Effect of heterogeneity on the lag time in onedimensional diffusion
Abstract
A new general equation has been developed for the lag time for a dilute diffusant permeating through a onedimensional membrane in which both diffusivity D and partition coefficient K are dependent on position. The lag time is given by t_{L}=∫^{h}_{0}K(x)[∫^{x}_{0} R(y)dy][∫^{h}_{x}R(y)dy] ×dx/ ∫^{h}_{0}R(x)dx, where h is the membrane thickness and R(x)=1/[D(x)K(x)]. Formulas derived from this equation include those for: lag time in the presence of an electrical potential gradient; lag time in a multilaminar periodic membrane; and an upper bound for lag time given by t_{L} <(h^{2}/ 4D_{eff}), where D_{eff} is the effective diffusivity as deduced from steadystate partitioning and permeability measurements. The lag time is shown to be independent of the direction of diffusion. A computational technique is presented in which the equation for t_{L} is rearranged to a system of two differential equations, which are readily solvable by numerical integration, even when the system has discontinuities in D and K which would increase the difficulty of evaluating the double integral directly.
 Publication:

Journal of Chemical Physics
 Pub Date:
 August 1988
 DOI:
 10.1063/1.455070
 Bibcode:
 1988JChPh..89.2278C