Immobilized particles in gel matrix-type porous media. Nonhomogeneous cell distribution

The conventional random pore model assumes a homogeneous cell distribution in the gel matrix used to immobilize cells. However, the validity of this model is restricted to values of the exponent alpha, between 1.8 and 2.25, of a model power function relating the diffusivity coefficient in the matrix with the overall cell volume fraction in the system. Based on the analysis of published data for diffusion in gels with immobilized cells and on the homogeneous approach for the random pore model developed in a previous work, a new, nonhomogeneous approach is proposed for alpha values outside the range 1.8-2.25. To explain these data, two main types of nonhomogeneous cell distribution were considered: (1) nonhomogeneous cell distribution in the gel for alpha > 2.25 (type 1) and (2) nonhomogeneity related with anisotropy of cell space orientation when alpha < 1.8 (type 2). In the case of nonhomogeneity of type 1, the cell volume fraction in the layers occupied by cells must be considered in place of the concept previously used for homogeneous distribution, viz., the average cell volume fraction. This model underlines that accumulation of cells in a thin layer close to the surface improves their nutrient intake. For nonhomogeneity of type 2, the tortuosity of such a system is smaller than should be expected if spherical cells were considered, thereby changing the effective diffusion. The model proposed in this work proved to fit into several real cases reported in the literature.