Counterdiffusion of lactose and lactic acid in κ-carrageenan/locust bean gum gel beads with or without entrapped lactic acid bacteria

Abstract

The effective diffusion coefficient ( D e) and equilibrium partition factor ( K p) for lactose and lactic acid in κ-carrageenan (2.75% w/w)/locust bean gum (0.25% w/w) (LBG) gel beads (1.5−2.0 mm diameter), with or without entrapped Lactobacillus casei subsp. casei (L. casei), were determined at 40°C. Results were obtained from transient concentration changes in well-stirred solutions of finite volume in which the beads were suspended. Mathematical models of unsteady-state diffusion into and/or from a sphere and appropriate boundary conditions were used to calculate effective diffusion coefficients of lactose and lactic acid from the best fit of the experimental solute concentration changes. The effective diffusivities of lactose and lactic acid were 5.73 × 10 −10 and 9.96 × 10 −10 m 2 s −1, respectively. Furthermore, lactic acid was found to modify gel structure since lactose diffusion characteristics ( D e and K p) differed significantly from an earlier study and in the literature. In gel beads heavily colonized with L. casei, the effective diffusion coefficients of lactose and lactic acid were respectively 17% and 24% lower than for cell-free beads. Partition coefficients also confirmed the obstruction effect due to the cells, and decreased from 0.89 to 0.79, and from 0.98 to 0.87, for lactose and lactic acid, respectively. External mass transfer was estimated by an unsteady-state model in infinite volume using the Biot number. The effect of external mass transfer resistance on D e results and the data reported in the literature are discussed.