Mass Transfer (Absorption) Coefficients Prediction from Data on Heat Transfer and Fluid Friction T. H. CHILTONAND A. P. COLBURN,E. I.
d u Pont de Nemours & Company, Wilmington, Del.
N T H E design of apparatus t r a n s f e r per unit of surface One of the authors previously suggested that a area : involving diffusional procset of curves proposed .for estimating heat transesses, s u c h a s dehumidifer coeficients, by means of a “heat transfer fication or partial condensation, factor,” (h/cG)( c ~ / k ) ~ could ‘ ~ , also be used for evaporation of a liquid into a estimating coeficients for transfer of material gas, drying of solids in the initial state, absorption of a gas by a by diffusion. It is shown in the present paper The function of the dimenl i q u i d , and rectification, it is that these curves predict aalues of mass transfer sionless group ( c p / k ) w a s n o t n e c e s s a r y to have a means of coeflcients in close agreement with data for flow included in the original Reynolds estimating the rate of transfer of inside of tubes taken f r o m the work of Greeneanalogy, although it was recogthe diffusing component per unit Walt, that of Sherwood and Gilliland, and some nized by Reynolds himself that of size of the apparatus consome function of the ratio of vissidered. Relatively few experiunpublished data of the authors; data for jlow cosity to thermal conductivity mental data have been obtained across a single tube from the work of Lorisch; and should b e i n t r o d u c e d . T h e for the vazious types of apparadata for jlow over plane surfaces from the work power function employed in the tus and conditions encountered; of Thiesenhusen. equations given is derived from and owing to the difficulties incinumerous correlations of data on dent to such studies, the reliability of the results is often open to question. There has, heat transfer in turbulent flow, where it serves to relate these therefore, been a great need for a convenient method of apply- factors as single-valued functions of the Reynolds number, ing the well-substantiated correlations from the analogous independent of the properties of the fluid. As shown in the previous paper ( 2 ) ,Equation 1 (the modiprocesses of fluid friction and heat transfer to test the diffusion data available and to permit predictions to be made fied Reynolds analogy) holds for fully turbulent flow inside where there are no applicable data. It is the purpose of this tubes, and for flow parallel to plane surfaces, but does not paper to describe such a method and by it to compare apply to streamline tubes or flow across tubes and tube banks. representative experimental data on diffusional processes with Hence, as indicated in Equations 2 and 3, different symbols have been used to represent the friction and heat transfer results of fluid friction and heat transfer studies. The method proposed has its basis in the Reynolds analogy factors. Processes in which material is transferred by diffusion are between heat transfer and fluid friction. Stated in words, this analogy postulates that “the ratio of the momentum closely related to heat transfer, since the latter can be conlost by skin friction between two sections a differential dis- sidered merely as the diffusion of hot molecules into a region tance apart to the total momentum of the fluid will be the of cold ones and a corresponding diffusion of cold molecules same as the ratio of the heat actually supplied by the surface in the reverse direction. Since the mechanism is so similar, to that which would have been supplied if the whole of the it would be expected that a relationship could be obtained fluid had been carried up to the surface.” The development for diffusional processes entirely analogous to that for heat of the present form of the resulting equations has been treated transfer. The diffusional process most nearly similar is recin some detail in a previous paper ( 2 ) . o, As applied to heat transfer, the equation reads: APg
&)
(e)(&> s
S =
cp 2’3
(1)
T h e q u a n t i t y o n the left of the equation has long been found to be a function of the R e y n o l d s n u m b e r , dup/p, and has often been represented by the symbol, 1/2f. This function can be expressed not only in terms of overall pressure drop and ratio of cross section to surface area, but also in terms of skin friction per unit surface area, as:
-&) APg
8
R
1
=2=5f
(2)
Similarly, for heat transfer the ratios can be expressed not only in terms of the temperature change but also in terms of the iilm coefficient of heat
OO1
IO
im
man
lox)
FIGURE 1. TRANSFER PROCESSES IN CONDUITS Heat transfer: j transfer: 3 Friction:
1/zj
1183
=
p
GZ
cG
fr - 11 d (CC) ‘’ (s)*’a Atm 4L P
(p%)
Kp,l (G/Mn) P
* GZ
4L
‘/a
E
PEILE
Apm
*/’
EC L)( ‘ Po 4L
pkd
l/a
INDUSTRIAL AND EKGINEERING CHEMISTRY
1184
tification, in which the total number of moles of material passing through the apparatus remains constant, and diffusion occurs in both directions. For this process the rate of material transfer, w, can be expressed either in terms of the change in partial pressure of one of the diffusing components or in terms of a mass transfer coefficient, K , in moles per unit time per unit area per unit partial pressure difference, as follows: (4)
Rearrangement of the terms of this equation leads to an expression involving the ratio of the change in partial pres-
Vol. 26, No. 11
In other processes, such as absorption, stripping, evaporation of a liquid into a gas, or condensation of a vapor from a mixture with inert gas, the total number of moles does change as the gar mixture passes through the apparatus, and also the diffusion is chiefly, if not wholly, in one direction. The differential rate of material transfer can then be expressed :
dw
= d
( L’ = K) ApdA Mmn
s(
Carrying out the differentiation, considering S and II constant and making use of the relation M G, = ,)%n leads
t o the equation: where p , = n - p (G,/Mi) = moIar mass velocity of the inert gas
The corresponding mass transfer factor for this case then becomes:
0
0
,m
Im)
FIGURE 2. TRANSFER PROCESSES ACROSS
ST.4GGERED
mcu
vlm
TUBEB A N K S
The quantity pot has been included on both sides of this equation, since K varies inversely with pQf, as follows from the Stefan diffusion equation; and the same function of ( p / p k d ) is included ar in Equation 5. When the diffusing vapor is relatively dilute throughout the apparatus, and in some other cases, average values may be used for pa), pol K , and G, and Equation 8 may be integrated to give:
( 7 )(E)( ;)( 2)’ ’3
&)
mres to the mean difference in partial pressures between the gas mixture and the surface, analogous t o that relating temperature change and temperature difference. An extension of the Reynolds analogy leads to the expectation that this ratio
will be the same function of Reynolds number as the corresponding heat transfer factor, and will equal the friction factor under the same conditions as it does. It is therefore designated by the same symbol, j, as the heat transfer factor defined by Equation 3. In Equation 5 a function of the ratio of viscosity to diffusivity has been inserted exactly analogous to that employed on the (cpllc) group in defining the heat transfer factor. The latter function has been shown ( 2 ) to give a satisfactory correlation of heat transfer data over a range of ( c p l k ) values from 0.7 to 1000; and since it has been shown further that the Prandtl equation, involving a different function of ( c p i k ) , is not so satisfactory for high values of this group, the power function of ( p / p k d ) included in the above equations is now preferred to the theoretical equation proposed several years ago by one of the present authors ( 1 ) for correlating diffusional data. It is possible that the correct value of the exponent may not be the same as on the (cp,lk) group for heat transfer, but it will be necessary to have data covering a wide range of ( p / p k d ) values to justify any considerable change in this function.
=
&)
2 /3
=3
(9)
When the diffusing component changes greatly in partial pressure through the apparatus, p,/ will change considerably, and sometimes (,u/pkd)2’3, so that K is not and also G, .V,,,, a constant. Furthermore, the true mean driving force, Ap,, is not in general equal to the logarithmic mean of the terminal driving forces. In such cases, K , Ap, and w must be computed at several intermediate values of composition; then from a plot of l / ( K A p )vs. w, the required surface area is obtained by a graphical integration, according to the equation:
Or instead of calculating values of K , the integration can almost as well be made in terms of partial pressures, as shown by the 1a.t term in Equation 10, since generally varies so slightly with velocity that an average value can be used satisfactorily. When, however, the diffusing component is so dilute that pol, G, and K can be considered substantially constant, and when the solute follows Henry’s law, or the solution exerts a negligible vapor pressure over the working range, then the driving force is equal to the logarithmic mean of the terminal values, and the required surface area is simply:
It should be emphasized that these equations apply only to diffusion into or out of the fluid undergoing relative mo-
IN DUSTR IA L AN D E N GI NEER IN G CH EM ISTR Y
November, 1934
FIGURE3. TRAUSFER PROCESSES PAR~LLE TO L PLANE SURF4CES
Friction
1/91
Heat tranefer Xasa transfer
=
% G2
I = j
=
CG
pkd
’tion, and do not, for example, allow for any liquor-film resistance. In the previous paper, friction and heat tranqfer factors were determined and compared by means of most of the reliable heat transfer data and pressure drop correlations for three important cases: (1) flow inside of conduits, (2) flow across single cylinders and tube banks, (3) flow parallel t o plane surfaces. Plots of curves which were found best to represent the existing data are given by Figurec, 1, 2, and 3, respectively, for the cases mentioned. It was suggested that the j factors from these same curves could be used to predict mass transfer coefficients by employing Equations 5 and 9, which are analogous to the corresponding heat transfer equation (Equation 3). Certain further modifications are necessary in using these charts over the whole range-for example, in allowing for the effect of free convection. For flow inside tuber in the viscous region-i. e., a t Reynolds numbers less than 2300-4 was found in the heat transfer correlations ( 2 ) that the effect of free convection was amroximated bv the function: ..
FIGURE4. HE.4T k N D h1.4SS TRANSFER FACTORS FOR l r A PORIZATION
OF W A T E R
IN
A
FALLING FILMTOWER (DATA OF AUTHORS) Gr.lf =
4.v
=
(d3p2g
(1
evaporation of water into air flowing countercurrent to it in a falling film tower 1.04 inches in diameter, 67 inches long. To insure that there would be no water-film resistance to heat transfer, the inlet water temperature was adjusted approximately to the vet-bulb temperature of the inlet air so that the heat for vaporization mould come from the air stream. Under these conditions the mater temperature did not change appreciably in passing down the tower, and the logarithmic mean values of Ap, and At, could be used. The data are given in Table I and are plotted in Figure 4. The velocity employed is the velocity relative to the wall of the tube. 90 consideration was given t o the relative velocity with respect to the falling water film; the latter was
‘’ (dZi3 (‘Y
( GK/p. qMf m )
~
1185
For mass transfer, the viscosity ratio can be neglected as being generally equal to unity. The a p p r o p r i a t e Grashof group, however, is a function of density difference caused by concentration drop instead of a temperature drop 13); thus :
A M Ap/pZM,JI)
+ 0.15 G T M ~ ” ) ~
IOOca
5
Y FIGURE3 . V4PORIZ\CIO\ OF LIQ~JIDS IV 4 FALLIYG T O ~ FFILW ~ R ( D 4 ~ 4O F SHERWOOD 4 x 1GILLIL~RD)
estimated to be about 1.5 feet per second, uhereas the gas velocity ranged much higher. It will be seen that the heat transfer factors lie generally somewhat above the line, while those for mass transfer are in substantial agreement with it. In all of these graphs the line drawn is that taken from the appropriate general curve, Figure 1, 2 , or 3, whereas the points represent experimental data. Extensive data on the evaporation of several liquids into an air stream in a falling film tower of about the same size (1.05 inches diameter, 41 .O inches long) have been recently published by Gilliland and Sherwood ( 5 ) . Their data for the turbulent region (again on the hacis of velocity relative to the tube wall) were represented by the equation:
This equation, transformed to the type of coordinates employed in the present paper, is represented by the line marked ‘[Sherwood and Gillilsnd” on Figure 5. This line represents 0.66 j as defined by $d) , while the definition for the “predicted” line is given by Equation 9. The difference between the 0.56 and the 0.67 powers of the group (p/Pkd) is, ~
(ggml(
(14) (1 5)
Otherwise it is suggested that the lines given for viscous flow can be used with the same provisos as for heat transfernamely, that the mean partial pressure difference is the arithmetic mean, and that, for constant equilibrium pressures, asymptotic values of j will be reached a t corresponding values Of ( L ; d ) / ( p pkd)’I3.
DATA As mentioned above, the data that can be used to check the application of these predicted curves to mass transfer processes are relatively few. An attempt has been made t o cover those which were regarded as most reliable and n-hich were reported in sufficient detail. In an investigation carried out by the authors, both heat transfer and mass transfer factors were determined for the C O M P A R I S O S I\ ITH E X P E R I M E N T A L
2
5
tow0
DG
P FIGURE6. ABSORPTIONOF WATER BY SULFURIC ACIDIN A FALLTNG FILMTOWER ( n A T . 4 O F GREENEWALT)
for the mixtures considered, less than 10 per cent. If the original data were correlated by the use of ( p / p k d ) *’3 instead of the 0.56 power, the result would be to bring the data for vaporization of water slightly nearer the predicted line, and those for organic liquids slightly farther away. The agreement of the viscous flow data of Gilliland and Sherwood with the “theoretical equation for rodlike flow”
INDUSTRIAL AND ENGINEERING CHEMISTRY
1186
TABLEI. HEATAND MASS TRANSFER FACTORS FOR VAPORIZATION OF WATERINTO AIR IN A FALLING FILMTOWER (DATAOF THE AUTHORS)
Vol. 26, No. 11
FLOW OVER PLANESURFACES
There have been a number of attempts to measure the rate of evaporization of liquids from flat surfaces, especially the evaporation of water from pans and from natural reservoirs. Since there is no movement of the liquid (as there is in a falling film tower), there may be an appreciable resistance to heat transfer from the body of the liquid through the quiescent film a t the surface in supplying the heat of vaporization unless the heat is supplied by the gas stream itself. rn the experimentsof T h i e s e n h u s e n (9) this effect was circum1.58 1.69 vented by an ingenious thermocouple just a t the liquid surface, so that the interface tem7450 perature and the corresponding vapor pressure could be measured, and the mass transfer coefficient could be determined unaffected by the liquid film resistance.
(Total pressure taken as 1 atm.: p = 0.042 lb./(hr.)(ft.): (cp/k)z’a = 0.83: ( p / p k d ) z ’ 8 = 0.71) Kun No. 1 2 3 4 5 Air velocity, ft./sec. 3.1 6.0 8.3 8.3 13.9 Water rate, lb./(hr.)(ft. perimeter) 252 254 254 254 254 Entering air temp., O C . : Dry bulb 19.6 19.8 2.0 20.2 20.3 Wet. bulb 6.7 6.7 6.7 6.7 6.7 Exit air temp., O C.: Dry bulb 12.0 12.2 12.0 12.2 12.3 Wet bulb 10.2 9.8 9.7 9.6 Partial pressure of water vapor, atm.: 10.4 Inlet air 0.0015 0.0015 0.0015 0.0015 0.0015 Outlet air 0.0115 0.0109 0.0106 0.0102 0.0100 Entering water temp., e C. 10.5 10.6 10.3 10.2 10.2 Vapor pressure of inlet water, atm. 0.0125 0.0126 0.0124 0.0123 0.0123 Exit water temp., O C . 11.0 11.0 10.8 10.6 10.5 0.0129 Vapor pressure of outlet water, atm. 0.0129 0.0128 0.0126 0.0125 (P!
(ti
--t Pd /IA)t /mA P ~
2.35 1.90
1.87 1.82
1.76 1.83
1.66 1.67
:::::;::::::i5 ::::ti$ :::::!:
j mass 3, heat transfer transfer
Reynolds number
1710
3320
4600
6130
and thereby with the empirical heat transfer correlations of McAdams (8) is considered as affording the same kind of basis for the predicted j values for mass transfer a t Reynolds numbers lower than 2300 as do the data on heat transfer, after allowing for the effect of natural convection (g). Data of Greenewalt (6) on the countercurrent absorption of water vapor from air by 72 per cent sulfuric acid in a falling film tower, 2 inches in diameter and 27 inches long, having a Venturi gas entrance, have been plotted on Figure 6. For all except the 1o.west velocities (where the gas velocity was lower than the liquid surface velocity) there is good agreement between the observed mass transfer factors and the appropriate line from Figure 1. The line used for comparison in the viscous region is that chosen for a value of [ ( L / d ) / 4 ~=] 10; the value of L/d in the tower used was 13.5 and the value of @M is estimated as being between 1 and 3.
FLOW ACROSS TUBES
am Im,
I 2
I I I I IIII 5
0003
2.”
I 2
ill^
I I 5
1ooooo
FIGURE8. EVAPORATION OF WATER FROM PLANE SURFACES (DATAOF THIESENHUSEN) Thiesenhusen’s apparatus consisted of an electrically heated circular vessel a t the bottom of a small wind tunnel, 2.16 X 5.3 inches; the rate of evaporation was measured a t three air velocities, 1.64, 3.28, and 4.92 feet per second, and a t several water temperatures from 52’ to 83” C. The diameter of the circular dish was 5.0 inches, but the average length, called for in the calculation of the Reynolds number, L G / ~ was , taken 8s ( ~ / 4 )x 5.0 inches = 3.95 inches. The average values of the j factors a t the several temperatures a t each of the three air velocities used are represented on Figure 8. Individual values varied by a maximum of about 20 per cent, It was shorn in the previous paper (2) that for flow over plane surfaces, the heat transfer factors checked closely with friction factors, not only in the turbulent but in t h e viscous region as well, The same agreement in the viscous region is shorn by these vaporization data.
Diffusional data for flow a t right angles to tubes are relatively few. LorisCh (7) obtained a few Points for flow across tube banks but did not report his original data. The original data of Lorisch (7) on absorption Of water from a stream of air flowing &Crossa single cylinder, which he using for the reverse purpose of estimating heat transfer COefficients, are given h a form such that they may be transposed fairly readily to the authors’ coordinates; they are shown in Figure 7. I n these experiments moist air Was blown across a stick of fused caustic soda, 0.396 inch in diameter, 5.23 inches long, and the gain in weight of the Caustic gave the amount of water absorbed. The experimental values are seen from Figure 7 to lie some 20 to 25 per cent higher than the line representing heat transfer factors for flow at CONCLUSION r i g h t angles toAs illustrated by these typical correlations, it is believed single cylinders that mass transfer factors can be estimated with a sufficient f r o m Figure 2, degree of certainty for design calculations, by analogy with and this is within heat transfer processes, not only for flow inside tubes, but also the limits of defor flow across tubes and tube banks and flow over plane surv i a t i o n of t h e faces. Such factors, defined by Equation 8, permit predicheat transfer tions of performance of falling film absorption columns; and d a t a o n which by the use of Equation 5 the efficiency of wetted wall columns this c u r v e was for distillation can be estimated in advance. The authors b a s e d . It i s hope to present further papers giving a comparison between t h e r e f o r e beFIGURE 7. ABSORPTION OF WATERFROM lieved t h a t t h e AIR FLOWING ACROSS A SINGLE CYLINDER such predicted values and those actually realized, and outlining the adaptation of similar methods of correlation to the (DATAOF LORISCH) previously o b performance of packed absorption and distillation columns. tained lines for heat transfer factors for flow across both single cylinders and NOMENCLATURE tube banks will give fairly reliable values for mass transfer Any set of self consistent units may be used; those of the, coefficients. An example of the use of these curves in predicting dehumidification coefficients is given in a contemporary foot-pound-hour-” C. system are given for illustration; totaL and partial pressures are, however, expressed in atmospheres.. paper (4).
-
November, 1534
INDUSTRIAL AND ENGINEEKING
A = surface area, sq. ft. G = mass velocity, lb./(hr.)(sq. ft.) G , = max. mass velocity (through min. cross section) G r = Grashof group, ( d 3 p 2 pAt g / p 2 ) GTM = Grashof group for mass transfer, ( d a p a A M A g / p * M , I I ) K = molar mass transfer coefficient, Ib. moles/$r.) (sq. ft.) (atm.) L = length, ft. M , = mean mol. weight A M = difference in mol. weights between inert and diffusing components N = number of rows of tubes A P = pressure drop, lb./sq. ft. R = frictional resistance per unit surface area, force units Re = Reynolds number, dG/p s = cross-sectional area, sq. ft. c = sp. heat at constant pressure, P. c. u./(lb.)(” C.) d = diam., or equivalent diam., ft. d, = outside t’ubediam., ft. d, = min. clearance between tubes, ft. f = friction factor (Equation 2) 9 = acceleration of gravity, 4.18 X 108 ft./(hr.)(hr.) h = film coefficient of heat transfer, P. c. u./(hr.)(sq.ft.)(” C.) j = heat transfer or mass transfer factor (Equations 3, 5, 9) k = thermal conductivity, P. c.u./(hr.)(sq. ft.)(”C./ft.) k d = diffusion coefficient, sq. ft./hr. P = partial pressure of diffusing component, atm. Po = partial pressure of inert component, atm. Par = log. mean partial pressure of inert component in ‘(film,” atm. A p = difference between p and the equilibrium partial pressure at the surface; A p , = mean difference t = temp., C. Af = temp. difference, usually log. mean, O C. O
CHEMISTRY
linear velocity, ft./hr. rate of material transfer, lb. moles/hr. 11 = total pressure, atm. P = coefficient of expansion, 1 / O C. P = viscosity, lb./(hr,)(ft.); pr = film viscosity; cosity in main body of fluid P = density, lb./cu. ft. d = free convection factor for heat transfer
1187
U = W =
(1
+ 0.015 Gr1’3)*
pa =
=
d .?4 = free convection factor for mass transfer = (1
vis-
(pLg/p,)
+ 0.015
G%M1’3)3
LITERATURE CITED (1) (2)
Colburn, A. P., IND. Ero. CHEM.,22, 967-70 (1930). Colburn, A. P., Trans. Am. Inst. Chern. Engrs., 29,
174-209
(1933). (3)
Colburn, A. P., and Hougen, 0. A., Bull. Uniu. Wis. Eng. E&.
(4)
Colburn, A. P., and Hougen, 0. A., IND.ENQ.CHEM.,26,
Sta. Ser. No. 70, esp. p. 54 (1930).
1178
(1934).
(5) Gilliland, E. R., and Sherwood, T. K., Ibid., 26, 516-23 (1934). (6) Greenewalt, C. H., Ibid., 18, 1291-5 (1926). (7) Lorisch, W., Forschungsarbeiten, Heft 322, 46-68 (1929). (8) Mc;idams, W. H., “Heat Transmission,” pp. 207-9, McGrawHill Book Co., Kew York, 1933. (9) Thiesenhusen, H., Gesundh.-Ing., 53, 113-19 (1930). RZICEWED September 15, 1934. Presented as part of the Symposium on Diffusional Processes before the Division of Industrial and Engineering Chemistry a t the 88th Meeting of the American Chemical Society, Cleveland, Ohio, September 10 t o 14, 1934. This paper is Contribution 145 from the Experimental Station of E. I. du Pont de Nemours & Company.
Surface Energy Relationships between Pigment Materials and Rubber HARLAN A. DEPEWAND M. K. EASLEY, American Zinc Sales Company, Columbus, Ohio
A
BOUT fifteen years ago SchiPPel (9) found that compounded rubber became less dense on stretching, and that t h e d e n s i t y c h a n g e varied g r e a t l y w i t h the cornpound. His data showed that when rubber was stretched: (1) The volume increase was especially large with coarse merits and approached zero
wKf;
whether the composition of the Pigment affected the bond* Endres (6) studied the vacuoles that f o r m w h e n pigmented r u b b e r is s t r a i n e d , a n d h e pointed out that agglomerates acted as large particles in some and broke up in O t h e r cases w h e n t h e r u b b e r was stretched, very large vacuum pockets. H e found no evidence that the s u r f a c e of nonreactive Pigments affected t h e a d h e s i o n of r u b b e r t o pigments and he believed that “rubber adhered t o r e a c t i v e pigments such as zinc oxide very tenaciously.” w ~ along ~ anGentirely ~ different ~ path, Bartell and his co-workers studied the adhesion of materials to liquids by measuring displacement pressures. By this method Bartell and Osterhof (2) showed that carbon was wet extremely well by organic liquids, such as benzene, but poorly by water, whereas silica was wet well by water but poorly by benzene. They predicted that lines could be drawn relating the wetting of other materials by liquids if the adhesion tension to one of them was known. They did not have finely divided solid materials that covered the wetting range satisfactorily to prove their contention. However, Bartell and Walton (3) found that antimony sulfide behaved similarly to carbon, and that the surface of the antimony sulfide particles could be
Microscopical observations hazre been made to determine the adhesion of rubber to pigment materials. The bond between carbon and rubber is relatively very strong in comparison with that of zinc oxide, while other pigment materials give intermediate results. Overcure lowers the adhesion, and particle shape influences the separation. Separation OCCUrS at partick Sizes which are Coarser than those found in mnmercial pigments, indicating that the breaking of rubber occurs within itself rather than at pigment-rubber interfaces.
fine pigments were incorporated in rubber. (2) W i t h pigments of t h e very finest kind, the volume increase was greater than would be expected from the general relationship of size to volume increase. (3) The volume increase increased as the pigment concentration increased; the volume increase was especially large for heavily compounded stocks. Schippel concluded that the volume increase was due to the pulling away of the rubber from the pigment particles, and he verified this conclusion by observing that vacuum pockets developed when rubber containing coarse material was stretched. I n the case of the very h e pigments, unmixed groups of pigment behaved as coarse particles. Green (6) further confirmed Schippel’s explanation by extending the microscopic observation to pigment-size particles and photographing the vacuum pockets that developed. This work, however, did not give any information as to
