Abstract
The behavior of many heterogeneous systems in technology and in nature relies upon the relative rates of molecular diffusion and reaction in structures containing inhomogeneous distributions of reactive sites. In this study, Monte Carlo simulations are used to calculate rate constants for particle diffusion and reaction in immobilized cell systems as a function of cell reactivities, particle diffusivities in the cells and matrix, and spatial arrangement of cells. A variety of conditions are examined, ranging from instantaneous reactions to slow reaction cases. For highly reactive (diffusion-limited) conditions, spatially homogeneous distributions of cells exhibit the largest rate constants. An increase in the heterogeneity of the cell distribution dramatically decreases the rate constants. However, for conditions of low reactivity (reaction-limited), homogeneous and heterogeneous distributions of cells yield similar rate constants. The molecular diffusivity inside a cell can also influence the rate constant by altering the molecule residence time inside a cell; rate constants increase as diffusivities decrease.