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The diffusion coefficients (D) for lactose and ethanol through calcium alginate gel beads were determined based on the mathematical approach of Fick's second law. Different experimental conditions were tested to evaluate the behavior of the diffusion coefficient of different concentrations of lactose and ethanol in Ca-alginate (3, 4, and 6) % at varying temperatures (298.15, 303.15, and 308.15) K. Results showed that diffusion coefficients were independent from the concentration of lactose and ethanol, as well as from the concentration of Ca-alginate. Diffusion coefficients were affected by temperature, increasing from 4.67·10–10 m2·s–1 to 6.96·10–10 m2·s–1 for lactose and from 1.46·10–10 m2·s–1 to 2.68·10–10 m2·s–1 for ethanol. These results can be used for the project and scaling up of immobilized bioreactors for the conversion of lactose into ethanol.

We investigated the kinetics of whey bioconversion into ethanol by Kluyveromyces marxianus in continuous bioreactors using the "accelerostat technique" (A-stat). Cultivations using free and Ca-alginate immobilized cells were evaluated using two different acceleration rates (a). The kinetic profiles of these systems were modeled using four different unstructured models, differing in the expressions for the specific growth (μ) and substrate consumption rates (r s), taking into account substrate limitation and product inhibition. Experimental data showed that the dilution rate (D) directly affected cell physiology and metabolism. The specific growth rate followed the dilution rate (μ≈D) for the lowest acceleration rate (a = 0.0015 h(-2)), condition in which the highest ethanol yield (0.52 g g(-1)) was obtained. The highest acceleration rate (a = 0.00667 h(-2)) led to a lower ethanol yield (0.40 g g(-1)) in the system where free cells were used, whereas with immobilized cells ethanol yields increased by 23 % (0.49 g g(-1)). Among the evaluated models, Monod and Levenspiel combined with Ghose and Tyagi models were found to be more appropriate for describing the kinetics of whey bioconversion into ethanol. These results may be useful in scaling up the process for ethanol production from whey.