Transport through a slab membrane governed by a concentration-dependent diffusion coefficient: Part II. The four time-lags for some particular D(C)

Expressions have been derived for the ‘adsorption’ (Lla(C0),L0a(C0)) and ‘desorption’ (L0d(C0),Lld(C0)) time-lags corresponding with 13 functional dependencies of the differential diffusion coefficient, D(C). A detailed analysis of the concentration dependence of the time-lags is given. The initial (C0 → 0) slope and curvature of a time-lag : (ingoing) concentration curve may be obtained from the corresponding limiting values of dD(C0)/dC0 and d2D(C0)/dC02. It is shown how the ‘desorption’ time-lags and ingoing ‘adsorption’ time-lag are related to the (experimentally) more readily determined outgoing ‘adsorption’ time-lag, Lla(C0) and may be evaluated using a master-plot of steady-state flux of diffusant, J∞(C0), against ingoing concentration, C0. The arithmetic mean of designated time-lag integral diffusion coefficients can, over a limited range of C0, approximate to the steady-state integral diffusion coefficient D̃(C0). This finding, combined with determination of the complementary J∞(C0) should allow an estimate of C0 to be made. Following upon experimental observations, attention has been directed towards the concentration dependence of ‘adsorption’ and ‘desorption’ time-lag ratios, Ra (C0) and Rd(C0) and of the arithmetic mean, RM(C0) = (1/2)[Ra(C0) + Rd(C0)]. Departures of RM(αC0) from the ideal value of 2 were not great and were hardly reflected in the corresponding larger variations of Ra(C0) and Rd(C0).