Immobilised particles in gels : homogeneous porous media model - Mota, M. (2001)
A model of diffusion assuming a homogeneous cell distribution in a gel was improved by considering the effect of tortuosity. By theoretical analysis and numerical modeling it was shown that the tortuosity of a gel with immobilised cells is the product of two factors: 1) tortuosity generated by the cells, T_c, and 2) tortuosity of the gel matrix, T_g, both variables being a function of cell volume fraction, Φ_c. Total tortuosity is thus T_Σ= T_c∙T_g. Based on this approach, it was possible to analyse diffusivity data for gels with immobilised cells. It was shown that, in these systems, the diffusivity η= D_e/D_o is a complex function of: 1) diffusivity in gel, η_g and 2) diffusivity in immobilised cells, η_c. The developed model allowed for the description of the dependence of D_e/D_o on Φ_c. Comparison with numerous published experimental data showed a good fit of the developed model. Observed deviations might be explained by non-homogeneous cell distributions inside the gel matrix.