Transport of Gases in Porous Membranes
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sport of Gases in Porous Membranes
Mechanisms for Gas Transport in Porous Membranes
Stratis V. Sotirchos and Vasilis N. Burganos Introduction The capability of membranes to affect differently, both qualitatively and quan titativer^ the transport rates of chemical species of dissimilar chemical structure through their inferior space renders them attractive for use in many Separation Prob lems. 1 Extensive research efforts have thus been undertaken on the preparation and characterization of membrane materials and the study of the transport processes involved in their use in Separation applications. The study of the transport of gaseous species through the pore Space of porous membranes and the analysis and understanding of the mechanisms that are involved in this process are a very important, if not the most important, d e ment in the development of membranebased Separation processes. The resistance that a gaseous species encounters as it is transported through the pore space of a porous membrane is a function of its molecular properties, of its interaction with the material that makes up the walls of the pores, and of the mem brane pore structure. Gaseous transport in pores can take place through various mechanisms, whose contribution to the Overall transport rate of a particular spe cies is, in general, determined by the strength of the interactions of the molecules of that species with the pore walls and by the relative magnitudes of three length scales that characterize the mo lecular size, the distance between pore walls, and the density of the fluid in the pore space.2"5 The basic building blocks of mathematical modeis for transport, reaction, and/or adsorption in a porous medium are the mass balance equations of the components of the mixture. The completion of these equations requires expressions relating the transport fluxes of the various species, N, for species A,, to the concentrations, partial pressures, or mole
MRS 6ULLETIN/MARCH 1999
fractions of the gaseous-mixture compo nents and their gradients. The derivation of such relationships and the estimation of the values of the parameters they involve form the principal objective of the experimental and theoretical study of transport in porous media and particularly porous membranes. If A, is the only gaseous species in the porous medium or is present in low quantities, then for each of the transport mechanisms N;=-DfF,-
(1)
where F, is the local driving force (pres sure, concentration, or mole fraction gradient) for mass transport in the porous medium for that particular mechanism, and Df is the corresponding effective mass transport coefficient in m 2 /s. In general, porous media, and especially p o r o u s m e m b r a n e s , are a n i s o t r o p i c structures, and, therefore, Df is a tensor quantity. However, for transport in one direction only, as is the case in most membrane applications, the tensorial character of the effective mass transport coefficient can be ignored. In studies of gas transport through po rous membranes, F, is usua
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