Steady flow through asymmetric membranes

Abstract
For the two special cases that the permeability of the membrane is (1) an exponential and (2) a power function of location and pressure, the pressure dependence of the current, the average permeability, and the asymmetry of permeability Δ = / — 1 were calculated on the basis of irreversible thermodynamics. The asymmetry is small in both cases. It increases rather fast for small pressure but reaches soon a slightly inclined plateau in the former case and a maximum with a small subsequent drop in the latter case. The maximum value is close to 0.5 in case 1 and about 0.2 in case 2. It is also shown that Fick's law cannot be applied to inhomogeneous or nonideal membranes.

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