Theory of capillary formation in alginate gels

The formation of capillaries in alginate gel is a dissipative process coupled with hydrodynamic flow in the immediate neighborhood of the front of gel formation. The hydrodynamic flow is due to the contraction of the alginate chains resulting from the crosslinking reaction. As shown earlier, capillary formation only occurs above a critical value of the contraction velocity. In this paper a complete theoretical model of the ratio of the actual to the critical contraction velocity is presented. The theoretical predictions are compared with experimental data for the formation of copper alginate gel from solutions of sodium alginate and copper dichloride. The ratio of the actual to the critical contraction velocity is described as a function of the bulk concentrations. the diffusion coefficients, the properties of the alginate molecules and the rate constant of copper alginate complex formation. For capillary formation to occur, the rate constant must be neither too small nor too large. In agreement with experimental data the model predicts that capillary formation is restricted to a finite time interval and will not take place if the copper concentration is too low or the alginate concentration is too high. (C) 2003 Elsevier B.V. All rights reserved.