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

Two (equivalent) sets of expressions have been derived for the four time-lags, L-l(a), L-0(d), L-l(d), L-0(a), 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 disusing 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-0(a) < L-l(d) < 0 < L-0(d) < L-l(a), (B) L-l(d) < L-0(a) < 0 < L-l(a) < L-0(d). The four time-lags have been employed to define four integral diffusion coefficients: (D) over tilde(L)(a), (D) over bar(L)(d), (D) over tilde(L)(d), (D) over bar(L)(a). these (time-lag) integral diffusion coefficients and the corresponding steady-state integral diffusion coefficient, (D) over bar, have been investigated. For the particular Classes (A) and (B) functions considered, the sequences of time-lag moduli are: (A) 2L(0)(d) < \L-l(d)\ < \L-0(a)\ < 2L(l)(a), (B) 2L(0)(d) > \L-l(d)\> \L-0(a)\ > 2L(l)(a). (C) 1999 Elseiver Science B. V. All rights reserved.