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' (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 dD(C-0)/dC(0) and d(2)D(C-0)/dC(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(infinity)(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 (D) over bar(Co). This finding, combined with determination of the complementary J(infinity)(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 Rd(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(alpha C-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). (C) 2000 Elsevier Science B,V. All rights reserved.