Mathematical model for analysis of mass transfer for immobilized cells in lactic acid fermentation

A new mathematical model is proposed to analyze the mass transfer behavior in lactic acid fermentation using immobilized cells entrapped in calcium alginate. The model is comprised of material balance equations for glucose, free lactic acid, and several ions. The dissociation rate of lactic acid (rdiss) is involved in the proposed equations. To solve the equations numerically, a modified calculating method is proposed. Through model analysis, the possible mass transfer behavior in the gel bead was discussed. The model is validated by comparisons with the experimental results obtained from batch and continuous fermentation. The simulations using the model were made to investigate the mass transfer limitation in the gel beads. The results showed that the cell density gradient was formed in the gel beads and it was caused by the accumulation of the inhibitory product (free lactic acid), not by substrate starvation. Moreover, unusual mass transfer behavior of lactate ion in the immobilization support was pointed out.