Transport through a slab membrane governed by a concentration-dependent diffusion coefficient. Part I. The four time-lags: some general considerations

Abstract

Two (equivalent) sets of expressions have been derived for the four time-lags, L a l , L d 0, L d l , L a 0, associated with transport through a slab membrane under `simple' boundary conditions and with the diffusion coefficient, D, a function of the concentration, C, of the diffusing species. The individual sign and relative magnitudes of the time-lags have been determined. Order of magnitude has been derived for two particular classes of D( C): Class (A): D( C) a strictly-increasing function of C and Class (B): D( C) a strictly-decreasing function of C, thereby establishing the two time-lag sequences: ( A) L a 0<L d l<0<L d 0<L a l, ( B) L d l<L a 0<0<L a l<L d 0. The four time-lags have been employed to define four integral diffusion coefficients: D ̃ a L, D d L, D ̃ d L, D a L. Inequalities between these (time-lag) integral diffusion coefficients and the corresponding steady-state integral diffusion coefficient, D̃, have been investigated. For the particular Classes (A) and (B) functions considered, the sequences of time-lag moduli are: ( A) 2L d 0<|L d l|<|L a 0|<2L a l, ( B) 2L d 0>|L d l|>|L a 0|>2L a l.