Characterisation of the shrinkage of calcium alginate gel membrane with immobilised Lactobacillus rhamnosus

To quantify the shrinkage of calcium alginate gel membrane as a support matrix for immobilising cells during the fermentation of Lactobacillus rhamnosus, factors including time, pH, membrane thickness, and the concentrations of immobilised cells, lactic acid, glucose, and calcium chloride were examined by statistical experimental design. A Plackett-Burman design was used for the first screening experiment to identify the important factors which caused the divergent effects. Uniform Design, a powerful modelling design technique, was thus chosen to design the modelling experiments. Through a non-linear step-wise regression analysis, the predictive mathematical model of the shrinkage in membrane thickness was established and the significant main effects and two-factor interactions were identified. However, no significant model equations could be obtained for the shrinkage in area and volume of gel membranes. The methodology developed can be extrapolated to the quantitative characterisation of shrinkage in other immobilised gel matrices, which will be very useful in mathematical modelling, design, operation and scale-up of gel immobilised cell systems.