Dynamic model for mass transfer of solutes in cucumber fermentation

A mathematical model for the mass transfer of solutes between whole cucumbers and brine in cucumber fermentation has been developed that takes into account permeation of solutes through stomata in the cucumber skin and through the epidermal cells in the skin, as well as film diffusion through the surrounding brine boundary layer. The model was used to fit experimental data for the time-dependent concentrations of solutes that permeate into the cucumbers (glucose and malate) and out of them (lactic acid, acetic acid, ethanol, and sodium chloride). The rate of lactic acid transport through the stomata was found to be three orders of magnitude greater than that through the epidermis, and the permeabilities of lactic and acetic acids were effectively independent of the brine circulation rate. These results indicate that the rate of permeation of solutes into and out of cucumbers was controlled by mass transfer through the stomata, with neither film diffusion nor epidermal diffusion having a significant effect. The model differential equation for solute transfer combined with a set of rate equations for microbial growth will provide a good basis to establish a complete mechanistic model for the cucumber fermentation process.