The effective reaction rate and diffusion coefficients for a two-phase medium

Abstract

The transport properties of a system composed of an ensemble of small particles moving in a two-phase medium are calculated. One phase is assumed to be finely dispersed in the other so that the homogeneous regions are small compared to the size of the system. The particles may diffuse and react (disappear) in either phase. The coarse-grained (effective) reaction rate and diffusion coefficients are calculated for arbitrary volume fractions of the two phases for various cases. The calculation utilizes the introduction of background rate and diffusion coefficients to motivate the definition of self- and local density fields. The introduction of these fields in conjunction with the assumption of the random distribution of the inclusions of one phase in the other leads to reasonable approximations for the effective transport coefficient for all volume fractions. The result of model calculations are presented.