Transport through a slab membrane governed by a concentration-dependent diffusion coefficient: Part IV. D( C)/ D0=1+( αC)− β( αC) 2

Abstract

Using the specific functional form D( C)/ D 0=1+( αC)− β( αC) 2 an investigation has been made of (isothermal) transport through a slab membrane under ‘simple’ boundary conditions and governed by a diffusion coefficient, D( C), which, with increasing concentration, at first increases, passes through a maximum value and finally decreases. The flux, integral diffusion coefficient and concentration profile characteristic of steady-state permeation have been evaluated; special attention has been paid to the positions of such profiles in relation to the corresponding linear distribution associated with a constant diffusion coefficient. The corresponding transient-state transport has been studied within a framework of the time-lag ‘early-time’ and ‘ t ’ procedures. Expressions for the ‘adsorption’ and ‘desorption’ time-lags are given. The concentration-dependence of these time-lags, of the (four) integral diffusion coefficients derived from them and of the arithmetic-mean time-lag ratios have been considered in some detail. The ‘early-time’ and ‘ t ’ finite-difference procedures have likewise been employed to derive four further integral diffusion coefficients, so enabling a comparison to be made of the nine integral coefficients pertaining to established experimental techniques. Particular interest attaches to the situation for which n≡ β( αC 0)=1 (where C 0 is the ingoing or upstream concentration of diffusant) resulting in D( C 0) being symmetrical about C 0/2. Some consideration has been given, in general, to features of transient-state transport when governed by a symmetrical D( C).