Steady state permeation through the membrane with different conditions on the inlet and outlet surfaces is considered. General equations with respect to the permeation flux and concentrations have been obtained. The permeation rate depends only on two dimensionless parameters, characterizing the rate of the bulk diffusion with respect to the rates of surface processes on the outlet and inlet sides: W2 = K2Lce/D and W1 = K1Lce/D. Three limit regimes of permeation through asymmetric membrane were characterized: diffusion limited regime DLR, outlet surface limited regime OLR, and inlet surface limited regime ILR. Permeation in OLR is limited by recombination on the outlet side. Permeation in ILR is limited by absorption on the inlet side. ILR has two modes ILR1 and ILR2, which differ by profile features. The boundaries between the regimes in the space of W1 and W2 values have been found. The approximation formulas for concentrations and permeation fluxes have been obtained for all the four limit modes of permeation. The permeation rate in the DLR is the upper limit of permeation through the membrane. The permeation rate through the asymmetric membrane does not depend on the permeation direction in all limit cases. But in intermediate cases (permeation is neither diffusion limited, nor surface limited) the permeation rate through the same membrane depends on the direction of the permeation: the permeation rate is higher if the inlet side has a smaller W value.
The work was supported by ISTC Grant 2805.
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