Immobilized particles in gel matrix-type porous media: homogeneous porous media model

Abstract

Diffusion in pure gels and gels with immobilized cells was analyzed. A model of diffusion assuming a homogeneous cell distribution in gel was improved by introducing a tortuosity value. By theoretical analysis and numerical modeling it was shown that the tortuosity of a gel with immobilized cells is the product of two factors: (1) tortuosity generated by the cells, Tc, and (2) tortuosity of the gel matrix, Tg, both variables being a function of cell volume fraction. Total tortuosity is thus T=TcTg. On the basis of this approach, it was possible to analyze diffusivity data for gels with immobilized cells. It was shown that, in these systems, the diffusivity = De/D0 is a complex function of (1) diffusivity in the gel, and (2) diffusivity in immobilized cells. The developed model allowed for the description of the dependence of De/D0 on fi_c. Comparison with numerous published experimental data showed a good fit. Observed deviations might be explained by nonhomogeneous cell distributions inside the gel matrix.