CALCULATION OF EFFECTIVE DIFFUSIVITIES AND REACTIVITIES IN IMMOBILIZED CELL SYSTEMS USING FINITE-DIFFERENCE METHODS

Immobilized cell systems typically consist of a single cell type encas ed in a semi-rigid polymer support. The rates at which nutrient molecu les diffuse and react in these materials determine the feasible longev ity and the amount of desirable product generated by the cells. Finite difference techniques were developed to calculate effective diffusivi ties and rates of reaction of small molecules in such immobilized cell systems. The structures analyzed consist of multiple cellular inclusi ons distributed in a continuous phase where molecules diffuse more slo wly in the cells than in the continuous phase. Diffusivities are in ex cellent agreement with available theoretical bounds. Under typical rea ctive conditions, the depth to which oxygen can penetrate ranges from 24-200 mu m, depending on the cell volume fraction, oxygen supply, and cellular uptake kinetics. Increases in the cell fraction beyond 0.55 yield minimal increases in the oxygen consumption rate, suggesting tha t such materials are limited by the diffusive supply of oxygen. (C) 19 98 Published by Elsevier Science Ltd. All rights reserved.