J. theor. Biol. (1977) 64, 237-251 Diffusion with Irreversible Chemical Reaction in Heterogeneous Media: Application to Oxygen Transport in Respiring Tissue PETER STROEVE Department of Physiology, University of Nijmegen, Nijmegen, The Netherlands (Received 15 July 1975, and in revisedform 28 January 1976) A heterogeneous model is proposed for determining transport in a two- phase medium where irreversible reaction takes place in the suspended phase but not in the continuous phase. The model is based on the classical approach of Maxwell for determining effective transport properties of heterogeneous media. The mathematical expressions are utilized for the theoretical study of oxygen transport in tissue. It is shown that the model is physically more realistic than the layered models of Tai & Chang (1974) which can only predict maximum and minimum values for the transport rate. Formation of anoxic conditions for oxygen-consuming cells inside a tissue are predicted. 1. Introduction The understanding of transport phenomena in heterogeneous media is an important problem in science. Heterogeneous media such as emulsions, dispersions, slurries and foams are frequently encountered in a variety of situations. Suspensions of cells, blood and tissues are notable examples of heterogeneous media in biological systems. Considerable theoretical work has been done to predict effective physical properties of heterogeneous media. The simplest type of system is a two-phase medium where a phase is dispersed or embedded in another continuous phase. Meredith & Tobias (1962) have reviewed the theoretical relations developed for such two-phase media. No chemical reactions were considered. The transport of oxygen into tissue is a more complicated problem because the oxygen is consumed as it diffuses into the heterogeneous tissue. The tissue can be considered to be composed of a two-phase system; cells suspended in the extracellular phase. The oxygen is consumed in the cells but not in the continuous phase. This is a problem of diffusion with irre- versible chemical reaction in heterogeneous media. It is desirable to obtain 237