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.
Mota
M
M
Centro de Engenharia Biológica-IBQF, University of Minho, Campus de Gualtar 4710-057 Braga, Portugal. mmota@deb.uminho.pt
Teixeira
J A
JA
Yelshin
A
A
D018914:Cells, Immobilized; D004058:Diffusion; D005782:Gels / Q000737:chemistry*; D008956:Models, Chemical
D005782:Gels