Immobilized particles in gel matrix-type porous media. Homogeneous porous media model

Diffusion in pure gels and gels with immobilized cells was analyzed. A mode l of diffusion assuming a homogeneous cell distribution in gel was improved by introducing a tortuosity value. By theoretical analysis and numerical m odeling it was shown that the tortuosity of a gel with immobilized cells is the product of two factors: (1) tortuosity generated by the cells, T-c, an d (2) tortuosity of the gel matrix, T-g, both variables being a function of cell volume fraction, phi (c). Total tortuosity is thus T-Sigma = TcTg. On the basis of this approach, it was possible to analyze diffusivity data fo r gels with immobilized cells. It was shown that, in these systems, the dif fusivity eta = D-e/D-0 is a complex function of (1) diffusivity in the gel, eta (g), and (2) diffusivity in immobilized cells, eta (c). The developed model allowed for the description of the dependence of D-e/D-o on phi (c). Comparison with numerous published experimental data showed a good fit. Obs erved deviations might be explained by nonhomogeneous cell distributions in side the gel matrix.