obtained from E y r i n g 1 s Theory. I n order to c a l c u l a t e t h i s l a t t e r value, the l a t e n t heat of v a p o r i s a t i o n was i n t e r p o l a t e d at the mean temperature of t e s t (about 50°) from the values of 25°C and the b o i l i n g p o i n t , g i v e n by Weissburger (30)j to give 16,680 cals./mole, Hence, A E D n = 16,680-323 R = 15,980 cal./mole and AF* = 1 5> 9 8 0 = 6,290 2 .45 mole Comparing the exponential c o r r e l a t i o n of the data f o r n-octanol w i t h that of lower members of the homologous ser-i e s shows that the trend observed by G o l i k , R a v i k o v i c h and Orishchenko (113) f o r C. to C members (see above on Theory) i s continued . The f o l l o w i n g i s a comparison of the a c t i v a t i o n energies and the pre-exponential f a c t o r s f o r the s e r i e s . A. X10 5 AF*/R C-, 22 1042 C 9 '5 1752 2.3 2079 1.0 2442 4 6 0.32 3006 (poise x K T ) (°Kelvin) 120 The apparent c o n s i s t e n c y of these two c o n s t a n t s s h o u l d mean t h a t a r e a s o n a b l e c o r r e l a t i o n m ight be d e v e l o p e d t o p r o v i d e good i n t e r p o l a t i o n f o r the v i s c o s i t y - t e m p e r a t u r e e q u a t i o n f o r the C,_, C^ and C normal a l c o h o l s , and e x t r a -s' 6 • 7 ' p o l a t i o n t o h i g h e r members. A l t h o u g h some measurements on o t h e r normal a l c o h o l s have been made (11,27, 112) the d a t a are s u f f i c i e n t l y i n c o n s i s t e n t t o w a r r a n t r e - e x a m i n a t i o n and e v e n t u a l l y c o r r e l a t i o n w i t h t h e o t h e r members. I n view of the f a c t t h a t t h r e e and f o u r c o n s t a n t e q u a t i o n s f i t t e d t h e n - o c t a n o l d a t a so much b e t t e r , i t i s recommended t h a t a more t h o r o u g h e x a m i n a t i o n of a l l the d a t a on n - a l c o h o l s be made, and t h e p o s s i b i l i t y of c o r r e l a t i n g the c o n s t a n t s w i t h the number of c a r b o n atoms be examined. E v e n t u a l measurement o f the e f f e c t o f p r e s s u r e on the v i s c o s i t y o f n - o c t a n o l s h o u l d a l s o p r o v i d e means of e s t a b l i s h i n g p r e s s u r e - t e m p e r a t u r e - v i s c o s i t y r e l a t i o n s f o r the homologous s e r i e s . The c o r r e l a t i o n o f J o b l i n g and Laurence (114) mentioned i n the t h e o r y seems the most l i k e l y t o g i v e good agreement and s h o u l d p r o v i d e a c c u r a t e p r e d i c t i o n s on members of the s e r i e s not p r e v i o u s l y measured. LITERATURE CITED 121 1. Newton, S i r Isaac, " P r i n c i p i a " , Book I I (1685) 2. Burgers, J.M. 2 n d Report on V i s c o s i t y and P l a s t i c i t y , Ch. 1,. Acad. S c i . Amsterdam, (1938) 3. Oldroyd, G.G. "Non-Newtonian Plow of L i q u i d s and S o l i d s " , Ch. 16, of "Rheology, Theory and A p p l i c a t i o n s " Academic Press, (1956) 4. Pr i e n d , J.N. and Hargraves, W.D. P h i l . Mag. 34,643, 810 (1914) 5. C h a c r a v a r t i , A.S. Current S c i . (India) 15,105 (1946) 6. Jones, W.J. and Bowden S.T. P h i l . Mag. 36, 705 (1945) 7. Sugden, S. J Chem.Soc. (London) 125, 32 (1924) 8. B i r d , R.B. H i r s c h f e l d e r J.O. and C u r t i s s C.F. Trans. ASME 77, 1011 (1954) 9. Bingham E.G. " F l u i d i t y and P l a s t i c i t y " , McGraw-Hill (1922) 10. P o i s e u i l l e , J . Compt. Rend. 15,1167 (1842) 11. Thorpe,T and Rodger, J . P h i l . Trans. 185A, 397 (1894) 12. Bingham, E.C. and White G.P. Z Phys. Chem. 80, 670 (1912) 13. Ostwald,W.Le.hrbruch der allgemeineu Chemie" 1, 548f (1903) 14. Cannon, M.R. and Penske M.R. Ind. Eng..Chem. (Anal.Ed.) 10, 297 (1938) 15. Ubbelohde, L. J . I n s t . P e t r o l . Tech. 19, 376 (1933) 16. Rankine A.O. Proc. Ray. Soc. (London) 83A, 265 (1933) 17. Bridgman, P.W. Proc. Am. Acad. Arts S c i . 61, 57 (1926) 18. Hoppler,P. Proc. 2 n d World Pet. Cong., London, 503 (1933) 19. Flowers, A.E. ASTM Proceeding 14, 565 (1914 122 20. Hersey, M.D. and Shore, H. Mech. Eng. 50,221 (1928) 21. K h a l i l o v , K. J . Tech. Phys. (U.S.S.R.) 8,1249 (1938) 22. S w i n d e l l s , J.P. Coe J.R. and G o d f r e y , T.B. J . R e s e a r c h N.B.S. 48, N o . l (1952) 23. Cannon, M.R. I n d . Eng. Chem. (Anal.Ed.) 16, 708 (1944) 24. S w i n d e l l s J.W. Hardy and C o t t i n g t o n J.R., J . R e s e a r c h N.B.S. 52, No.3 (1954) 25. ASTM Standards on P e t r o l e u m P r o d u c t s and L u b r i c a n t s , p.192, 1954 E d i t i o n . 26. I n t e r n a t i o n a l C r i t i c a l T a b l e s , 5,10, 7 211, McGraw H i l l , (1927) 27. " L a n d o l t - B o r n s t e i n , Tables" 5 t h E d i t i o n , V o l . I . 4hd .'. .  Supplements (1927-38) 28. " L a n d o l t - B o r n s t e i n , T a b l e s " , 6 t h E d i t i o n , V o l . IV P t . l . (1955) 29. Timmermans, J . " P h y s i c o - C h e m i c a l C o n s t a n t s o f Pure Organic Compounds", E l s e v i e r , (1950) 30. We i s s b u r g e r , A. e t a l . "Techniques o f Organ i c C h e m i s t r y " V o l . V I I "O r g a n i c S o l v e n t s " I n t e r s c i e n c e . (1955) 31. American P e t r o l e u m I n s t i t u t e , "Thermodynamic P r o p e r t i e s of Hydrocarbons and R e l a t e d Compounds, P r o j e c t 44, C a r n e g i e P r e s s , P i t t s b u r g h , P a . (1953) 32. Tonomura, T. and M i t s u k u r i , S. P r o c . Imp. Acad. Tokyo, 3, 155 (1927), 5, 23 (1929) 33. Bridgman, P.W. P r o c . Nat. Acad. S c i . 11, 603 (1925) 34. Bridgman, P.W. P r o c . Am. Acad. A r t s S c i . 77, 115 (1949) 35. Bridgman, P.W. "The P h y s i c s of H i g h P r e s s u r e s " , Ch.12, B e l l , (1949) 36. Sage, B.H. I n d . Eng. Chem. (Anal.Ed.) 5, 261 (1933) 37. Mason, D.M. W i l c o x , O.W., and Sage B.H., J . Phys. Chem. 56, 1008 (1952) 38. C a r m i c h a e l , L.T. and Sage, B.H, I n d . Eng. Chem. 44, 2728 (1952) 123 39. Sage, B.H. Sherborne, J.E. and Lacey, W.N. I n d . Eng. Chem. 27, 954 (1935) 40. S h e m i l t , L.W. Mann, R.S. and E s p l e n , R.W. Can. J . Chem. Eng., a c c e p t e d f o r p u b l i c a t i o n . 41. Howey, G.A.R, M.A.Sc. T h e s i s , U.B.C. 1951 42. S i n g h , R. and S h e m i l t , L.W. J . Chem. Phys. 23, 1370 (1955) 43. W a l d i c h u k , M. S i n g h , R. and S h e m i l t , L.W. 3 9 t h Ann. Conf., Chem. I n s t . Can., M o n t r e a l , (1956) 44. S h e m i l t , L.W. P r o c . Conf. Thermodynamic and T r a n s p o r t P r o p s , o f F l u i d s , London, (1957) 45. S p e e r s , E.A. M.A.Sc. T h e s i s , U.B.C, 1958. 46. W h i t t l e , D.J. M.A.Sc. T h e s i s , U.B.C. 1958. 47. Gemant, A. J . App. Phys. 12, 829 (1941) 48. Andrade, E.N. daC. Endeavour, 13, 117 (1954) 49. V o l a r o v i c h , M.P. "The V i s c o s i t y o f L i q u i d s " , Moscow Peat I n s t . (1957) 50. B o n d l , A. "Theory o f t h e V i s c o s i t y o f L i q u i d s " , Ch .9 o f "Rheology - Theory and A p p l i c a t i o n s " , Academic P r e s s , (1956) 51. Andrade, E.N.daC. P h i l . Mag. 17, 497, 698, 712 (1934) 52. Andrade, E.N.daQ. and Dobbs, E.R. P r o c . Ray. Soc. (London) 211A, 12 (1952) 53. E y r i n g , H. J . Chem. Phys. 4, 283 (1936) 54. E w e l l , R.H. and E y r i n g , H. I b i d . 5, 726 (1937) 55. Roseveare, W.E. P o w e l l , R.E. and E y r i n g , H. J . App. Phys. 12, 669 (1941) 56. Lindemann, F.A. P h i s i k , Z. 11, 609 (1907) 57. van der Waals J.D. J r . , P r o c . Acad. S c i . Amsterdam, 21, 743 (1918) 58. J a e g e r , F.M. Second R e p o r t on V i s c o s i t y and P l a s t i c i t y , Ch. 2 Acad. S c i . , Amsterdam, (19380 124 59. F r e n k e l , J . ,Z. P h y s i k . 35, 662 (1926) 60. F r e n k e l , J . T r a n s . F r a d a y S o c , 33, 58 (1937) 61. MacLeod, D.B. I b i d . 19, 6 (1923) 62. Macleod, D.B. I b i d . 32, 872 (1936) 63. G l a s s t o n e , S. L a i d l e r , K . J . and E y r i n g , H. "Theory o f Rate P r o c e s s e s " , M c G r a w - H i l l , (1941) 64. Panchenkov, G.M. D o k l a d y Akad. Nauk., S.S.S.R. 63, 701 (1948) Chem. Abs. 44, 9755d. 65. Panchenkov, G.M. Zhur. F i z . Khim. 24, 1390 (1950) Chem. Abs. 45, 36731. ' 66. Kirkwood, J.G. B u f f , F.P. and Green, M.S., J . Chem. Phys. 988 (1949) 67. Zwanzig, R.W. Kirkwood J.G. S t r u p p , K.F. and Oppenheim, I . , J . Chem. Phys. 21, 2050 (1953) 68. Born, M. and Green, H.S. "A G e n e r a l K i n e t i c Theory o f L i q u i d s " , Cambridge, (1949) 69. Hougen, O.A. and Watson, K.M. " Ch e m i c a l P r o c e s s P r i n c i p l e s " P a r t I I I . K i n e t i c s , W i l e y , (1947) 70. P i t z e r , K.S. e t a l . J . Am. Chem. Soc. 77, 3427 (1955) 71. R i d d e l , L. Chem. I n g . Tech., 26, 83, 259, 679 (1954) 72. L y d e r s o n , A.L. Greenkorn, R.A. and Hougen, O.A., U n i v e r s i t y o f W i s c o n s i n , Eng. E x p t . S t a t i o n R e p o r t No. 4. (1955) 72a. Grunberg, L. and N i s s a n , A.H., I n d . Eng. Chem., 42, 885 (1950) 72b. Comings, E.W. and E l g y , R.S. I b i d . 32, 714 (1940) 72c. Comings, E.W. and Mayland, B . J . Chem. Met. Eng., 52, (3) 115 (1945) 73. C a r r , M. P a r e n t , . J . D . and Peck, R.E. Chem. Eng., Synopsium S e r i e s , 16, 51, 91 (1955) 74. de Boer, J . P h y s i c a , 14, 139 (1948) 75. S m i t h , A.S. and Brown, G.G. I n d . Eng. Clhem. 85, 705 (1943) 125 76. Souders, M.J. Am. Chem. Soc. 59, 1252 (1937), 60, 154 (1938) 77. H e l l e r , M.W. Phys. Revs. 94, 1426 (1954) 78. P a r t i n g t o n , J.K. " An Advanced T r e a t i s e on P h y s i c a l C h e m i s t r y " , V o l . I I , p. 95, Longmans, 1(1951) 79. Bowden, S.T. and Morgan, A.R. P h i l . Mag. 29, 367 (1940) 80. S a r i n i v a s a n , M.K. and P r a s a d , B. I b i d . 33, 258 (1942) 81. B a n e r j i , B.K. C u r r e n t S c i . ( I n d i a ) , 17, 214 (1948) 82. B r a n k e r , A.V. N a t u r e , 166, 905 (1950) 83. L i t o v i t z , T.A. J . Chem. Phys. 20, 1088, 1980 (1952) 84. Gutmann, P. and Simmons, L.M. J . App. Phys. 23, 977 (1952) 85. M i t r a , S.S. C u r r e n t S c i . ( I n d i a ) 22, 329 (1953) 86. W i t t e n b u r g e r , W. B r e n s t o f f - C h e m . 34, (1953) 87. Baum, E. K o l l o i d - Z . 135, 176 (1954) 88. B r a n k e r , A.V. I n d . Chemist 30, 112 (1954) 89. M i t r a , S.S. J . I n d i a n Chem. Soc. 32, 297 (1955) 90. M i t r a , S.S. C u r r e n t S c i . ( I n d i a ) 24, 44 (1955) 91. C o r n e l i s s o n , J . and Watermann, H.I. Chem. Eng. S c i . 4, 238 (1955) 92. G i r i f a l c o , L.A. J . Chem. Phys. 23, 2446 (1955) 93. I n n e s , K.K. J . Phys . Chem. 60, 617 (1956) 94. Hovorka, P. Lankelma, H.P. and S t a n f o r d , S.C. J . Am. Chem. Soc. 60, 820 (1938) 95. D o u g l a s , R.W. N a t u r e , 158, 415 (1946) 96. Thomas, L.H. I b i d . 158, 622 (1946), J . Chem. Soc. (London) 1947, 822. 97. B l o k , H. P r o c . World P e t . Cong., The Hague, S e c t . V I I , p. 304 (1951) 126 98. Dow, R.B. " R h e o l o g i c a l P r o p e r t i e s Under H i g h P r e s s u r e " , Ch.8 of " Rheology, Theory and A p p l i c a t i o n s " Academic P r e s s , (1956) 99. Cohen, R. Ann. Phys. 45, 666 (1892) 100. Hauser, L. I b i d . 5, 597 (1901) Z. Phys, Chem. 86, 479 (1914) 101. Suge, Y. B u l l . I n s t . Phys. Chem. R e s e a r c h (Tokyo), 11, 977 (1932), 12, 643 (1933) 102. B a c h i n s k i i , A . J . Phys. Z. 13, H 5 7 (1912) Z. Phys, Chem. 84, 643 (1913) 103. Bingham, E.C. Adams, H.E. and M c C o u s l i n , G.R. J . Am. Chem. -Soc. 63, 466 (1941) 104. MacLeod, D.B. T r a n s . F a r a d a y Soc. 41, 771 (1945) 105. De C a r v a l h o H.C. A n a i s . A s s o c . quim. B r a z i l 8, 49 (1949). Chem. Abs. 45, 15d. 106. Warburg and Sachs, Weid Ann. 22, 518 (1884), see a l s o r e f . (9) 107. Kuss, E. E r d o l u K o h l e , 6, 266 (1933), Chem. Abs. 47, 10203a. 108. I r a n y , E.P. J . Am. Chem. Soc. 60, 2106 (1938) 109. Hersey, M.D. and Hopkins R.F. " V i s c o s i t y of L u b r i c a n t s Under P r e s s u r e " A.S.M.E. (1954) 110. Sanderson, R.T. Mech. Eng. 71, 349 (1949) 111. C l a r k , O.K. T r a n s . A.S.M.E. 78, 905 (1956) 112. Dunstan, A.E. T h o l e , F.B. and Benson, P. J . Chem. Soc. (London) 105, 782 (1914) 113. G o l i k , A . Z . . R a v i k o v i c h , S.D. and O r i s h c h e n k o , A.V. U k r a i n . Khim. Zhur. 21, I67 (1955) 114. J o b l i n g , A. and L a u r e n c e , A.S.C. J . Chem. Phy s . 20, 1296 (1952) 115. B r i t i s h Columbia E l e c t r i c Co. L t d . , P r i v a t e communication Feb. 1958. 116. Cannon, M.R. " D e r i v a t i o n of the V i s c o s i t y E q u a t i o n and Sources o f E r r o r i n V i s c o m e t r y " - P r i v a t e r e p o r t t o ASTM committee D-Z, 1950) 127 117 B a r r , G. "A Monograph on V i s c o m e t e r " , Oxford (1933) 118 Sugden, S. J . Chem. Soc. (London) 119, 1483 (1921) 1 1 9 P e r r y , J.H. "C h e m i c a l E n g i n e e r s Handbook", p.363 M c G r a w - H i l l (1950) 120 Hersey, M.D. and Shore, H. J . Wash. Acad. S c i . , 6, 525 (1916) 121 Hersey, M.D. and Shore, H. Mech. Eng. 41, 537 (1919) 122 Hersey, M.D. and Shore, H. I b i d . 45, 315 (1923) 123 H o c o t t , C R . and B u c k l e y , S.E. I n s t . M i n . Met. E n g r s . Tech. Pub. No. 1220 X-5940) 124 E x l i n e , P.G. and Endean, H.J. O i l Gas J . 45 (45) 82 (1947) 125 M a k i t a , T. Rev. Phys. Chem. Japan, 24, 74 (1954) 126 M a k i t a , T, Kyoto Tech U n i v . , S c i . and T e c h n o l . , No.4 19 (1955) 127 Lundberg, S. J . I n s t . P e t r o l e u m 40, 104 (1954) 128 Hubbard, R.M. and Brown, G.G. I n d . Eng. Chem. ( A n a l . Ed.) 15, 212 (1943) 129 L e w i s , H.W. A n a l . Chem. 25, 507 (19530' 130 C a t a l o g 595, "Time R e g i s t e r i n g A p p a r a t u s , Jaquet L t d . , B a s l e , S w i t z e r l a n d . 131 F r a n c i s , A.W. P h y s i c s , 4 , 403 (1933) 132 Bacon, L.R. J . F r a n k l i n I n s t . , 221, 251 (1936) 133 B l o c k , R.F. J . App. Phys. 11, 635 (1940) 134 Young, J.W. "Development o f V i s c o m e t e r s f o r O i l D i l u t i o n Measurement" I m p e r i a l O i l L t d . , C a l g a r y , A l b e r t a (1954) 135 Bauer, N. Ch. VI of "Techniques of Organic C h e m i s t r y " V o l . 1 . P a r t I , Ed. W e i s s b u r g e r , I n t e r s c i e n c e (1949) 136 Handbook o f P h y s i c s and C h e m i s t r y , p. 1971, C h e m i c a l Rubber P u b l i s h i n g Co., 37 ed. (1955) 128 137 I m p e r i a l O i l L t d . , P r i v a t e Communication,August,1958 138 Perry, J.H. " Chemical Engineering Handbook", p.1238 McGraw-Hill (1950) 139 Superpressure Catalog 407, American Instrument'Co., Inc. S i l v e r Spring, Maryland, Washirigton,D.C. (1957) 140 Comings, "High Pressure Technology" McGraw-Hill, (1956) 141 High Pressure Equipment Catalog, High Pressure Equipment Co., Inc. E r i e , Pa. 142 Kay, W.B. and Donham, W.E. Chem. Eng. S c i . , 4, ( 1 ) 1 (1955) 143 Smythe, C P . and Stoops, W.N. " J . Am. Chem. Soc. 51, 3312 (1929) 144 Bingham, E.C and D a r a l l , L.B. J . Rheology, 1, 174 (1930) 145 Mumford,. S.A. and P h i l l i p s , J.W.C. J . Chem. Soc. (London) 1950, 75 146 Derkin, W.K. I b i d , 45, 421 (1884) 147 Zander, Ann. 224, 84 (1884) 148Gartenmeister, R. Z, Physik. Chem. 6, 524 (1890) 149 Dunstan, A.Ev Thole, P.B. and Benson, P. J . Chem. Soc. London) 105, 782 (1914) 150 Lowry, T.M. I b i d , 105, 81 (1914) 151 Behal, A. B u l l . Soc. Chim (Prance) 25, 473 (1919) 152 Verkade, O.E. and Coops, J . Rec. Trav. Chim, 46,903 (1927) 153 D e f f e t , L. B u l l . Soc. Chim. B e l g . 40, 385 (1931) 154 E l l i s , L.M. and Reid, E.E. J . Am. Chem. Soc. 59, 1674 (1932) 155 B u t l e r , J.R.V. Thomson, D.W. and MacLennan, W.H. J . Chem. Soc. (London) 1933, 674 156 N e v j i , G.V. and J a t k a r , S.K.K. Indian J . Phy s i c s , 397 (1934) 129 157 B u t l e r , J.A.V. Rac h a n d a n i , C.N. and Thomson, D.W. J . Chem. Soc. (London) 1935, 280 158 O l i v e r , P. Rec. T r a v . Chim. 56, 247 (1937) 159 Komarewsky, V . I . and C o l e y , J.R. J . Am. Chem. Soc. 63, 3269 (1950) 160 Dorough, G-.L. e t a l . I b i d . 63 3100 (1941) 161 M u l l e r , A . , P e t t e u S e i f e n 49, 572 (194), Chem. Abs. 37, 6510^ 162 Jones, W.J. Bowden, S.T. Y a r n o l d , W.W. and Jones, W.H. J . Phys. Chem. 52, 753 (1948) 163 D r e i s b a c h , R.R. and M a r t i n , R.A. I n d . Eng. Chem. 41, 2875 (1949) 164 Mumford, S.A. and P h i l l i p s , J.W.G. J . Chem. Soc. (London) 1950, 75 165 U.B.S. Computing C e n t r e , R o u t i n e S-3, " C o r r e l a t i o n and R e g r e s s i o n " (1957) 130 r APPENDIX I B i b l i o g r a p h y on P r e s s u r e V i s c o m e t r y 1. Bridgman, P.W. P r o c . Nat. Acad. S c i . 11, 603 (1925) 2. Bridgman, P.W. P r o c . Am. Acad. A r t s S c i . 61, 57 (1926) 3. Hersey, M.D. and Shore, H. Mech. Eng. 50, 221 (1928) 4. Suge, Y. B u l l . I n s t . Phys. Chem. R e s e a r c h (Tokyo) 11, 977 (1932) . 5. Sage, B.H. I n d . Eng. Chem. (Anal.Ed.) 5, 261 (1933) 6. H o p p l e r , P. Z. t e c h . P h y s i k , 14, 165 (1933) 7. H o p p l e r , P. P r o c . 2 n d World P e t . Congr. London, 503 (1933) 8. F r a n c i s , A.W. P h y s i c s , 4, 403 (1933) 9. Knop, W. Z. V e r . d e n t . Z u c k e r i n d , 83, 932 (1933) 10. Suge, Y. B u l l . I n s t . Chem. Phys. R e s e a r c h (Tokyo) 12, 643 (1933) 11. Knapp, R.T. I n d . Eng. Chem. ( A n a l . Ed.) 6, 80 (1934) 12. Dow, R.B. P h y s i c s , 6, 71 (1935) 13. Sage, B.H.- Sherborne, J.E. and Lacey, W.N. I n d . Eng. Chem. 27, 954 (1935) 14. Mason, C.C. P r o c . Phys. Soc. (London) 47, 519 (1935) 15. Ebbecke, U. and H a n d b r i c h , R. A r c h . ges. P h y s i o l . ( P f l u g e r s ) 238,. 429 (1936) 16. B l o k k e r , P.C. Rec. t r a v . chim. 55, 170 (1936) 17. Bacon, L.R. J . F r a n k l i n I n s t . 221, 251 (1936) 18. V e r s l u y s , J . M i c h e l s , A. and Be r b e r J . P h y s i c a 3, 1093 (1936) 131 19. Thomas, B.W. Dow. R.B. and Ham, W.R. Phys. Rev. 53, 926 (1938) 20. K h a l i l o v , K. J . Tech. Phys. (U.S.S.R.) 8, 1249 (1938) 2D. Sage, B.H. and Lacey, W.N. Ind. Eng. Chem. 30, 829 (1938) 2 2 . Dow, R.B. P h i l . Mag. 28, 403 (1939) 23. K h a l i l o v , K. J . Exp. Theoret. Phys. (U.S.S.R.) 9, 335 (1939) 24. van Wyk, W.R. et a l . , Physica 7 45, (1940) 25. Sage, B.H. and Lacey, W.N. Ind. Eng. Chem. 32, 587 (1940) 26. Hocott, C R . and Buckley, S.E. I n s t . Mining Met. Engrs. Tech. Pub. No. 1220 (1940) 27. Hubbard, R.M. and Brown, C C End. Eng. Chem. (Anal.Ed.) 15, 212 (1943) 28. Pugh, H.L.D. J . S c i . Instruments 21, 177 (1944) 29. E x l i n e , P.G. and En Dean, H.J. O i l Gas J . , 45, (45) 82 (1947c) 30. Walter, P. and Weber, W. Angew Chem. B19, 123 (1947) 31. Bridgman, P.W. Proc. Am. Acad. A r t s S c i . 77, 115 (1949) 32. Thompson, A.M. J . S c i . Instruments 26, 75 (1949) 33. Lazarre, P. J . phys. radium 11, D51 (1950) 3 4 . Iwasaki, H. S c i . Repts. Res. I n s t . Tohoku Univ. 3A, 247 (1951) 3 5 . Kuss, E. Naturwissenschaften, 38, 102 (1951) 3 6 . J o b l i n g , A. and Laurence, A.S.C. Proc. Roy. S 0 c . (London) 206A, 257 (1951) 37. Mason, D.M. Wilcox, 0.W, Sage, B.H. J . Chem. Phys. 5 6 , 1008 (1952) 38. Carmichael, L.T. and Sage, B.H. Ind. Eng. Chem. 44,2728 (1952) 1.32 39. N a i k i , T., e t a l . B u l l . I n s t . Chem. Res., Kyoto U n i v . 31,(1) 56 (1953) 40. L e w i s , H.W. A n a l . Chem. 25, 507 (1953) 41. Kuss, E. E r d o l . u Kohle 6, 266 (1953) 42. Young, J.W. "Development of an I n s t r u m e n t f o r O i l D i l u t i o n Measurement", I m p e r i a l O i l L t d . C a l g a r y , Alberta, (1954) 43. Lundberg, S . J . I n s t . P e t r o l e u m , 40, 105 (1954) 44. M a k i t a , T. Rev. Phys. Chem. (Japan) 24, 74 (1954) 45. Derazhne, R . I . Popov, V.D. and T r e n k e l , Y.B. Zavodskaya Lab. 21, 731 (1955) 46. Kuss, E. Z. Angew Phys. 7, 372 (1955) 47. M a k i t a , T. Mem.'Fac. I n d . A r t s . Kyoto U n i v . , S c i . and T e c h n o l . No.4. 19 (1955) 48. Kuss, E. ChemTlng^-Tech. 28, 141 (1956) 49. H e i k s , J.R. and Orban, E. J.Phys. Chem. 60, 1025 (1956) 133 APPENDIX I I CERTIFICATE OF CALIBRATION VISCOMETER NO. g°g CANNON*FENSKE-OSTWALD TYPE Co n s t a n t a t 100° F. 0 . 0 1 2 4 5 C e n t i s t o k e s / S e c o n d C o n s t a n t a t 210° F. 0 . 0 1 2 3 9 C e n t i s t o k e s / S e c o n d To o b t a i n v i s c o s i t y i n c e n t i s t o k e s m u l t i p l y t ime i n seconds by t h e v i s c o m e t e r c o n s t a n t . The v i s c o m e t e r c o n s t a n t a t o t h e r t e m p e r a t u r e s may be o b t a i n e d by i n t e r p o l a t i o n o r e x t r a p o l a t i o n . V i s c o s i t i e s of the s t a n d a r d used i n c a l i b r a t i n g were e s t a b l i -shed i n Ma s t e r V i s c o m e t e r s as d e s c r i b e d i n I n d . Eng. Chem.Anal. Ed. 16, 708 (1944) by M.R. Cannon. T h i s method has been f a v o r -a b l y checked a t the U n i t e d S t a t e s Bureau o f Standards by S w i n d e l l s , Hardy and C o t t i n g t o n and t h e i r work i s p u v l i s h e d - i n the J o u r n a l o f R e s e a r c h of t h e N a t i o n a l Bureau of S t a n d a r d s , V o l . 52, No.3 March, 1954, R e s e a r c h Paper 2479. V i s c o s i t i e s a r e based on the new v a l u e f o r water adopted by t h e U n i t e d S t a t e s Bureau o f Standards and The American S o c i e t y f o r T e s t i n g M a t e r i a l s J u l y 1, 1953. The new v i s c o s i t y b a s i s i s 1.0038 c e n t i s t o k e s f o r water a t 68° F. CALIBRATION DATA AT £00° F. V i s c o s i t y V i s c o s i t y E f f l u x Time C o n s t a n t S t a n d a r d C e n t i s t o k e s Seconds C e n t i s t o k e s / S e c o n d s 20K 4.598 369.0 0.012461 3D2D 3.480 279.7 0.012442 Average= 0.01245 Room Temp, (approx.) 78 F. Charge (approx.) 7 . 1 m l . D r i v i n g f l u i d head (approx.) 9 . 6 cm. .134 Working d i a m e t e r o f lo w e r r e s e r v o i d 3 cm. Con s t a n t a t 210° P. i s 0.5 % d i f f e r e n t t h a n a t 100° P. C a l i b r a t e d by RVS-I46PP under s u p e r v i s i o n of R.E.Manning R.E.Manning,Ph.D., Ch e m i c a l Engineer-M.R.Cannon, Ph.D., C o n s u l t i n g C h e m i c a l E n g i n e e r R e g i s t e r e d P r o f e s s i -o n a l E n g i n e e r S t a t e C o l l e g e , Penn. D i r e c t i o n s f o r use are p u b l i s h e d i n A.S.T.M. St a n d a r d s on P e t r o l e u m P r o d u c t s and L u b r i c a n t s and a l s o i n I n d . Eng. Chem. A n a l . Ed. V o l . 10, page 297, June 1938 V i s c o m e t e r s f o r opaque l i q u i d s are a v a i l a b l e . F o r t h e i r d e s c r i p t i o n and use see I n d . Chem. A n a l . Ed., V o l . 13 299 (194D. 1-35 APPENDIX I I I CALIBRATION OP THERMOMETERS The mercury thermometers used i n t h i s work were c a l i b r a t e d a g a i n s t a Leed and N o r t h r o p p l a t i n u m r e s i s t a n c e thermometer, No.679368 w h i c h had been r e c e n t l y c a l i b r a t e d by the N.B..S. The r e s i s t a n c e of t h e thermometer was measured w i t h a Leeds and N o r t h r o p .temperature b r i d g e . B e f o r e any c a l i b r a t i o n was made, t h e r e s i s t a n c e of t h e thermometer a t the i c e p o i n t was determined w i t h the same b r i d g e used f o r the c a l i b r a t i o n s . Crushed i c e p r e p a r e d f r o m d i s t i l l e d water and t h r o u g h w h i c h a i r was c o n t i n u o u s l y b u b b l e d was used f o r t h i s d e t e r m i n a t i o n . The r e s i s t a n c e was c o n v e r t e d t o t e m p e r a t u r e by a p p l i -c a t i o n of t h e well-known e q u a t i o n , R,-R +. . t o , c /_JL 1 ^ t o< R o 0 ^100 *' 100 where R = 25.5395 abs. ohms (determined i n t h i s work) o - -= 0.0039232 c (N.B.S.) " 75 = 1.49^ ( M B S . ) 34 J The c a l i b r a t i o n of the t h r e e thermometers used i n t h i s work are g i v e n i n f i g u r e 12, where the c o r r e c t i o n i s p l o t t e d a g a i n s t the t r u e t e m p e r a t u r e . S i n c e the e m e r s i o n was kept c o n s t a n t d u r i n g t h e d e t e r m i n a t i o n s , the l a r g e d e v i a t i o n s a t h i g h e r t e m p e r a t u r e s i s m a i n l y accounted f o r i n terms of a stem c o r r e c t i o n . 137 APPENDIX IV OPERATING INSTRUCTIONS FOR PRESSURE VISCOMETER Note. F i g u r e 1. i s re p r o d u c e d as f i g u r e 3, o f t h i s t h e s i s . Humble Type P r e s s u r e V i s c o s i m e t e r Type D The Humble Type P r e s s u r e V i s c o s i m e t e r i s an i n s t r u -ment o f t h e r o l l i n g b a l l t y p e f o r m e a s u r i n g the v i s c o s i t y o f s u b s u r f a c e samples of o i l under v a r i o u s c o n d i t i o n s of temper-a t u r e and p r e s s u r e . The a p p a r a t u s c o n s i s t s e s s e n t i a l l y o f a removable, a c c u r a t e l y bored c y l i n d r i c a l b a r r e l of o n e - f o u r t h i n c h n o m i n a l i n t e r n a l d i a m e t e r , e i g h t i n c h e s l o n g , i n w h i c h a c l o s e l y f i t t i n g s t e e l b a l l r o l l s t h r o u g h the o i l w i t h the b a r r e l i n c l i n e d a t a d e f i n i t e a n g l e . The b a l l makes c o n t a c t a t one end o f the b a r r e l w i t h an i n s u l a t e d e l e c t r o d e , c l o s i n g an e l e c t r i c a l c i r c u i t w h i c h a c t u a t e s a b u z z e r . The measure-ments c o n s i s t e s s e n t i a l l y i n d e t e r m i n i n g the time r e q u i r e d f o r the b a l l t o t r a v e l t he l e n g t h of the b a r r e l . The d e t a i l s of the c o n s t r u c t i o n a re shown by d r a w i n g . The b a r r e l i n w h i c h t h e b a l l r o l l s i s made fr o m s t a i n l e s s s t e e l , e s p e c i a l l y bored t o an e x a c t u n i f o r m d i a m e t e r and p o l i s h e d . F o r extreme c o r r o s i v e c o n d i t i o n s a monel b a r r e l c a n be f u r n i s h e d . The b a r r e l s l i d e s s n u g l y i n t o a h o l e bored i n a s o l i d s t a i n l e s s s t e e l c y l i n d e r , an upper e x t e r n a l s h o u l d e r of the b a r r e l c o m p r e s s i n g a s m a l l s p r i n g , and i s h e l d i n p l a c e by a h o l l o w n u t . The s p r i n g p r e v e n t s the b a r r e l f r o m s e a t i n g a g a i n s t t h e bottom of the bored h o l e i n the c y l i n d e r , w h i l e narrow e x t e r n a l l o n g i t u d i n a l s l o t s i n the b a r r e l p e r m i t f l u i d t o f l o w around i t and t h r o u g h the bottom. The upper p a r t of the r e c e s s i n the s t e e l c y l i n d e r i s e n l a r g e d t o fo r m a t a p e r e d chamber w h i c h a c t s as a r e s e r v o i r f o r t h e o i l a f f o r d s space f o r a g i t a t i o n t o i n s u r e e q u i l i b r i u m between t h e gas and o i l . The t a p e r p e r m i t s the b a l l t o r o l l r e a d i l y i n t o the b a r r e l when the i n s t r u m e n t i s at.' an a n g l e o f v i n c l i n a t i o n o f 75 d e g r e e s . The upper end of the-chamber i s s e a l e d by a p o l i s h e d p i s t o n s e a t e d on a s h o u l d e r , the c l o s u r e made w i t h a neoprene g a s k e t " o f a r e a s m a l l e r t h a n t h a t o f the lo w e r s u r f a c e of the p i s t o n . The p r i m a r y g a s k e t c o m p r e s s i o n i s e f f e c t e d by means o f a h o l l o w n u t w h i c h s l i p s over the p i s t o n . 138 A r e t r a c t a b l e p l u n g e r w i t h a p o l i s h e d l o w e r s u r f a c e i s screwed t h r o u g h t h e c y l i n d e r head i n such a f a s h i o n t h a t i t i s a c c e s s i b l e and may be t u r n e d w i t h a s m a l l wrench w h i l e the i n s t r u m e n t i s immersed i n a h i g h t e m p e r a t u r e b a t h . W h i l e t h e v i s c o s i m e t e r i s b e i n g charged w i t h o i l o r t h e c o n t e n t s b e i n g a g i t a t e d t o b r i n g about e q u i l i b r i u m , the p l u n g e r i s kept p a r t l y o r f u l l y r e t r a c t e d . D u r i n g the c o u r s e of a measurement, however, t h e p l u n g e r i s screwed i n t o the c y l i n d e r , s e a l i n g the upper end o f t h e b a r r e l and s i m u l t a n e o u s l y s e a l i n g the l o w e r end o f t h e b a r r e l by p r e s s i n g i t a g a i n s t a g a s k e t i n the bottom of the bored r e c e s s i n the c y l i n d e r . S i n c e the p r e s s u r e i s a t a l l t i mes e q u a l i n s i d e and o u t s i d e of the r o l l b a r r e l , the i n s t r u m e n t has no p r e s s u r e c o e f f i c i e n t , and t h e doub l e s e a l i n g o f the b a r r e l a d e q u a t e l y p r e v e n t s l e a k a g e d u r i n g a measurement. The s t e e l c y l i n d e r i s mounted on t r u n n i o n s i n s u c h a manner t h a t i t may be r o t a t e d t h r o u g h an a n g l e of a p p r o x i m a t e l y 330 degre e s . The t r u n n i o n b e a r i n g s a r e s e t i n aluminum p l a t e s w h i c h are f a s t e n e d i n t u r n t o a t h i r d aluminum p l a t e equipped w i t h f o u r l e v e l i n g s c r e w s . The s u p p o r t i n g p l a t e s were s e t c a r e f u l l y p e r p e n d i c u l a r t o the base p l a t e and machined accrua--t e l y i v i t h the tops p a r a l l e l to' the base and o f the same h e i g h t , t o p e r m i t use of an o r d i n a r y b u b b l e type l e v e l i n a l i g n i n g the i n s t r u m e n t f o r v i s c o s i t y measurement. Handles on t h e p l a t e s make the i n s t r u m e n t r e a d i l y p o r t a b l e . The t r u n n i o n p l a t e s a re equipped w i t h one f i x e d s t o p , c o n s i s t i n g of a c y l i n d r i c a l b a r , w h i c h g i v e s the b a r r e l an a n g l e o f i n c l i n a t i o n a p p r o x i m a t e l y 75 degrees f r o m t h e h o r i z o -n t a l , and two removable p o s i t i v e s t o p s a t a n g l e s o f i n c l i n a t i o n o f a p p r o x i m a t e l y 23 degrees and 11 degree s , p e r m i t t i n g t h e r o l l t ime t o be v a r i e d i n the r a t i o s of a p p r o x i m a t e l y 4:2:1 f o r any y g i v e n v i s c o s i t y and s i z e of b a r r e l and b a l l . A d d i t i o n a l f l e x i -b i l i t y i n the r o l l time i s o b t a i n e d t h r o u g h t h e use of remova-b l e r o l l b a r r e l s and b a l l s of d i f f e r e n t d i a m e t e r s . The r o l l time u s u a l l y i s ke p t between 20 and 60 seconds. F o r the r§nge of v i s c o s i t y thus f a r e n c o u n t e r e d , 0.5 to 10 cp. A b a r r e l of 0.258 i n c h d i a m e t e r w i t h b a l l s of .2495, .250, .2505 and .2510 i n c h d i a m e t e r have s u f f i c e d . The bottom of t h e c y l i n d e r e n c l o s i n g the b a r r e l i s c l o s e d by means o f an e l e c t r o d e assembly. The a u x i l i a r y a p p a r a t u s c o n s i s t s o f a vacuum tube r e l a y and b u z z e r c i r c u i t f o r i n d i c a t i n g the i n s t a n t of c o n t a c t o f t h e b a l l w i t h ' t h e e l e c t r o d e , a c a l i b r a t e d s t e e l tube bourdon p r e s s -u r e gauge,-a m a n i f o l d w i t h V a l v e s f o r a d m i t t i n g and w i t h d r a w i n g the sample, and a water b a t h w i t h e l e c t r i c a l h e a t i n g c e l l s and t h e r m o s t a t . A s m a l l f i l t e r , used o n l y when a b s o l u t e l y n e c e s s a -r y ; i s p l a c e d i n the l i n e between the m a n i f o l d and the v i s c o -s i m e t e r i n such p o s i t i o n t h a t the sample w i l l be f i l t e r e d a t the r e s e r v o i r t e m p e r a t u r e . 139 V i s c o s i t y d e t e r m i n a t i o n s can r e a d i l y be made on as l i t t l e as 20-cc . of l i q u i d . The e n t i r e system, i n c l u d i n g the v i s c o s i m e t e r , p r e s s u r e g a u g e , m a n i f o l d , and c o n n e c t i n g 1/8 i n c h s t e e l t u b i n g r e q u i r e s a charge of a p p r o x i m a t e l y 80* c c . of s a t u r a t e d s u b s u r f a c e o i l , l e e s t h a n 20$ of the c o n t e n t s of t h e u s u a l s u b s u r f a c e s a m p l e r . Due t o t h e ' s m a l l c l e a r a n c e between the r o l l i n g b a l l and the b a r r e l , a b s o l u t e c l e a n n e s s i s e s s e n t i a l t o s u c c e s s f u l o p e r a t i o n . A f t e r each s e r i e s o f measurements, the b a r r e l i s removed, washed w i t h e t h e r , and p o l i s h e d w i t h a s i l k r a g , and the c y l i n d e r and c o n n e c t i n g l i n e s washed c a r e f u l l y w i t h e t h e r and e v a c u a t e d . CALIBRATION The i n s t r u m e n t s h o u l d be r e c a l i b r a t e d f r o m t i m e to-time w i t h a s e r i e s of f l u i d s c o n s i s t i n g o f hexane, k e r o s e n e , a l i g h t l u b r i c a t i n g o i l , and v a r i o u s b l e n d s of these t h r e e mater-i a l s . The v i s c o s i t i e s of the c a l i b r a t i n g f l u i d s were d e t e r -mined w i t h a Ubbelohde suspended l e v e l c a p i l l a r y i n s t r u m e n t c a l i b r a t e d by the U.S. Bureau o f S t a n d a r d s . As i t i s p r a c t i c a l l y i m p o s s i b l e , now, t o purchase , Ubbelohde suspended l e v e l c a p i l l a r y i n s t r u m e n t s t h r e e Ostwald-H a r r i s c a l i b r a t e d ' V i s c o s i m e t e r s c o v e r i n g c e n t i s t r o k e ranges of 0.8-2.0, 1.8-4.0 and 4.0-15 can be u s e d . The d e n s i t i e s of the c a l i b r a t i n g f l u i d s a r e determined w i t h a pycnometer. C a l i b r a t i o n c h a r t s are p r e p a r e d f o r a g i v e n s i z e b a r -r e l and b a l l by p l o t - t i m e the a b s o l u t e v i s c o s i t y o f each f l u i d a g a i n s t the p r o d u c t of the r o l l t i m e and the d i f f e r e n c e i n d e n s i t y between the f l u i d and the b a l l , a c c o r d i n g t o the method suggested by Kennedy and used by Sage5. EXPERIMENTAL PROCEDURE Measurements a t r e s e r v o i r t e m p e r a t u r e a r e ,made w i t h t h e i n s t r u m e n t immersed i n a water b a t h , the temp e r a t u r e o f w h i c h i s c o n t r o l l e d t o i 0.5°P. O i l and gas a r e expanded i n t o t h e v i s c o s i m e t e r t h r o u g h 1/8 i n c h o u t s i d e d i a m e t e r s t e e l t u b -i n g d i r e c t f r o m a s u b s u r f a c e sampler, the c o n t e n t s of w h i c h have been s a t u r a t e d p r e v i o u s l y . D u r i n g c h a r g i n g , t h e r e t r a c t a -b l e p l u n g e r i s t u r n e d t o a p o s i t i o n midway between the s e a t e d and f u l l y r e t r a c t e d p o s i t i o n s , w i t h the b a l l i n the e n l a r g e d p o r t i o n of t h e c y l i n d e r . The p a r t i a l l y r e t r a c t e d p l u n g e r p r e v -e n t s the b a l l f r o m e n t e r i n g the r o l l b a r r e l b u t p e r m i t s f l u i d s t o pass back and f o r t h f r e e l y . The c h a r g i n g I s done w i t h the v i s c o s i m e t e r t i l t e d t o t h e p o s i t i o n w i t h the e l e c t r o d e up and the e n l a r g e d p a r t of the c y l i n d e r down, so t h a t d u r i n g the i n i t i a l s t a g e s of c h a r g i n g t h e o i l : ' . i s r e t a i n e d i n t h e e n l a r g e d p a r t of the c y l i n d e r and o n l y gas i s t r a p p e d i n the b a r r e l . As the p r e s s u r e i n the i n s t r u m e n t b u i l d s up w i t h t h e a d d i t i o n 140 o f o i l and gas, the o i l i s r e s a t u r a t e d by v i g o r o u s r o c k i n g o f the c y l i n d e r , t h e b a l l a s s i s t i n g i n k e e p i n g t h e o i l homogeneous. C h a r g i n g i s c o n t i n u e d u n t i l the o i l i n the v i s c o s i m e t e r i s c o m p l e t e l y r e s a t u r a t e d and the p r e s s u r e c o n s i d e r a b l y exceeds the s a t u r a t i o n p r e s s u r e . The p l u n g e r i s t h e n r e t r a c t e d the f u l l amount, the c y l -i n d e r t i l t e d t o the 75 degree i n c l i n a t i o n , t h e e l e c t r i c a l system con n e c t e d , and the b a l l a l l o w e d t o e n t e r the b a r r e l . The f a l l -i n g b a l l a c t s as a pump, d i s p l a c i n g the o i l i n t h e b a r r e l down and out the bottom and up t h r o u g h t h e e x t e r n a l s l o t s i n the b a r -r e l t o the e n l a r g e d upper p a r t o f the c y l i n d e r . When the b u z z e r i n d i c a t e s c o m p l e t i o n of t h e f a l l , the c y l i n d e r i s r o t a t e d t o t h e r e v e r s e p o s i t i o n and the b a l l a l l o w e d t o r o l l out of the b a r r e l , f l u s h i n g the o i l downward i n t o the e n l a r g e d p a r t of the c y l i n d e r , w i t h the b a r r e l r e p l e n i s h e d t h r o u g h the e x t e r n a l s l o t s . O i l i s thus pumped back and f o r t h between the b a r r e l and the c y l i n d e r a number of t i m e s t o i n s u r e a b s o l u t e homogeneity. The b a l l i s t h e n a l l o w e d t o e n t e r the b a r r e l and t h e r e t r a c t a b l e p l u n g e r s e a t e d f i r m l y on the t o p o f the b a r r e l , c o m p r e s s i n g the s p r i n g , and s i m u l t a n e o u s l y s e a t i n g the b a r r e l a g a i n s t the l o w e r g a s k e t . The c y l i n d e r i s r o t a t e d ' t o approxima-t e l y a v e r t i c a l p o s i t i o n w i t h the e l e c t r o d e and up, s u f f i c i e n t t i me a l l o w e d f o r the b a l l t o t r a v e l the l e n g t h o f the b a r r e l and s t o p a g a i n s t the p l u n g e r , and the c y l i n d e r t h e n r o t a t e d t o a p o s i t i o n j u s t s h o r t of h o r i z o n t a l . The r o l l t i me i s t h e n d e t e r -mined by r o t a t i n g the c y l i n d e r s u d d e n l y u n t i l i t s t r i k e s the p o s i t i v e s t o p w i t h the e l e c t r o d e down, a t the time measured w i t h a s t o p w a t c h f o r the b a l l t o r e a c h the e l e c t r o d e and sound the b u z z e r . S e v e r a l d e t e r m i n a t i o n s a r e made, u s u a l l y a t two a n g l e s o f i n c l i n a t i o n . The r o l l t i mes are r e a d i l y r e p r o d u c i b l e t o 0.2 second. A f t e r d e t e r m i n a t i o n o f the r o l l t i me i n the supercomp-r e s s e d s a t u r a t e d o i l , t h e p l u n g e r i s r e t r a c t e d s l i g h t l y and the p r e s s u r e reduced by w i t h d r a w i n g a s l i g h t amount of o i l t h r o u g h the i n l e t c o n n e c t i o n , the p l u n g e r r e s e a t e d , and the r o l l time determined a t the new p r e s s u r e . A f t e r the s a t u r a t i o n p r e s s u r e has been r e a c h e d , gas or gas and o i l are w i t h d r a w n i n i n c r e -ments w i t h the p l u n g e r f u l l y r e t r a c t e d - and the e n l a r g e d p a r t o f the chamber up. A f t e r each w i t h d r a w a l , the f l u i d s i n the cy-l i n d e r a r e a g i t a t e d by r o t a t i n g t h e c y l i n d e r back and f o r t h f r o m a h o r i z o n t a l p o s i t i o n u n t i l the p r e s s u r e becomes c o n s t a n t , i n d i c a t i n g e q u i l i b r i u m between the r e s i d u a l o i l and g a s . The p l u n g e r i s t h e n r e s e a t e d and the r o l l time measured as b e f o r e . T h i s p r o c e d u r e i s r e p e a t e d u n t i l the p r e s s u r e i n the v i s c o s i -meter has been reduced t o a t m o s p h e r i c . The d e t e r m i n a t i o n o f the complete p r e s s u r e - r o l l t ime c u r v e r e q u i r e s u s u a l l y t h r e e t o f o u r h o u r s . O c c a s i o n a l l y some d i f f i c u l t y i s e x p e r i e n c e d i n a t t a i n i n g e q u i l i b r i u m a t a t m o s p h e r i c p r e s s u r e , i n w h i c h case t h e i n s t r u m e n t i s u s u a l l y a l l o w e d t o s t a n d f o r s e v e r a l hours or over n i g h t b e f o r e t h i s p o i n t i s d e t e r m i n e d . 141 A f t e r c o m p l e t i o n o f the d e t e r m i n a t i o n a t atmos-p h e r i c p r e s s u r e , the r e s i d u a l o i l i s d r a i n e d f r o m the p r e s s u r e v i s c o s i m e t e r and the v i s c o s i t y d e t e r m i n e d a t the Same temper-a t u r e w i t h t h e Ubbelohde, o r the O s t w a l d - H a r r i s - v i s c o s i m e t e r . T h i s f u r n i s h e s a check on the o p e r a t i o n o f the p r e s s u r e v i s -c o s i m e t e r f o r each s e r i e s o f measurements. The d e n s i t y of t h e r e s i d u a l o i l d r a i n e d f r o m the v i s c o s i m e t e r i s d etermined a t room tem p e r a t u r e w i t h a pycno-meter and c o r r e c t e d t o the r e s e r v o i r t e m p e r a t u r e w i t h the N a t i o n a l S t a n d a r d P e t r o l e u m O i l T a b l e s . The d e n s i t y o f the s a t u r a t e d o i l charged t o t h e v i s c o s i m e t e r i s d e t e r m i n e d s e p a r a t e l y d u r i n g the c o u r s e of the r e g u l a r s u b s u r f a c e sample e x a m i n a t i o n . The d e n s i t y a t the i n t e r m e d i a t e p r e s s u r e s i s e s t i m a t e d by a l i n e a r i n t e r p o l a t i o n . S i n c e the d e n s i t y of the s t e e l b a l l i s 7 . 8 5 gm./cc/ and the d e n s i t y o f most o f the o i l s examined i s of the o r d e r o f 0 . 7 t o 0 .8 gm./cc, e s t i -m a t i o n of the o i l d e n s i t y t o the n e a r e s t 0 . 0 7 gm./cc. s u f f i c e s t o g i v e an a c c u r a c y o f 1% i n the d e n s i t y d i f f e r e n c e . The v i s c o s i t y a t each p r e s s u r e i s d e t e r m i n e d by m u l t i p l y i n g t h e r o l l t i me by the c o r r e s p o n d i n g d e n s i t y d i f f e r e n c e and r e a d i n g the a p p r o p r i a t e v a l u e f rom th e c a l i b r a t i o n c u r v e . 142 APPENDIX V ELECTRONIC TIMER The e l e c t r o n i c t i m e r w h i c h was d e v e l o p e d as an a l t e r n a t i v e to the J a c q u e t m a g n e t i c a l l y - o p e r a t e d s t o p - w a t c h , c o n s i s t e d o f an e l e c t r o n i c b i n a r y p u l s e c o u n t e r w h i c h was o p e r a t e d f r o m 115 V o l t s a . c , and a m a i n - s y n c h r o n i z e d p u l s e g e n e r a t o r . The p u l s e c o u n t e r was a "Type 37-7-C, s c a l e of 128", manufactured by C.S.R.D.E. of Canada, used by the N a t i o n a l R e s e a r c h C o u n c i l of Canada. The d e v i c e r e g i s t e r e d up t o 128 p u l s e by a seven p l a c e b i n a r y n u m b e r 7 d i s p l a y e d on a cascade of "magic eyes", and u n i t s of 128 were r e l a y e d t o a s m a l l d e c i m a l c o u n t e r . The p u l s e g e n e r a t o r was d e s i g n e d t o o p e r a t e f r o m a power s u p p l y o f 6.3 V o l t s a.c. and 400 V o l t s d . c , w h i c h was s u p p l i e d f rom the power u n i t of a n o t h e r p u l s e c o u n t e r s i m i l a r t o the one mentioned above. A c i r c u i t d iagram f o r t h e p u l s e g e n e r a t o r i s g i v e n i n f i g u r e 13. P u l s e s w i t h mains f r e q u e n c y were f e d f r o m the o u t p u t t e r m i n a l , B, t o t h e c o u n t e r , t h e f i r s t s t a g e of w h i c h counted a t the mains f r e q u e n c y . I t was t h e r e f o r e p o s s i b l e t o r e a d the time t o the n e a r e s t l / 6 0 s e c . The a c c u r a c y of the d e v i c e i s n e c e s s a r i l y dependent on the f r e q u e n c y of t h e d o m e s t i c power s u p p l y , but as mentioned 143 above, t h i s i s not a s e r i o u s l i m i t a t i o n . T h i s t i m i n g d e v i c e was t e s t e d a g a i n s t the J a c q u e t s t o p - w a t c h and found t o g i v e c o n s i s t e n t r e s u l t s to w i t h i n 0.01$ over p e r i o d s o f about one h o u r . + 400V. • • C *3 O H) O H H O p © H F i g u r e 13. Pulses-Generator APPENDIX VI 144 DESIGN OP PRESSURE BOMB The d e s i g n i s based on the A.S.M.E. Code f o r P r e s s u r e V e s s e l s w h i c h i s d e s c r i b e d by P e r r y . 1 The maximum s t r e s s e s i n the w a l l s of a t h i c k w a l l e d p r e s s u r e v e s s e l due t o an i n t e r n a l p r e s s u r e o f P are g i v e n by the r e l a t i o n s , ( S t ^max r 'max (a,.) s / R + 1 P l ( ~2 ) R2 - 1 R where and (S. ) t max (s-n )max maximum hoop s t r e s s maximum r a d i a l s t r e s s l o n g i t u d i n a l s t r e s s ( c o n s t a n t ) ' d i a m e t e r r a t i o O.D./ I.D. F o r a maximum w o r k i n g p r e s s u r e o f 10,000 p s i . , t h e maximum s t r e s s e s f o r the p r e s s u r e v i s c o m e t e r and t h e t r a n s f e r bomb a r e as f o l l o w s , V i s c o m e t e r , R = 2 . 0 < St) max = 1 6 > 7 ° 0 P s i ( s r ) max = 10,000 p s i 1. P e r r y , J.H. - " C h e m i c a l E n g i n e e r s Handbook", p.1238, M c G r a w - H i l l (1950) 145 S Q = 3,300 p s i Maximum s t r e s s = 16,700 S a f e t y f a c t o r = 5*4 T r a n s f e r bomb, R Q = 1.72 <Vmax = 20,200 p s i < S r W = 10,000 p s i S e = 5,100 p s i Maximum s t r e s s = 20,200 S a f e t y f a c t o r = 4.5 The s a f e t y f a c t o r s a r e based on a v a l u e o f 90,000 p s i f o r the u l t i m a t e s t r e n g t h o f 304 or 316 s t a i n l e s s s t e e l , The A.S.M.E. recommend a f a c t o r of s a f e t y of 4- t o 5 on the u l t i m a t e s t r e n g t h . 

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