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

Abstract

Expressions have been derived for the ‘adsorption’ ( L l a( C 0), L 0 a( C 0)) and ‘desorption’ ( L 0 d( C 0), L l d( C 0)) 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 ( C 0 → 0) slope and curvature of a time-lag : (ingoing) concentration curve may be obtained from the corresponding limiting values of d D( C 0)/d C 0 and d 2 D( C 0)/d C 0 2. 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, L l a( C 0) and may be evaluated using a master-plot of steady-state flux of diffusant, J ∞( C 0), against ingoing concentration, C 0. The arithmetic mean of designated time-lag integral diffusion coefficients can, over a limited range of C 0, approximate to the steady-state integral diffusion coefficient D̃( C 0). This finding, combined with determination of the complementary J ∞( C 0) should allow an estimate of C 0 to be made. Following upon experimental observations, attention has been directed towards the concentration dependence of ‘adsorption’ and ‘desorption’ time-lag ratios, R a ( C 0) and R d( C 0) and of the arithmetic mean, R M( C 0) = (1/2)[ R a( C 0) + R d( C 0)]. Departures of R M( αC 0) from the ideal value of 2 were not great and were hardly reflected in the corresponding larger variations of R a( C 0) and R d( C 0).