R. Ash et Se. Espenhahn, Transport through a slab membrane governed by a concentration-dependent diffusion coefficient. Part I. The four time-lags: Some general considerations, J MEMBR SCI, 154(1), 1999, pp. 105-119
Two (equivalent) sets of expressions have been derived for the four time-la
gs, L-l(a), L-0(d), L-l(d), L-0(a), associated with transport through a sla
b membrane under 'simple' boundary conditions and with the diffusion coeffi
cient, D, a function of the concentration, C, of the disusing species. The
individual sign and relative magnitudes of the time-lags have been determin
ed. 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 se
quences:
(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 coe
fficients: (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 th
e corresponding steady-state integral diffusion coefficient, (D) over bar,
have been investigated. For the particular Classes (A) and (B) functions co
nsidered, 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.
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