A MODEL OF FACILITATED TRANSPORT IN CONCENTRATED TWO-PHASE DISPERSIONS

Abstract

Abstract A mathematical analysis is given of steady-state, reaction-enhanced diffusion through a heterogeneous medium consisting of a highly concentrated dispersion of quasi-spherical particles or cells suspended in a continuous phase. The paniculate or cellular phase is assumed to contain one or more mobile carrier species which undergo reversible homogeneous chemical reaction with several permeant species that are free to move in either phase. Thus, this type of system can serve as a model of facilitated transport in biological systems, such as oxygen transport in whole blood or in muscle tissue. The present work is addressed to the limiting case of rapid reaction with very large equilibrium enhancement and, hence, it provides something of a theoretical upper limit for the rate of transport in dispersions. In this limit, the main resistance to diffusional transport arises from the thin layers of extracellular phase separating individual cells and from the adjacent reaction boundary layers situated just inside the cells. We find that the asymptotic rates of transport are much smaller, in fact logarithmically so, than those predicted by simpler series-resistance models. By combining the asymptotic methods of Batchelor and O'Brien (1977) for ordinary conduction in concentrated dispersions with a previous general analysis of facilitated transport in homogeneous media (Schultz et al., 1974), a rather general formula is derived for the corresponding effective Fickian diffusivity of monodisperse, isotropic dispersions. The relevance to oxygen transport in blood and the possibility of non-Fickian diffusion are discussed.