November, 1534
INDUSTRIAL AND ENGINEEKING CHEMISTRY
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’ube diam., 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
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 fine pigments were incorporated in rubber. (2) W i t h p i g m e n t s 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.
wKf;
whether the composition of the Pigment affectedthe bond* Endres (6) studied the vacuoles that f o r m w h e n pigmented r u b b e r is strained, a n d he pointed out that agglomerates acted as large particles in some and broke up in O t h e r cases when t h e rubber was stretched, very large vacuum p o c k e t s . 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 t o 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 comnercial pigments, indicating that the breaking of rubber occurs within itself rather than at pigment-rubber interfaces.
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
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1188
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N U I N 1s F: I< I N
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C H E X I I S 'l 11 Y
Vol. 26, No. 11
liigineiit is bruk
EXPERIMENTAL I'ILOCEDURE To obtain this informatioir, anthracite c o d ((;I), fused zinc oxide (ZnO), and several crystnlline inaterials were selected tirat included galena (PbS), sphalerite (ZIIS), Icclnnd spar (CaCO,), and Crystal quartz @io2).
FIX:^,^ S ~ o w r Ilow ~ o PAWTICL~ Srzli I~'IGUI~E 1. Mrcrroaao~~rc I ~ a ~ u a ~ ~c ieisxSE:P.MMTION OF Kusu~:ir FIWM ProxcvTs
parlially oxidized by heating ill air at 170"(:. so that it would wet like silica. 13y heating for certain periods, a range of materials was obtaincd that developed air adhesional loree intermediate bctwwn earboil and silica. fising these materials, the earlier predictions were fully proved. The f < J l l O w ing data are from Bartell a r i d Waltorr's paper on the "Wetting of Antimony Sulfide lry Liquids" (3). snssaiux TI,E*TMENT
"I A h P I M O N I
Sabrror
T I N R i O N "I S N T l h l U N Y SUL. I I U E ,To:
water
n,,,rrs p m None Kested 3 hours *t 17U0 C. Heated 8 houm a t 170" C.
56.6 00.a
76.0
Benzene ly.
Crn.
18.4 72.6 47.0
Itulitier is so viscous that it is difiicult to see liow tlre metliod can be applied to the study of the adhesion tension of rubber
thrm 50 microns. The A. 8. T. hf. dtunda,rds (1) give t6e si& opening in a 325-mesh screen as 44 microns with tl tolerance in avcriigp opening of 8 per cent and a to1er:tnee in maximum opening of 90 per cent. The m n t e d s were then iocoqmated in very small amounts (approximately 0.5 gram of pigrlient miiteriil to 100 gr:inm of r u b k r ) ir, the following trmsp:ircnt rubber C
