Ind. Eng. Chem. Process Des. Dev. 1981, 20, 662-665
662
T = temperature V = molar volume of adsorbed phase W = volume of adsorbed phase W , = volume adsorbed at saturation X = adsorbent loading greek letters Greek Letters @ = affinity coefficient = adsorption potential
Bering, E. P.; Dublnin, M. M.; Sperpinsky, V. V. J. Cotb&i Interface Scl. 1972. 38, 186. Every, R. L.; Dell’Osso, L. Ponca Chy, Oklahoma, Feb 1971, Conoco Research Report. Dubinin, M. M. Chem. Rev. 1980, 60, 235. Dubinin, M. M. J. ColW Interface Sci. 1987, 23, 487. Eberiy, P. E., Jr. J. Appl. Chem. 1984, 74, 330. Lewis, K. W.; Qllllland, E. R.; Chertow, B.; Cadogan, W. F. Ind. Eng. C k m . 1950, 42, 1326. Paniego, A.; Guii, J. M. J.CoIloid Interface Sci. 1976, 57, 166. Polanyi, M. Z . Physik 1920, 2 , 111.
Receiued f o r reuiew September 12, 1980 Revised manuscript received May 26, 1981 Accepted May 26, 1981
Literature Cited Bering, B. P.; Dubinin, M. M.; Sperpinskv. V. V. J . Colloid Interface Sci. 1966, 27, 378.
Predicting Diffusion Coefficients in Nonpolar Solvents Napoleon 0. Umesi and Ronald P. Danner’ Department of Chemical Englneering, The Pennsylvania State Universly, UnlversHy Park, Pennsylvania 16802
A simple method for predicting diffusion coefficients of dilute solutes in nonpolar solvents has been developed.
In these sytems the relative size and/or shape of the solvent and solute is the predominant factor in determining the diffusivity. The radius of gyration has been used to define this slze-shape relationship. For dilute nonpolar
or polar solutes diffusing into nonpolar solvents or for hydrocarbon gases diffusing into nonpolar solvents, one equation is applicable which gives predictions equivalent to or better than all the prominent methods now available. The dilute diffusion coefficients can be used to predict diff usivities in concentrated and multicomponent systems.
Introduction In the separation processes as in almost every area of chemical engineering, problems of diffusion and mass transfer occur. Experimental diffusion coefficient data are used whenever they are available. Such data are scarce, however, because of the difficulties and cost of experimentally determining diffusion coefficients. The necessity of predicting diffusivities therefore often arises. Most of the available methods of predicting diffusion coefficients have used molal volumes, critical volumes, or molecular weight as correlating parameters. The methods generally are restricted to either liquids diffusing into liquids or gases diffusing into liquids. The objective of this work was to develop a predictive equation for diffusivity that is applicable to both liquid-liquid and gas-liquid systems and that uses conveniently available input parameters. There are at least four theories of diffusion-(1) hydrodynamic, (2) kinetic, (3) statistical-mechanical and (4) irreversible thermodynamics. The hydrodynamic theory has been most productive in terms of practical application. Einstein (1905) assumed random walk motion of the solute molecules as a model to express the diffusion coefficient as D0m = k T ( U A / F A ) (1) Lamb (1932) found that at the surface of a rigid sphere moving in creeping flow (Le.)Reynolds number
