Estimation of apparent permeability in heterogeneous membranes. Part 1. - Model calculations through cubic chequer assembled membranes

The apparent permeability of a specific model of a heterogeneous polymer membrane has been estimated by applying a finite-difference method of integration to Fick's first law and the continuity equation. The model was assumed to be a simple chequer one composed of alternate rectangular cells of two different kinds. The cells were defined so as to give repeating concentration profiles under periodic boundary conditions. The apparent permeability of a permeant was calculated from the concentration in sufficiently small lattices in the cell by the iteration method. The effect of membrane heterogeneity or cell dimensions on the permselectivity of permeants is discussed by taking an example, O₂ + N₂, with polystyrene (PSt)-poly(dimethyl siloxane) (SR) as membrane substrates.