The effective diffusion coefficient and the distribution constant for small molecules in calcium-alginate gel beads

The effective diffusion coefficient, D(e), and the distribution constant, K(i), for selected mono- and disaccharides and organic acids were determined in homogeneous calcium-alginate gel with and without entrapped bacteria. Results were obtained from transient concentration changes in well-stirred solutions of limited volume, in which the gel beads were suspended. The effective diffusioncoefficients and the distribution constants were estimated by fitting mathematical model predictions to the experimental data using a nonlinear model fitting program (MODFIT). Both single solute diffusion and multiple solute diffusion were performed. A small positive effect was obtained onthe values of D(e) for the system of multiple solute diffusion; however, the values of K(i) were not significantly influenced. For the nine solutes tested, D(e) for 2% Ca-alginate gel beads was found to be approximately 85% of the diffusivity measured in water. The effects on D(e) and K(i), for lactose and lactic acid were determined for variations of alginate concentration, pH, temperature, and biomass content in the beads. D(e) decreased linearly for both lactose and lactic acid with increasing cell concentration in the Ca-alginate gel. K(i), was constant for both lactose and lactic acid with increasing cell concentration. D(e) was significantly lower at pH 4.5 than at pH 5.5 and 6.5 for both lactose and lactic acid. Furthermore, D(e) seemed to decrease with increased alginate concentration in the range of 1% to 4%. The diffusion rate increased with increasing temperature, and the activation energy for the diffusion process for both lactose and lactic acid was constant in the temperature range tested. (c) 1995 John Wiley & Sons Inc.