Multi-species diffusion and reaction in biofilms and cellular media

In this paper we examine the problem of diffusion and reaction in biofilms and cellular systems when the reaction rate is limited by both a substrate and an electron acceptor. The intercellular kinetics is represented by a co nventional multiplicative expression for the reaction between the substrate and oxygen, and by a first-order endogenous respiration rate. The membrane transport process for substrate and oxygen occurs through two different me chanisms. The transport of the electron acceptor is described by a permeabi lity model while the transport of the substrate is treated in terms of a si mple carrier model. The microscopic (sub-cellular) description is used to d evelop an upscaled version of diffusion and reaction in biofilms and other cellular media. The effective diffusivity that appears in the macroscopic d escription is predicted by a closure problem. Solutions to this closure pro blem are presented for simplified geometries, and the effective diffusivity predicted by the theory is compared with experimental values. (C) 2000 Els evier Science Ltd. All rights reserved.