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

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, phi(c). Total tortuosity is thus T(Sigma) = 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 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(0) on phi(c). Comparison with numerous published experimental data showed a good fit. Observed deviations might be explained by nonhomogeneous cell distributions inside the gel matrix.