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Some studies on liquid viscosity, with special reference to the isomers of decahydronaphthalene Leslie, John Duncan 1941

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SOME STUDIES ON LIQUID VISCOSITY, WITH SPECIAL REFERENCE TO THE ISOMERS OF DECAHYDRONAPHTHALENE by John DiT L e s l i e , B.A. , B.A.Sc. A Thesis submitted i n P a r t i a l Fulfillment of The Requirements for the Degree of MASTER OF APPLIED SCIENCE i n the Department of CHEMICAL ENG-INEERING-The University of B r i t i s h Columbia A p r i l , 1941. PREFACE The work described In the following pages was undertaken as part of a large scale study of the physical and chemical properties of the various hydrocarbon types found i n petroleum. From time to time during the course of this program, i t has been found necessary to devise new and better methods for studying certain of these properties and also to investigate the theory underlying them. This has been especially true with v i s c o s i t y , a property about which much has been said and concerning which many empirical relationships have been devised but about the theory of which l i t t l e i s d e f i n i t e l y known. That the investigation and study of such properties i s of value to the petroleum industry i s evidenced by the large amount of physicoohemical research thereby sponsored. In particular, the work outlined i n t h i s thesis was made possible by a scholarship from the Standard O i l Gompany of B r i t i s h Columbia. The author wishes to acknowledge this generous assistance, and to commend the Standard O i l Company for i t s support of such research. The author wishes also to acknowledge the help and advice of Dr. W. F. Seyer of the Department of Chemistry, under whose direction the work has been carried out. In addition, thanks are due to Messrs. H. Hipkin and D. M i l l e r for help i n making the measurements and calculations and i n drawing some of the graphs. In p a r t i c u l Mr. Hipkin has "been i n charge of the operation of a micro-visoometer f o r the investigation of various hydrocarbon mixtures. CONTENTS Introduction General background .... Outline of the problem .......c. Part I* Theory and Procedure General theory ... The measurement of Yiscosity (a) Resume of methods ......... (b) The transpiration method Experimental technique . * • (a) General ««.«»»»».•»««.««»«o. (b) Constant temperature bath .. (c) Heating ..«.«••*...«.>*••.«* (d) Temperature control ........ (e) Temperature measurement .... (f) Time measurement ... Viscometer and errors i n measurement Calibration ...«•«•.»»*.......«....«. (a) Procedure (b) Calculations anft.checking Genera1 procedure C0KTE1TS Part II. Treatment of Data for Pis and Trans Pecalin 1. Observations and caloulations 2 e Variation of the viscosities, with temperature . . a« 1 SOME STUDIES OK LIQUID VISCOSITY, WITH SPECIAI REFERENCE TO THE ISOMERS OF DECAHYDRONAPHTHALENE Introduction 1. General background In t h i s world of increasing technological complexity the development of any country i s becoming more and more dependent upon i t s natural resources, both of materials and of energy. Of the l a t t e r , the three most important are coal, petroleum, and hydro-electric power, and amongst^the greatest advances today are being made with petroleum. For a long time petroleum was used as a f u e l , lubricant, and source of power without much attention being paid to i t s exact nature and properties. How, however, a vast amount of research has been and i s being carried out, and with the development of methods for the fractionation of petroleum into i t s components, i t has become possible to investigate the actual types of compounds i n petroleum. Knowledge of these has enabled petroleum chemists to make use of various waste products and to produce many useful by-products, and the almost unlimited p o s s i b i l i t i e s suggested by these l a t t e r have i n turn motivated s t i l l deeper research into the chemical composition ana properties of the compounds i n petroleum fractions. Petroleum, an extremely complex and variable mixture of many different types of organic compounds, consists c h i e f l y of various families of hydrocarbons and their derivatives. This makes i t s study a d i f f i c u l t problem since i n order to achieve s i g n i f i c a n t results concerning chemical or physical properties one must deal with either pure compounds or mixtures of known composition. As i n any organic investigation two methods of approach are possible. One may (!) analyze a complex mixture into i t s simpler constituents, or (2) attempt by synthesis from certain known compounds to build up a substance similar i n properties to the o r i g i n a l . Usually one method supplements the other, and this i s so i n petroleum research. '"' Petroleum products are d i v i s i b l e into certain more or less d e f i n i t e groups, one of the most important of which i s l u b r i c a t i n g o i l s . It i s to the general subject of lubrication and lubricating o i l s that this laboratory has devoted much of i t s e f f o r t during the past two decades, and a very small part of this effort i s represented i n this thesis. To go into the theory of lu b r i c a t i o n here, i s impossible, but a few general remarks may be enlightening. As everyone knows, the function of a lubricant i s to reduce the f r i c t i o n between the moving surfaces in machinery. There are two main types of lu b r i c a t i o n (a) boundary, and (b) flooded. The f i r s t type accompanies heavy loads and high speeds and i n i t we are dealing with films of a few molecules i n thickness. Under such conditions the c o e f f i c i e n t of f r i c t i o n rather than that of v i s c o s i t y appears to be the co n t r o l l i n g factor, and hence the properties of the surfaces are important. Vegetable o i l s and polar compounds such as long chain acids,give the best results since orientation at right angles to the surfaces i s one of their chief functions. In flooded lub r i c a t i o n , the situation i s different* It i s assumed that the o i l layers next to the surfaces are at rest, and hence we have only the flow of o i l over oil,. Thus the problem i s one i n hydrodynamics and the v i s c o s i t y must be the determining factor. For this type of l u b r i c a t i o n , petroleum o i l s are found to be best, but even here a considerable choice i s possible depending upon both the properties of the o i l and the conditions under which i t must operate. O i l s may be c l a s s i f i e d according to density i g n i t i o n point, chemical s t a b i l i t y or v i s c o s i t y c h a r a c t e r i s t i c s . The l a t t e r i s the basis of the common S.A.E. scale of l u b r i c a t i n g o i l s , and i s the property of chief interest i n the present work. In pa r t i c u l a r we are interested i n the temperature variation of v i s c o s i t y , i t being desirable that this v a r i a t i o n be small i n a l u b r i c a t i n g o i l . It has been found, while studying the properties of the d i f f e r e n t hydrocarbons thought to be present i n o i l s , that the normal paraffins have the lov/est viscosity-temperature gradient but have an unfavorable 4 tendency to form carbon and to c r y s t a l l i z e . On the other hand, while benzene also c r y s t a l l i z e s , the hydrogenated c y c l i c hydrocarbons, the naphthenes, do not,and are also low i n carbon. Since the l a t t e r , however, have not the desirable v i s c o s i t y characteristics of the paraffins i t has been thought that an ideal lubricant might be evolved by blending the two types. In practice,certain procedures are followed to give lubricating o i l s desirable c h a r a c t e r i s t i c s , ^ but space does not permit a discussion of these. Before any progress can be made in studying such mixtures as are suggested above, the properties of the individual hydrocarbons, themselves must be thoroughly investigated. For this purpose the naphthenes mentioned a l i t t l e e a r l i e r may be subdivided into several classes. The mononaphthenes are mostly derivatives of oyclohexane, CgH^g, and extensive work has been carried out on this compound. Coming to the dinaphthenes we f i n d the basic compound to be decahydronaphthalene, ^x.0^18' o r a s i * i s u s u a ^ - l y called, decalin. As there i s reason to believe that l u b r i c a t i n g o i l s may contain up to sixt y percent derivatives of this hydro-carbon, i t has been the object of extensive study for the l a s t two decades. Early investigators soon found that decalin exists i n at least two isomeric forms, the c i s and the trans. Because of certain abnormal behavior some think that these may be only the l i m i t i n g , stable forms of two series of isomers the members of which are stable under dif f e r e n t 5 conditions of preparation, temperature* pressure, etc. The apparent abnormality of the two p r i n c i p a l forms further increased the interest i n decalin, and i t i s now some seven years since Dr. Seyer and his assistants undertook the task of making a thorough study of i t s properties. ;.2» Outline of the problem Since the commercial product i s always a mixture of the two, the f i r s t problem was to separate the c i s and trans forms. This was d i f f i c u l t but was f i n a l l y effected by a process of vacuum r e c t i f i c a t i o n . It i s not deemed necessary to go into the d e t a i l s of this process nor to further recount the early work done on the properties of the isomers, since an excellent summary with references i s given by C. H. Davenport i n his Masters Thesis. In parti c u l a r , he f u l l y describes the separation of the isomers and t h e i r f i n a l p u r i f i c a t i o n by f r a c t i o n a l c r y s t a l l i z a t i o n . This part of the work i s also treated by Morel, 'Watson, and Yip i n t h e i r Bachelors Thesis.^ From what has been said above concerning l u b r i c a t i o n and v i s c o s i t y , i t i s clear that i t would be of value to determine the v i s c o s i t i e s of the decalin isomers and the temperature gradient thereof. C. H. Davenport did this over the complete l i q u i d range, and at the same time measured the densities and surface tensions. From a c r i t i c a l study of his data and using several empirical or semi-empirical relationships Davenport attempted to establish the r e a l i t y of the structural changes suspected of taking place i n the decalin at more or less d e f i n i t e temperatures. He also t r i e d to determine the approximate temperatures of these changes, and to what extent i f any they were reversible* The general method was to plot some function of the property against the temperature (or i t s reciprocal) such that a straight l i n e would res u l t , and to examine these lines for discontinuities or sudden changes of slope. In addition he worked out certain characteristic constants such as the parachors, the c r i t i c a l temperatures, the latent heats, and the Eotvos constants. As w i l l be explained l a t e r there /.isi more than one scale of v i s c o s i t y . Davenport's method gave him the s p e c i f i c v i s c o s i t y which i s not a true property of the l i q u i d . The more fundamental scale i s that of absolute v i s c o s i t y and hence i t was thought that a determination of t h i s property might throw further l i g h t on the abnormalities of c i s and trans decalin. This then, was ray o r i g i n a l problem. During the course of the work, however, we encountered certain d i f f i -c u l t i e s , and observed certain p e c u l i a r i t i e s i n the behavior of the decalin which led to a more c r i t i c a l study of the nature of l i q u i d v i s c o s i t y i t s e l f . At the same time, considerable controversy has arisen regarding the possible molecular structure and orientation of the two isomers. This i s t i e d up with the mathematical treatment of the data obtained, and the net result has been to show that a great deal s t i l l , remains to be found out about the nature of liqu i d s and the forces present within them. Contemporaneously with the work outlined i n Davenport's and the present thesis, other properties have 4 5 been undergoing study. G. Davies and B. R. Mead have determined the heat capacities, and Morel, Watson, and Yip the cooling curves of the isomers. Considerable work has also been done on the vapor pressures , but owing to the - d i f f i c u l t i e s involved, the results are not yet certain. At 7 the present time S. Mizuhara i s determining the re f r a c t i v e indices of the two isomers and the re s u l t s show promise of .. shedding considerable l i g h t on parts of the problem. The correlation of some of t h i s data with the results of the v i s c o s i t y measurements w i l l be attempted l a t e r . As suggested above, one of the ultimate aims was to study mixtures of decalin and the normal paraffins. Considerable work has been done in this laboratory i n preparing long chain paraffins and determining their densities and tra n s i t i o n p o i n t s . 8 ' 9 During the present year S. W. Y i p 1 0 has started the problem of finding the phase relationships i n mixtures of c i s or trans decalin and certain of these paraffins. At the same time the author has supervised the construction and operation of a microviscometer with which to determine the v i s c o s i t y temperature gradients of these mixtures. It i s thus seen that my problem has become manifold, and may be subdivided into (1) a careful determination of the absolute v i s c o s i t i e s of c i s and trans decalin, (2) a c r i t i c a l 8 study of the data i n the l i g h t of past and present v i s c o s i t y theories and an attempt thereby to determine the possible structural or other changes apparently taking place i n the decalin, (3) an investigation of certain phenomena peculiar to the v i s c o s i t i e s and an attempt to t i e these up with the general problem of l i q u i d structure, and (4) a determination of the v i s c o s i t y characteristics of decalin paraffin mixtures., This more or less arbitrary subdivision w i l l be the basis of the plan for what i s to follow, except that I w i l l f i r s t give a b r i e f discussion of the general theory of v i s c o s i t y measurement and of the experimental methods which I used. Owing to the fact that the last two projects mentioned above are s t i l l i n progress, they w i l l not be discussed i n the present write up, but w i l l be considered i n a supplement to be added at a later date. Part I. Theory and Procedure 1. General theory Viscosity i s ord i n a r i l y thought of as a measure of the internal f r i c t i o n i n a f l u i d , and since f r i c t i o n manifests i t s e l f only when there i s re l a t i v e motion between bodies or between portions of the same body v i s c o s i t y may be called the sp e c i f i c dynamic property of f l u i d s . That the theory of l i q u i d v i s c o s i t y i s not well understood and that most of the equations for p r a c t i c a l purposes are empirical only r e f l e c t s our general ignorance of (1) the structure of liquids,and (2) the flow mechanism of matter. In any theory of flow we should of course consider solids and gases as well as l i q u i d s , but since the theories for the former are somewhat different we s h a l l confine our attention to l i q u i d s . It i s impossible here to go into the theory of flow i n d e t a i l . Several references are given i n the bibliography",''" and i n these the interested reader w i l l find many others. A l i t t l e consideration w i l l be given to the structure of li q u i d s and the various forces involved, i n a l a t e r part of the thesis Suffice to say at this point that the chief characteristics of l i q u i d s are (1) coherence, (2) f l u i d i t y , and (3) irre g u l a r 10 distributions of molecules which may change under heat or mechanical stress. Flow in liquids i s ordinarily divided into two types (1) turbulent, and (2) viscous or laminar. Turbulent flow i s characterized by eddies and discontinuous stream-li n e s , and occurs above a certain c r i t i c a l v e l o c i t y . This type of flow i s extremely complex, and attempts at a n a l y t i c a l treatment have so f a r been unsuccessful. Below the c r i t i c a l velocity we get viscous flow i n which the streamlines are regular, continuous curves, and eddies are absent. Considering two p a r a l l e l l i q u i d laminae of area A, Newton postulated that the force, F, necessary to maintain a constant v e l o c i t y gradient between them i s given dv by F =r>A - j — , where & i s taken perpendicular to the laminae. Experience has shown that r> i s a characteristic constant f o r each l i q u i d and i s independent of — , i n a l l simple l i q u i d s . di. It i s call e d the c o e f f i c i e n t of absolute v i s c o s i t y and has the dimensions M i f 1 T ~ 1 . In the C.G.S. system the unit of v i s c o s i t y i s the poise, i t being the value of the c o e f f i c i e n t when a force of one dyne per square centimeter gives unit v e l o c i t y gradient. As mentioned before there are several different scales of v i s c o s i t y . The kinematic v i s c o s i t y i s defined by V r 9/p> where p = density. Relative and s p e c i f i c v i s c o s i t i e s are measured i n terms of the absolute v i s c o s i t y of a reference l i q u i d at some de f i n i t e temperature. The reciprocal of the absolute v i s c o s i t y i n poises i s called the f l u i d i t y and i s denoted by>cp. In spite of Newton's great contribution the theory of viscous flow developed slowly. The hydrodynamics of B e r n o u l l i i and Euler considered only i d e a l l i q u i d s i n which tangential stresses were not allowed. The results, con-sequently, were not In accordance with experimental evidence. In their early experimental work the French t r i e d to f i n d the law governing flow through c y l i n d r i c a l tubes,but obtained incorrect results. l a t e r , the mathematical theory of viscous flow was worked out independently by Navier, Stokes and Poisson, and i n the nineteenth century. Hagen and P o i s e u i l l e , i n a series of accurate measurements, determined the correct law f o r the flow of l i q u i d s through c a p i l l a r y tubes. The l i m i t i n g conditions f o r t h i s law were supplied by Reynolds, who showed the c r i t i c a l v e l o c i t y i n tubes to depend upon the kinematic rather than upon the absolute v i s c o s i t y . Again, certain corrections to make Poi s e u i l l e ' s simple formula applicable i n p r a c t i c a l cases were given by Hagenbach. Before closing these general remarks we might mention p l a s t i c flow. This does not obey Newton's primary hypothesis and i s defined as the property of solids by virtue of which they hold their shape permanently under small shearing stresses but are r e a d i l y deformed under somewhat larger stresses. In other words, there i s a l i m i t i n g stress below which no deformation takes place. The l i m i t i n g case i s , of course, i n true solids where we have e l a s t i c deformation 1.2 limited "by a certain y i e l d stress. For further information 15 on this subject the reader should consult Bingham and Scott B l a i r 1 6 . 2. The measurement of v i s c o s i t y (a) Resume of methods Since the work of Hagenbach, many methods f o r measuring the coef f i c i e n t of v i s c o s i t y have been devised but the transpiration method, based on the flow through c a p i l l a r y tubes, i s s t i l l the most widely used. It i s r e l a t i v e l y simple to carry out, requires only a small amount of l i q u i d , i s capable of exact mathematical treatment, and has been found to give the highest degree of precision. Before considering this i n more d e t a i l we sh a l l mention a few other methods. " 17 Bingham divides a l l methods into three groups: (1) those involving measurement of the resistance offered to a moving body i n the f l u i d ; (2) those involving measurement of the rate of flow of a viscous f l u i d , and (3) methods i n which neither the flow nor the resistance to flow are measured. The f i r s t group includes (a) a horizontal disc submerged i n the l i q u i d and o s c i l l a t i n g about a wire, (b) a sphere f i l l e d with l i q u i d and o s c i l l a t i n g about a v e r t i c a l axis, (c) concentric cylinders with l i q u i d between, one suspended and the outer rotating at constant speed, (d) the f a l l i n g sphere of Stokes. The second type i s ess e n t i a l l y the transpiration method, although there are several variations. Under the t h i r d group may be l i s t e d (a) the deoay of l i q u i d o s c i l l a t i o n s i n U-tubes, (b) the decay of vibrations i n a viscous substance and (c) the rate of c r y s t a l l i z a t i o n . Of these the concentric cylinders and f a l l i n g sphere methods are the most successful next to the c a p i l l a r y tube method. 18 Their theory i s given i n Hatschek . (b) The transpiration method This transpiration method consists essentially of measuring the time f o r a certain volume of l i q u i d to flow through a horizontal or v e r t i c a l c a p i l l a r y tube under d e f i n i t e conditions. The basic equation i s that of P o i s e u i l l e , namely where V - volume of f l u i d the P s pressure on^fluid r s radius of c a p i l l a r y 1 r length of c a p i l l a r y >p r absolute v i s c o s i t y of the l i q u i d t s time of flow A derivation of t h i s 1aw5from the equations of hydrodynamics,is given i n Appendix I. P o i s e u i l l e deduced the equation experimentally, but i t was soon a f t e r obtained on theoretical grounds by several other investigators. It i s , however, applicable only under id e a l conditions where among other things, the f l u i d i s incompress-i b l e and there i s no sl i p p i n g at the c a p i l l a r y walls. 14 Unaer actual conditions several corrections must be applied, and furthermore, to f a c i l i t a t e p r a c t i c a l v i s c o s i t y measure-ments P o i s e u i l l e f s method has been modified i n several ways. Of especial interest i s Ostwald's method for measuring r e l a t i v e v i s c o s i t i e s , i t being an adaptation of this l a t t e r that the author used i n h i s work. Suppose we have a c a p i l l a r y of uniform c i r c u l a r bore connected at either end to reservoirs f i l l e d with f l u i d . I f the levels i n the two reservoirs d i f f e r , flow w i l l take place through the tube and the pressure energy w i l l be expended i n various ways. (1) Near the entrance to the c a p i l l a r y the f l u i d , p a r t i c l e s undergo a rapid acceleration and hence their k i n e t i c energy i s increased. At the exit, t h i s kinetic energy i s lost i n overcoming turbulence and. viscous resistance, and hence does not add to the effective pressure. (2) Within the c a p i l l a r y there may be slipping of the f l u i d over the walls, and hence work w i l l be done against external f r i c t i o n . (3) Unless the external f r i c t i o n i s aero the layers of f l u i d near the walls w i l l move more slowly than those near the axis. The drop i n pressure caused by this viscous resistance i s that appearing i n the simple equation shown on the previous page. (4) I f the flow i s not laminar, additional energy w i l l be consumed i n the eddy motion. As mentioned before,this turbulent flow occurs i f the v e l o c i t y exceeds a c r i t i c a l value. 15 (5)* Even i n laminar flow the streamlines may be distorted at the exit and entrance to the tube and this causes some loss i n energy. (6.) Heat i s produced during the flow, and there may be a va r i a t i o n i n temperature along the tube which w i l l change the v i s c o s i t y and hence the work-done. Also, i f the f l u i d i s compressible there w i l l be some expansion due to the gradual f a l l i n pressure along the tube. We s h a l l now consider some of these effects b r i e f l y * 19 A f u l l e r discussion i s to be found i n Bingham , or i n Hatsehek^* Taking into account the change i n kin e t i c energy, Hagenbach showed that the simple formula f o r x> becomes: T r P r 4 t mpT i 8T1 8TT1 "t V) v where p i s the density, and m a constant f o r which many values have been suggested, the best probably being 1.12, Some doubt has been expressed as to whether m is' a true constant or a function of the tube dimensions and the rate of flow. The evidence, however, indicates that i t i s probably constant for a l l perfect cylinders, although i r r e g u l a r i t i e s i n the bore w i l l certainly cause variations* The correction term i s generally much smaller than the other, but i t should not be neglected as i s so often done. For a given tube, volume of l i q u i d and pressure, the v i s c o s i t y obviously depends only upon t, and thus i f the l a t t e r i s increased the second term becomes r e l a t i v e l y smaller. 16 The conditions under which this correction may be neglected w i l l be mentioned l a t e r . Another correction, due to Couette, takes care of the extremities of the tube by adding a f i c t i t i o u s amount, A, to i t s length. This gives us x i V " * 1 * 4 * - m P 7 . I (1) / 8V(1+A) 8-rr(l+?\) t A must be determined experimentally. A convenient way to test the accuracy and a p p l i c a b i l i t y of the Hagenbaoh-Couette equation i s to measure the constancy of the product Pt. We have, rearranging, IT r * 8vp where v s — — 9 i s the average v e l o c i t y of flow. For a given liquid'and tube, a l l the quantities on the right hand side are constants except A and v. The t h i r d term i n the brackets has the dimensions of a length, and i f we c a l l i t <\, i t i s found that A+ i s constant for- small v e l o c i t i e s but increases l i n e a r l y with v f o r larger values. To take care of slipping, Helmholtz derived the where (§ i s the c o e f f i c i e n t of s l i d i n g f r i c t i o n . Numerous experiments have shown, however, that whether or not the l i q u i d wets the tube there i s no appreciable slipping so long as the flow i s laminar. 17 The question of turbulence i s important, as such a condition invalidates a l l of the equations thus f a r developed. Reynolds has shown that the conditions of flow can be characterized by a dimensionless number R. For c y l i n d r i c a l tubes R - ~~^y~s where v i s the mean vel o c i t y and D the diameter of the tube. The change from one type of flow to the other appears to take place at R between 1400 and £000. Hence the c r i t i c a l v e l o c i t y i s given by v 1400^ I n the 0 D p p r a c t i c a l measurement of v i s c o s i t y turbulence does not occur, since, for a given l i q u i d and tube, the ef f l u x time must not be too small, (and hence the v e l o c i t y too great) otherwise the errors of time measurement are magnified* Up to this point we have assumed the pressure to remain constant throughout the period of flow. In experi-mental work the pressure i s produced by a column of l i q u i d with or without compressed a i r . The l a t t e r pressure can be kept constant by using a large reservoir, but the column of l i q u i d w i l l vary during the flow. I f we have only the l i q u i d pressure to consider we may replace P i n equation (1) by pgH, where H i s some function of the head. It can. be shown that, i f h^ and hg are the i n i t i a l and f i n a l heads respectively, our o r i g i n a l equation takes the form 871 l n d i ^ ) when the i n l e t and outlet tubes are c y l i n d r i c a l * .18 For praetioal purposes the, c a p i l l a r y of a visco-meter i s usually v e r t i c a l rather than horizontal,and has one or more bulbs joined to each end. This makes the l i q u i d pressure a more complicated function of the l i q u i d head and also makes i t d i f f i c u l t to evaluate the various constants in equation (1) unless the viscometer i s sp e c i a l l y designed. For a given viscometer and constant volume of l i q u i d (determined by the volume of the upper bulb), and i f no external pressure i s used, equation (1) becomes 4 8Y(l-b?0 S-tt(l-t-A) t H i s some constant function of the head, and we may therefor w r i t e ? = Opt - ^ I t where 0 and e are constants to be determined by c a l i b r a t i o n with l i q u i d s of known v i s c o s i t y . This was es s e n t i a l l y the method employed by the author, and the various errors entering into the measurements w i l l be discussed below. Many such types of c a p i l l a r y viscometers have been devised. The Ostwald (Fig. 1) i s commonly used when only r e l a t i v e v i s c o s i t i e s are desired, as was the case i n C. H. Davenports work. He used a viscometer of this type and a sim p l i f i e d equation Y) s C p t . The l i q u i d i s drawn up and the time taken f o r i t to f a l l between the f i d u c i a l marks A and B. If t i s the time f o r a l i q u i d of v i s c o s i t y , r> , and density, 19 a then p 1 for another l i q u i d of density p 1 may he obtained by measuring t 1 since f * If Y) i s taken equal to unity the result i s a r e l a t i v e v i s c o s i t y , and i f the actual value of v? i s used the result i s a spec i f i c v i s c o s i t y . 3. Ebcperimental t ectini que (a) General We are now in.a-position to describe the actual experimental procedure of this investigation. The arrange-ment f o r the main part of the work was based on that of Davenport's-- apparatus. As the adjoining plate and diagram (Fig. 2) show, i t consisted essentially of an e l e c t r i c a l l y heated constant temperature bath, containing the viscometer, a platinum resistance thermometer with i t s a u x i l i a r y equipment and a precision timing device. 20 22 >The microviscoraeter for the work on the decalin paraf f i n mixtures was a separate project and w i l l he described l a t e r . (b) Constant temperature bath For the early part of the work, i n which Mr. J". D. B e l l collaborated, the bath used was a c y l i n d r i c a l pyrex jar (30 cm. deep and 15 cm. i n diameter) lagged with 0.5 cm* of asbestos. It was f i l l e d with about 4.5 l i t e r s of a medium petrolatum o i l (Stanolax) which was circulated by an u p l i f t propellor. At f i r s t , a £ H.P. motor drove the propellor, the speed being reduced through a jack-shaft, but l a t e r t h i s was replaced by a small variable speed motor to reduce the vi b r a t i o n . A lead disc i n the bottom of the bath provided a support for the v e r t i c a l brass rod to which the viscometer was clamped. The top of the brass rod was clamped to r i g i d horizontal bars. Two diametrically opposite windows were cut i n the asbestos covering to permit observation of the f i d u c i a l marks on the viscometer. A l i g h t at the rear window provided illumination. 21 Hatschek states that, to get constant temperatures a capacity of 30 to 50 l i t e r s i s desirable, but with e f f i c i e n t s t i r r i n g we found the temperature control s u f f i c i e n t l y close. Later, however, to make the control easier, a bath of about 11 l i t e r s capacity (45 cm. deep and 20 cm. i n diameter) was substituted. This was lagged i n asbestos as before and was also encased i n a metal p a i l with approximately one inch of 23 cotton "batting between. A t r i p l e propellor and the large 1- H.P. motor provided c i r c u l a t i o n , but the motor was located off the table to prevent vibration. Some trouble was. caused at the high temperatures by the o i l charring and becoming opaque. A lubricating o i l , Marvelube 40, was t r i e d but was found to be worse, so we returned to the petrolatum and t r i e d to maintain the bath at high temperatures f o r as short a time as possible. (c) Heating Three separate elements gave the necessary heat. In the f i r s t bath the two main heaters were a Cenco immersion knife and a nichrome wire c o i l wound around the bath under-neath the lagging. In the larger bath a second knife replaced the nichrome c o i l . The t h i r d element i n each case was a small nichrome c o i l (1 i n . i n diameter) immersed i n the bath and hooked up to a precision thermoregulator. A suitable switchboard was constructed by J. D. B e l l and the e l e c t r i c a l connections were made so that the two main heaters could be used independently, or together i n series or i n p a r a l l e l / and also with or without external variable resistance. The thermostatic heater, designed to operate with a minimum temperature lag ' was i n series with a variable resistance and i n p a r a l l e l with a p i l o t l i g h t * For the measurements below room temperature a double walled, evacuated, pyrex f l a s k (25 em. deep by 7 cm. i n diameter) was found convenient. Acetone served as a bath 24 l i q u i d and; the temperature was lowered and kept constant at the desired points "by dropping i n small pieces of dry i c e . (d) Temperature control To keep the "bath temperature roughly constant the main heaters were supplied wi th enough current to balance roughly the heat losses of the apparatus* The thermostatic heater gave the fine control by operating i n series with a precision regulator. The thermoregulator was the type which makes use of the rapid increase i n a liquids Vapor pressure near the b o i l i n g point. A l i q u i d was chosen having i t s beoiling point i n the region of the desired temperature. As long as the contact i s broken, heat goes into the bath, but a sligh t increase i n temperature causes the vapor pressure of the l i q u i d to increase and the consequent vapor expansion causes the mercury to r i s e i n the tube and thus make contact with the needle. Under the best conditions the mercury moved about 1 cm. per degree and thus afforded a temperature control o of 0.01 C. At higher temperatures considerable d i f f i c u l t y was experienced i n getting suitable l i q u i d s and the control was not so close. It should be noted, however, that as the temperature increases the temperature c o e f f i c i e n t of the v i s c o s i t y decreases, and hence the greater variation i n temperature i s not serious* For optimum s e n s i t i v i t y the bulb of the thermo-regulator should be r e l a t i v e l y large and of thin glass and £5 o:~ <,•<;.,.; the tube should be narrow because for a given vapor expansion i n the bulb we want as great a r i s e i n the "tube as possible. The uniformity of the temperature throughout the bath depends c h i e f l y upon the efficiency of s t i r r i n g . In the larger bath, at lower temperatures where the bath l i q u i d was more viscous, some trouble was caused by temperature strata* (e) Temperature measurement The temperature was measured with a platinum resistance thermometer, Ho. 169314, which had recently been checked by the Bureau of Standards, Washington, D.G. The resistance of the thermometer at 0°C, R Q s 2.5117-n., has been checked several times i n this laboratory. Approximate temperatures were read on a thermometer graduated i n tenths, and. a Beckman thermoscope checked the e f f i c i e n c y of s t i r r i n g and the thermoregulator lag. A plan of the arrangement of the resistance box, commutator key, and galvanometer i s given i n F i g . 2, and for de t a i l s on the construction and modus operandi of the resistance thermometer the reader may refer to the thesis of Morel, Watson and Yip . From the observed resistance R, at t C, the temperature was found by means of Callendar* s equations: „ _ p t = 1 0 0 ~ o R 1 00" R 0 26 where RQ* >s observed resistance at 0°C = 2.5117JV R100 = observed resistance at 100°C & 3»4849-rL and . . t - P*. s S(-^- - 1)__L * l10G 'lOO where S i s a constant dependent on the purity of the platinum. For our thermometer S ~ 1,502. . For f a c i l i t y i n calculating the following formula may be used, *• 100 100 It gave s u f f i c i e n t l y accurate results i n the range of the authors work. A l i s t of resistances for thermometer No. 169314, at 10° intervals, i s given i n Appendix I I . (f) Time measurement : The efflux time depends upon the dimensions of the viscometer, the vi s c o s i t y of the l i q u i d , and the pressure applied. It i s preferable to use one instrument over the whole range of measurements and having chosen a viscometer of suitable dimensions one can make the efflux time convenien by varying the external pressure. In our method, where a l i q u i d head was the only pressure, the l a t t e r was not var i a b l at w i l l and hence the.time could not be made convenient at a l l temperatures. A Meylan stopwatch reading to 0.2 sees, served as timing device. It was checked against several r e l i a b l e timepieces, and also against an e l e c t r i c stopwatch over a 27 period of^several hours. Che net result indicated a loss of 0.02 sec. per minute on the part of the Meylan, and while this i s well within the l i m i t of accuracy required by 23 Bingham a correction for i t appears i n a l l of the author's results. The e l e c t r i c stopwatch was found unsuited to measurements of small time intervals because of transient fluctuations i n the A*C. frequency* Since the viscometers were designed for an efflux time of not less than.100 sees, the maximum error i n reading the stopwatch was 0.1 percent. In the main part of the work, namely the determination of the absolute viscosity-temperature gradients of the two isomers, the f i n a l results were always averages of from f i v e to f i f t e e n readings and hence the mean error i n the stopwatch reading was l i k e l y much less than 0.1 percent. Care was taken to always run the watch i n a horizontal position* 24 Washburn and Williams believe the stopwatch accuracy to be the l i m i t i n g factor i n v i s c o s i t y determinations and say that a watch reading to 0.2 sec. i s not good enough. In view of what has just been said this was probably not true under the conditions of the author's work. The above workers also consider errors due to var i a t i o n i n the observers reaction time when timing the passage of the l i q u i d past a f i d u c i a l mark. They found i n a series of experiments that the average deviation was 0.016 sec. and the maximum difference between any two observations was 0.09 sec. I f these l a t t e r happened £8 to occur' at the beginning and end of a measurement, an error of 0.09 sec. would be introduced, but the probability of this i s very s l i g h t and i n a series of determinations the average value would apply. From these considerations the author believes that errors i n timing could affect his f i n a l results no more than 0.05 percent, and this only when the eff l u x time was 100 sec. or less. .4* viscometer and errors i n measurement As mentioned above,the visco-meters at our disposal were a modification of the Ostwald type. They were made i n accordance with B r i t i s h Standards Specifications 118, 192.9 and were designed to • reduce deviations from P o i s e u i l l e J s law to a minimum (Fig. 3). Although the k i n e t i c energy effect was supposed to be minimized by the design, i t was deemed advisable to use the more accurate equation (3) involving two c a l i b r a t i o n constants* We see that V - ^/p - C t — | Twhere V i s the kinematic visoosity (i n stokes or centistokes). 29 Henoe, to get absolute v i s c o s i t i e s from the measurements we required the densities f o r a l l temperatures. Davenport's values were considered accurate enough, and are probably not the l i m i t i n g factor i n the accuracy of the author's work. Gruneisen .-has shown that by properly designing a viscometer the deviation from Po i s e u i l l e ' s law can be reduced to a minimum, and that i n any ease, i f the instrument i s properly standardized the effect of even a comparatively large deviation from this law can be nearly eliminated by applying a suitable correction. The principles upon which a viscometer of the Ostwald type should be constructed and the various corrections to be applied are f u l l y described by Gruneisen. 26 Bingham discusses the optimum dimensions for a viscometer, th e i r measurement, and also the determination of the mean effective pressure. Since, however, the author calibrated his instrument rather than determine, the various dimensions, and since external pressure was not used we s h a l l pass on to the more pertinent characteristics and errors. The ki n e t i c energy correction i s only appreciable for small v i s c o s i t i e s since i t i s clear from equation (2) that the second term i s not more than 2i§- percent of the f i r s t , and hence the effect can be made negli g i b l e by selecting a viscometer with a s u f f i c i e n t l y long efflux time. Dividing the second term of equation (2) by the f i r s t , the f r a c t i o n a l correction i s seen to be mT2 . Thus }for a given time -rr 2gHr 4t 2 so the ef f e c t w i l l be reduced by decreasing the efflux volume or by increasing the l i q u i d head. A small volume of l i q u i d has the additional advantages of attaining the bath temperature and of material economy. Loading errors did not arise i n this work since the same l i q u i d was used throughout any one series of measure-ments and the l i q u i d levels were kept constant. This also ensured that the mean l i q u i d head was constant, and. hence that equation (3) was v a l i d over the entire temperature range. Drainage errors, a r i s i n g from the f a c t that a l l liqu i d s do not drain from a surface with equal ease, may be minimized by having (1) the drainage surfaces as nearly v e r t i c a l as i s possible, and (2) the diameters of the constricted portions of the. viscometer no less then i s necessary for accuracy i n timing. Such errors might aff e c t 27 both the efflux volume, and l i q u i d head but Gannon and Fenske have shown that they are n e g l i g i b l e i n the type of viscometer • under consideration here* I f the constricted parts of the instrument are of too small diameter and d i f f e r at the two f i d u c i a l marks, the surface tension effect w i l l not be the same at both readings. This w i l l cause errors i f the surface tensions of the c a l i -brating and test l i q u i d s d i f f e r . Again, the diameters of the two large bulbs should be equal else an error due to c a p i l -l a r i t y w i l l be introduced, and the effective driving head w i l l be changed by an amount given by Cannon and Fenske i n 31 their formula A H' - - i W S ! E1 . ST2;\ where r s radius, ST » surface tension, d s density, and the numbers 1 and 2 refer to upper and lower bulbs, or to c a l i b r a t i n g and test l i q u i d s respectively* F i g . 3 shows that i n our instrument both of these errors were ne g l i g i b l e since the diameters of the bulbs and constrictions are nearly equal. The small bulb, A, helped to reduce eddy effects and to make the entrance the same as the exit. To u t i l i z e the maximum available head the visco-meter must be held v e r t i c a l at a l l times. The error i s obviously proportional to (1 - oos 6 ) , where 6 i s the angular deviation from the v e r t i c a l , and hence, i s about 0.1 percent f o r 6 s 2.5°. Such a deviation is e a s i l y detected by a small plumbob, but smaller errors due to this catse probably entered into the author Ts work since no accurate means were available f o r maintaining the viscometer v e r t i c a l . Other possible errors include variation i n the gravitational constant between the point of cal i b r a t i o n and the point of measurement, and the absorption of radiant heat. If the l i q u i d being tested i s darker than the bath l i q u i d , the former w i l l absorb more heat from neighboring l i g h t sources and hence w i l l be at a higher temperature than the bath. We considered these errors to be negligible i n our work. 32 - ', A very important question i s whether or not the constants of the instrument remain truly constant throughout the series of experiments. One possible effect is that of . temperature. As stated above, specail pains were taken to ensure that the same apparent efflux volume, V, was used at a l l temperatures, but there might s t i l l have been an error caused by expansion of the glass. From equation (2) we have: G s .TT'V , and c = ~ ^ — s Considering m constant, and taking the mean coefficient of expansion f o r glass as 0.1X 10 "% we have C200 _ ( l - f 2,00(.00001) 200(.00001 ) )- i. 002 G 0 " ( l + 200 (.000.01) )""(n- 200(.00001) ) Similarly, °20Q B 1.004 c o Since the second term i s less than 2-J- percent of fie f i r s t , unless the efflux time i s less than 100 s e c , a vari a t i o n of 0.4 percent i n c would produce a negligible error i n the value of V. We see, however, that the f i r s t constant may suffer a change of 0.2 percent over an interval of 2QQ°C. Since the c a l i b r a t i o n covered the range from 20°C to 10Q°C the constants are probably correct near 60°C, and hence the max error due to variation i n C would not l i k e l y exceed 0.1 percent. Washburn and Williams 2 9 say that the constants of 33 a viscometer can be affected by other than temperature changes The following are l i s t e d : (1) the presence of small s o l i d p a r t i c l e s i n the c a p i l l a r y , (S) continuous changes in the c a p i l l a r y bore owing to solvent action of the liquids and cleaning solutions used. The f i r s t of these can be reduced only by using as large a c a p i l l a r y as possible. As to the second, i t was considered very u n l i k e l y that.the decalin would act on the glass, and care was always taken not to leave strong cleaning solutions i n the viscometer over long periods of time. For purposes of cleaning the viscometers the usual solutions of potassium dichrornate i n concentrated sulphuric acid, and alcoholic potassium hydroxide were employed. After copious washing with water the viscometer was dried and further washed with clean alcohol or ether after which i t was dried again. In some eases, the ordinary l i q u i d soap solution proved useful. Before a l l series of measurements, the instrument was rinsed and l e f t i n contact with the test l i q u i d f o r some time. After a careful analysis the author believes that the errors i n his results, excepting those due to cal i b r a t i o n and neglecting the extremes of temperature, are not more than ± 0 . 1 percent. Owing to d i f f i c u l t i e s i n keeping the temperature constant at the extremes, the maximum errors i n the absolute v i s c o s i t i e s f o r these values are probably about ± 0 . 2 to ± 0.3 percent. 34 5,» Calibration (a) Procedure We had at our disposal several viscometers a l l of the same type but of varying size and hence suitable for different ranges of v i s c o s i t y . Among them were two already calibrated and as a test of our technique we determined the known v i s c o s i t y of a reference l i q u i d with one of these* For this purpose a sixty percent solution of sucrose was chosen. The solution was made up by weighing and the concentration was checked by measuring the r e f r a c t i v e index with a P u l f r i c h refractometer. From several measurements the following data were obtained: Temperature . J40»19 o0 Average efflux time 56.55 sec* Specific gravity 1.2766 . (60.1$) Using the given equation v, - p (o.2951t - —ty , where the symbols have their usual meanings, we found 9 = 21.15 cp. Bingham^0 gives the value 21.10 cp., and assuming his results to be correct we see that the error i n our measurement i s -0.24 percent* The author does not think that concentrated solutions are well suited to v i s c o s i t y work as they tend to c r y s t a l l i z e and to evaporate at higher temperatures, thus giving variable ooneent rat ions. To cover the v i s c o s i t y range of the decalin isomers and to keep the ef f l u x times greater than 100 sec. we had to 35 choose an unealibrated viscometers To calibrate the instru-ment we measured the efflux times of water at several tem-peratures and from the results calculated the constants as below. These measurements were carried out under the same conditions and with the same precautions as a l l subsequent measurements. To check the ca l i b r a t i o n , a sample of o i l was obtained from the National Bureau of Standards, Washington, D.C., for which the kinematic v i s c o s i t y had been accurately determined at 20°, 40° and 100°G. • Tests were made i n viscometer #1 with this o i l and the v i s c o s i t i e s calculated from the ca l i b r a t i o n constants determined before. Comparing with the given valves, we found the calculated ones a l i t t l e low, and after some further calculations i t was decided to determine the constants using the measurements on the o i l and water together. Only t h i s l a t t e r calibration i s worked out below since i t superceded the f i r s t . Later on i n the work, when measurements were desired at temperatures below 0°C, another viscometer of large bore ($2) was calibrated to avoid the excessively long efflux times of viscometer #1. Cis decalin was the l i q u i d f o r this c a l i b r a t i o n as values f o r i t s v i s c o s i t y from 0°C up were already known. Owing to the smaller range covered and the shorter efflux times, this calibration was not so satisfactory, but la t e r measurements indicated that i t was s u f f i c i e n t l y accurate down to -30°C. 36 (b) Oalculatlons and cheeking The absolute v i s c o s i t i e s of water were taken from, the data of Bingham and Jackson3*-, and the re l a t i v e densities from the Smithsonian Tables. At each temperature several runs were made and the average efflux time taken. Water Temp. (°G) Time (sec.) Density (gm/ml) Viscosity (cp.) 20.25 249*6 0.9982 0.9989 29.93 200.8 0.9957 0.8019 40.02 165.8 0.9922 0.6558 60*21 121.6, 0.9831 0.4673 80.47 95.5 0.9715 0.3644 O i l Temp. (°0) Time (see.) Viscosity (os.) 20.01 646.0 2.609 40.00 449.8 1.819 100.00 .214.8 0.8582 As has already been six own the general equation f o r this type of viscometer i s r) = (D (G^t - c/t) where C^ and e are the constants to be determined. How from the above data we can write eight equations in the form 9/^ ~ yp - C^t - c/^, as: 37 0.6609 s 165.8 g1 - .006031 c 1.0007 r 249*6 C l ~ .004006 e 0.805.4 s 200*8 G l - .004980 G 0.4753 s 121.6 Cl ~ .008224 e 0.3751 95.5 °1 - .010471 c 2.609 646.0 G l » .001550 e 1.819 ' s 449.8 C l " .002223 c 0.8582 s 214.8 ° 1 - .004655 C These equations were solved by the method of least squares giving - 0*004043 and o - 1.52 and hence the desired equation i s ^ .= V/p - 0.004043t - 1.52/t A check calculation follows: O i l at 40°C: t = 449.8 see. V s 0.004043(449.8) - 1 , 5 2 = 1.815 cs. 449*8 Given value = 1.819 cs. . \ Error - - = ^ ~ X 100 = -0.22^ - 1800 A further check was made with benzene. The kinematic v i s c o s i t y was measured at 40 °G with the call i bra ted viscometer, and found to be 0.579 cs. From the values f o r V) and p given i n the International C r i t i c a l Tables, the value calculated was 0.573 cs, but with the v i s c o s i t y data 38 of Thorpe and Rodger, claimed by many to be the most accurate on record, the calculated value became 0.580 cs. The figure i s doubtful i n any case because there i s great variation in the recorded values of both the absolute v i s c o s i t y and density of benzene. The constants for the second viscometer were calculated i n the same way, from the data of runs made at four temperatures with c i s decalin. Temp. (°C) Time (sec.) Kinematic Viscosity (os.) S5.00 59.6 20.00 • 65.9 9.87 83.2 0*00 107.7 The resulting equation was 3.391 3.76.9 4.770 6.162 The f i n a l standard f o r a l l these measurements i s the absolute v i s c o s i t y of water (r> = 1.005 at 20.00°C) and 32 thi s , Cannon and FensJce say, may be i n error by ± 0.5 percent. Relative to this value, however, the author believes his measurements to be correct within ± 0 . 5 percent. 6. General procedure After c a l i b r a t i n g the f i r s t viscometer we proceded to measure the kinematic v i s c o s i t i e s of f i r s t the c i s and then the trans isomer at 10° intervals between -30°C and 180°C. 39 Most of-the measurements above 0°C were made with viscometer #1, those below 0°C were made with viscometer #2. The samples used were part of lo t s prepared by C, H. Davenport and co-workers i n 1938-39. Each temperature was maintained for some time, overnight i n a few cases, and the average of numerous readings taken. At one time i t was thought that the vibration from the s t i r r i n g apparatus might affect the results, and a few runs were made with the motor turned o f f to see i f any difference could be detected. No difference was found. After t h i s , for reasons to be discussed later, the measurements on c i s decalin were repeated between 110° and 180°C. With both the c i s and trans decalin the measurements were repeated at intervals coming down the scale of temperature, after the upper l i m i t had been reached. In a l l cases these a i so l a t t e r were higher. This w i l l A b e discussed later* It may be noted that, whereas i n the determinations with c i s decalin the temperature v/as allowed to return to normal between successive runs, i n those with trans decalin the temperature v/as continuously increased or decreased. This completed the data for the f i r s t part of the investigation, and from these results the absolute v i s c o s i t i e s were calculated and examined as i n the following section. In the course of the investigation certain anomalies were observed and these led to a number of "time runs" being 40 made, "both with material which had been heated to 180°0 and with fresh material. She runs were made at certain fixed temperatures, over periods varying from a few hours to two weeks, and readings were taken at intervals of minutes, hours, or days as was convenient. Care was taken to maintain constant conditions such as, the time of drawing up the l i q u i d into the ef f l u x "bulb, of holding i t steady before l e t t i n g i t run down, and of temperature. The la t t e r condition was not always realized since i t was not possible to watch the apparatus day and night for variations i n the barometric pressure, which affects the thermoregulator, and for minor accidents. To save time several samples were done together, and for this purpose a viscometer of very small bore (#0) and the old type Ostwald viscometer employed by Davenport were also used. Since we were interested i n small variations only, the efflux times were taken d i r e c t l y and the v i s c o s i t i e s were not calculated. Thus no d i f f i c u l t y was caused by the various viscometers being of different types. These runs w i l l be discussed more f u l l y below. The theory and operation of 5and the results from, the microviscometer w i l l also be discussed i n a later section. 41 Part II* Treatment,of Data for Gis and Trans Decalin 1* Observations and calculations As mentioned i n the l a s t section, some of the p r i n c i p a l measurements were repeated coming down the temperature scale. These l a t t e r were a l i t t l e higher i n both the c i s and the trans,and since they were not complete over the whole range, the o r i g i n a l values w i l l be the only ones considered here. The same procedure was followed i n the runs made between £0°C and -<30°C but no appreciable difference was found i n the two cases. We s h a l l also take the f i r s t values for c i s decalin between 110° and 180°C as they were thought to be, the more accurate. The absolute v i s c o s i t i e s were calculated, using Davenport's densities, from the equations of the two visco-meters. The values are l i s t e d i n the following tables,and for the sake of comparison,Davenport 1s specific v i s c o s i t i e s are also given. The results are plotted i n Graph 1. As already stated, previous work on the v i s c o s i t i e s and other physical properties of c i s and trans decalin had led to the hypothesis that several forms of each might exist s and that at certain temperatures one form might change to another. 4 2 Calculations for Gis D R R H I i n Temp. (°K) 1 T Kinematic Viscosity (cs.) Density (gm/ml) Absolute Viscosity (cp.) Specific Viscosity 2 4 3 . 0 0 . 0 0 4 1 1 5 1 6 * 8 5 7 0 . 9 3 5 0 1 5 . 7 6 1 1 5 . 2 5 9 2 5 3 . 0 0 . 0 0 3 9 5 3 1 1 . 5 1 2 0 . 9 2 7 4 1 0 . 6 7 7 1 0 . 8 4 8 2 6 3 . 0 0 . 0 0 3 8 0 2 8 . 2 4 5 0 * 9 1 9 6 7 . 5 8 2 7 . 3 8 2 2 7 3 . 0 0 . 0 0 3 6 6 3 6 . 1 6 2 0 . 9 1 2 0 5 . 6 2 0 5 * 4 7 2 • 2 8 3 . 0 0 . 0 0 3 5 3 4 4 . 7 5 6 0 . 9 0 4 4 4 . 3 0 0 4 . 1 7 6 2 9 3 . 0 0 . 0 0 3 4 1 3 " 3 . 7 7 0 0 , 8 9 6 7 3 . 3 8 1 3 . 3 2 3 3 0 3 . 0 0 . 0 0 3 3 0 0 3 . 0 6 2 0 . 8 8 9 2 2 . 7 2 3 2 . 6 7 9 3 1 3 . 0 0 . 0 0 3 1 9 5 2 . 5 3 9 0 . 8 8 1 7 2 . £ 3 9 2 © 2 X 2 3 2 3 . 0 0 . 0 0 3 0 9 6 2 ft X.*D 13 0 . 8 7 4 2 1 . 8 6 7 1 . 8 5 1 3 3 3 . 0 0 . 0 0 3 0 0 3 1 . 8 3 2 0 . 8 6 6 7 1 . 5 8 8 1 . 5 7 1 3 4 3 . 0 0 . 0 0 2 9 1 5 1 . 5 8 6 0 . 8 5 9 2 1 . 3 6 3 1 . 3 5 8 3 5 3 . 0 0 . 0 0 2 8 3 3 1 . 3 9 3 0 . 8 5 1 9 1 . 1 8 8 1 . 2 0 1 3 6 3 . 0 0 . 0 0 2 7 5 5 1 . 2 3 8 0 . 8 4 4 2 1 . 0 4 5 1 . 0 5 5 3 7 3 . 0 0 . 0 0 6 8 1 0 1 . 1 0 0 0 . 8 3 6 8 0 . 9 2 0 0 . 9 2 7 3 8 3 . 0 0 . 0 0 2 6 1 1 0 . 9 8 8 0 . 8 2 9 4 0 . 8 1 9 0 . 8 2 6 3 9 3 . 0 0 . 0 0 2 5 4 5 0 . 9 1 5 0 . 8 2 1 8 0 . 7 5 2 0 . 7 4 2 4 0 3 . 0 0 . 0 0 2 4 8 1 0 . 8 4 0 0 . 8 1 4 4 0 . 6 8 4 0 . 6 7 4 4 1 3 . 0 0 . 0 0 2 4 2 1 0 . 7 7 1 0 . 8 0 6 6 0 . 6 2 2 0 . 6 1 2 4 2 3 . 0 0 . 0 0 2 3 6 4 0 . 7 1 3 0 * 7 9 8 6 0 . 5 6 9 0 . 5 6 1 4 3 3 . 0 0 . 0 0 2 3 0 9 0 . 6 5 9 ' 0 . 7 9 0 6 0 . 5 2 1 0 . 5 1 5 4 4 3 . 0 0 . 0 0 2 2 5 7 0 . 6 1 2 0 . 7 8 2 5 0 . 4 7 9 0 . 4 7 6 4 5 3 . 0 0 . 0 0 2 2 0 8 0 . 5 6 6 0 . 7 7 4 5 0 . 4 3 9 0 * 4 4 0 43 Calculations for Trans Decalin Temp. CK) 1 T Kinematic Viscosity (cs.) Density (gm/ml) Absolute Viscosity (cp.) Specific Viscosity 243.00 .004115 8.058 0.9072 7.310 7.300 253.00 .003953 5.996 0.8997 5.394 5.345 263.00 .003802 4.589 0.8922 4.094 4.081 273.00 .003663 3.654 0.8849 3.233 3.201 283.00 .003534 2.949 0.8775 2.588 2.571 293.00 *003413 2.446 0.8700 2.128 2.120 303.00 .003300 2.056 0.8627 1.774 1.785 313.00 .003195 1.746 0.8553 1.493 1.509 323.00 .003096 1.511 0.8480 1. 282 1.290 333.00 .003003 1.325 0.8405 1.114 1.119 343.00 .002915 1.173 0.8331 0.978 0.986 353*00 .002833 1.048 0.8255 0.865 0.877 363.00 .002755 0.944 0.8178 0.772 0.787 373.00 .002681 0*854 0.8104 0.692 0*707 383.00 .002611 0.780 0.8025 0.626 0.637 393.00 .002545 0.719 0.7952 0.572 0.578 403.00 .002481 0.662 0.7876 0.521 0.536 413.00 .002421 0.610 0.7798 0.476 0.490 423.00 .002364 0.568 0.7717 0.438 0.459 433.00 .002309 0.532 0.7638 0.406 0.422 443.00 .002257 0.496 0.7555 0.375 0.383 453.00 *002208 0.468 0.7474 0.350 0.361 44 Such changes were thought to take place near 50°C, 120°C, ana perhaps also at 0°C ana 10°C. In addition, conversion to cyclopentane derivatives,above 120°C,was also believea possible. More recent work on the s p e c i f i c heats ana r e f r a c t i v e inaices indicates that the trans isomer i s probably normal s but that the cis does undergo changes i n the intervals 35°to 50°C, and 110°to 120°C. The author's Immediate problem, then, was to see what,if any,indication of the changes could be obtained from the absolute v i s c o s i t i e s . 2. Variation of the v i s c o s i t i e s with temperature Observation shows that the v i s c o s i t i e s of a l l liquids decrease as the temperature increases. Many equations 3 3 have been proposed to express the function v> = f ( T ) , but so far no single r e l a t i o n has been found to hold for a l l l i q u i d s . For our purpose we desired a true function which would give us a straight l i n e graph, hence we proceded to try a number of the suggested functions on our data. C. H. Davenport plotted the logarithms of the s p e c i f i c v i s c o s i t i e s against the reciprocals of the absolute temperatures and joined the points with a series of straight l i n e s as shown i n Graph 2. Similar plots from the author's data are shown i n Graph 3, and the resulting curves are seen to be smooth, except i n the region above 110°C f o r the c i s isomer. It should be noted that a l l curves reproduced i n this thesis were coxvs+Tucled on a large scale (IK 1.5ms) so that small deviations could be detected. 45 Data for Logarithmic Curves 2? . -X10 4 1 - 1 X 10 4 Cis Trans ' logrj Logx) log(V^) ; 1*1152 . 1.626 1*1976 0.1692 0.8639 0.1320 3.9526 1.503 1.0284 0.1487 0.7319 0.1198 3.8023 1.393 0.8798 0.1301 0.6121 0.1025 ' 3.6630 1.294 0*7497 0.1162 0.5096 0.0966 3.5336 1.206 0.6335 0.1044 0.4130 0.0850 3.4130 1.127 0.5291 0.0940 0.3279 0.0790 3.3003 1.054 0.4350 0.0850 0.2489 0.0748 3.1949 0.989 0.3500 0*0789 0.1742 0.0665 3.0960 0.930 0.2710 0.0702 0.1077 0.0609 3.0030 0.875 0.2009 0.0664 0.0469 0.0566 2.9155 0.826 0.1345 0.0598 -Q.0098 0.0532 2.8329 0.781 0.0747 0.0555 -0.0630 0.0496 2.7548 0.738 0.0191 0.0551 -0.1126 0.0471 2.6810 0.700 -0*0361 0.0507 -0.1596 0.0437 2.6110 0.665 -0.0867 0.0372 -0.2034 0.0393 2.5445 0.634 :. -0.1240 0.0410 -0.2426 0.0406 2.4814 0.601 -0.1650 0.0414 -0.2832 0.0397 2.4213 0.572 -0.2064 0.0383 -0.3229 0.0353 2.3641 0.546 -0.2447 0.0381 -0.3581 0.0328 2.3095 0.522 -0.2828 0.0370 -0.3909 0.0355 2.2573 0.498 -0.3195 0.0385 -0.4264 0.0295 2.2075 -0.3579 -0.4559 . 46 In his work, Davenport assumed the equation A T In 9 ~ £ + B, or m eB . where A and B are supposedly constants.. Although this equation does hold f a i r l y well for many li q u i d s , i t i s known from theoretical considerations to be i n general only an approximation. Hence, i t w i l l not necessarily give a straight li n e plot. The author believes his results support this and that the curves are not series of straight lines. In the case of the c i s , however, abnormality i s d e f i n i t e l y indicated above 110°C. The conditions under which the above simple equation i s valid, and the departures therefrom,are discussed 34 by A. G. Ward ; other references are given i n the same publication* Davenport also plotted log Y> against T, and f o r comparison's sake the corresponding plot i s shown i n Graph 4. Again, i t seen, smooth curves r e s u l t . To get a plot more sensitive to small changes i n the v i s c o s i t i e s , the author considered the differences between successive values of the logarithms used above. I f r}^ and p2 are values at temperatures T^ and Tg, respectively, then the above equation gives ^ ( v i / % ) = A < i - ¥ s ) Hence, i f the equation i s correct a plot of ln(p /r> ) against 1 1 1 2 . . (•m ~ ~ ) should give a straight l i n e . Such a plot i s shown - 1 i2. i n Graph 5. That the curves are not linear, further proves 47 the inadequacy of the simple equation; also no discontinuities are indicated except at 110°G i n the c i s l i n e . The smaller deviations are caused by the loss of the f i r s t s i g n i f i c a n t figure when the differences are taken. There are other and more complicated functions for the relationship between absolute v i s c o s i t y and temperature, some of which w i l l be discussed later, but the author feels that the above plots are representative, and hence believes that no conclusions can be drawn regarding changes i n the structure of c i s and trans decalin from such simple treatment of viscosity data. Appendix I I , Resistances for Platinum Thermometer No. 169314 • T (°C) ' M A ) T (°C) -30.00 2.2140 80.00 3.2925 -£0.00 2.3136 90.00 3.3889 -10.00 2.4128 100.00 3.4849 0.00 2.5117 110.00 3.5806 10.00 2.6104 120.00 3.6760 20.00 2.7087 130.00 3.7712 3Q.00 2.8067 140.00 3.8660 40.00 2.9045 150.00 3.9605 50.00 3.0019 160.00 4.0548 60.00 3.0992 170.00 4.1488 70.00 3.1960 180.00 4.2360 Bibliography "The Science of Petroleum", Vol. I-IV, Oxford University • Press, 1938. Davenport, C.H., Master's Thesis: "The Determination of Physical Properties of the Cis and Trans Isomers of Decahydronaphthalene", 1939. Bote: A l l other references to Davenport's work to be found i n this thesis. Morel, Watson and Yip, Bachelor's Thesis: "Physical Properties of Cis and Trans Decalin",1940. Davies, G.F., Master's Thesis: "Investigation of the Specific Heat of Cis Decahydronaphthalene", 1939. Mead, B.R., Master's Thesis: "The Heat Capacities of Cis and Trans Decahydronaphthalene", 1940. Nemetz, H., Master's Thesis: "The Vapor Pressures of the Cis and Trans Isomers of Decahydronaphthalene", 1938. Mizuhara, S., Master's Thesis: "The Temperature Variation of the Refractive Index and Dispersion of Cis and Trans Decahydronaphthalene", 1941. Morris, W.M., Master's Thesis: "The Density and Transition-Points of Dicetyl", 1938. Patterson, R.F., Master's Thesis: "The Densities and Transition-Points of Certain Long-Chain Paraffin •i Hydrocarbons, 1940. 10. Yip, S.W., Master's Thesis: "The S o l u b i l i t i e s of Long-Chain Paraffins i n Cis and Trans Dec ahydronaphthalen 1941, 11. Scott B l a i r , G.W.,: "An Introduction to Industrial Rheology", Blackiston's Son and Co., Inc., 1938. 12. Bingham, E.: " P l a s t i c i t y and F l u i d i t y " , McGraw-Hill Boole Co., Inc., 1922. 13. A col l e c t i v e work: "The Mechanical Properties of Fluids", Blackie and Son Ltd., 1936.-14. Hatschek, E.: "Viscosity of Liquids", D. Van .Bostrand Co. Inc., 1928. 15. Bingham, E.: Loc. c i t . , Chp. VIII. 16. Scott B l a i r , G.W.: Loc. c i t . 17. Bingham, E.: Loc. c i t . , 6. 18. Hatschek, E.-: Loc. c i t . , 30-37, 50-57. 19. Bingham, E.: Loc. c i t . , Chp. III. 20. Hatschek, E.j Loc. c i t . , Chp. I I . 21. Hatschek, E.: Ibid, 46. 22. Morel,Watson and Yip: Loc. c i t . 23. Bingham, E.• Loc. c i t . , 306. 24. Y/ashburn, E.W. and Williams, G.Y.: J. Am. Chem. Soc. 35: 737, 1913. 25. Gruneisen: Wiss Abhandl phys. tech. Reichsanstalt, 4: 159, 241, 1904. 26. Bingham, E.: Loc. c i t . , 65, 297. 27. Cannon, M.R. and Fenske, M.R.: Ind. ; and • Eng. Chem. 10: 297, 1938. 28. Camion, M.R. and Fenske, M.R.: Ibid, 10:297, 1938. 29. Washburn, S.W. and Williams, G.Y.: Loc. c i t . , 35: 737, 1913. 30. Bingham, E.: Bureau Std's. B u l l . , 14: Appendix B, 86, 1918. 31. Bingham, E. and Jackson: Ibid, 14: 75, 1918. 32. Cannon, M.R. and Fenske, M.R.: Loc. c i t . , 10: 297, 1938. 33. Bingham} E.: Loc. c i t . , Chp. I I I . . 34. Ward, A.G.: Transactions of the Faraday Society, 33, Pt.I: 88, 1937. 


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