Coupling of diffusion and reaction in the process of capillary formation in alginate gel

• Published in: Chemical physics 2000-01, Vol.252 (1), p.199-208
• Main Authors: Treml, H., Kohler, H.-H.
• Format: Article
• Language: English
• ISSN: 0301-0104
• DOI: 10.1016/S0301-0104(99)00361-4

The formation of capillaries in a gel obtained by cross-linking alginate chains with divalent metal ions is caused by a microscopic hydrodynamic circular flow in the immediate neighborhood of the gel formation front. This flow is due to the contraction of the alginate chains accompanying the cross-linking reaction. In an earlier paper we have shown that capillary formation will occur above a critical value of the contraction velocity. The critical contraction velocity is determined by a number of parameters, such as the coefficient of friction between the contracting chains and the surrounding water, the viscosity of the fluid and the coefficient of convective transport. We show here that the latter depends on the gradient of the alginate concentration profile in front of the contraction zone. To establish a quantitative theory, the diffusional transport of the alginate chains and the divalent metal ions towards the contraction zone is investigated. The diffusive mass transport is described theoretically by a diffusion-reaction-model that is confirmed by the experimental data obtained for the alginate concentration profile in a long tube. As a final result the coefficient of convective transport is represented as a function of the bulk concentrations and the effective diffusion constants of the alginate and the metal ions.