Effect of heteroporosity on flux equations for membranes.

An investigation is made of the possible errors in simple integrated equations for solute flux across both non-sieving and sieving porous membranes that can result from variations in the membrane structure. Detailed structural models are used, beginning with a membrane consisting of a parallel array of pores and progressing to series--parallel combinations of pore segments of various lengths and cross-sectional areas, with internal cross connections among pore segments allowed. It is shown that there are both upper and lower mathematical bounds on the possible variations that can be produced in a curve of solute flux versus volume flow by arbitrary variation in the membrane structure, subject only to certain general conditions. In particular, the flux equation for a homoporous membrane is a lower bound. The maximum deviations from this lower bound for a membrane of arbitrary structure are only moderately large, and require rather extreme pore size distributions; most distributions introduce only small errors. Implications of these results in studies of real membrane structure and in the design of experiments are discussed.