(333c) High Order Mass Preserving Finite Volume Approach for Rennet-Induced Coagulation Equation

The coagulation of casein micelles caused by milk-clotting enzymes is a critical step in the dairy industry for cheese manufacture. During enzymatic coagulation of milk, three distinct but overlapping processes occur (a) enzymic proteolysis, (b) coagulation, and (c) gelation. This study presents a first ever numerical approach based on finite volume scheme for a enzyme-induced coagulation of casein micelles (first two phases). The finite volume scheme is mainly concerned with adhering to the mass preservation and developed on the assumption that the particles are concentrated on the mean of the cell. The key advantages of the new technique are its simple mathematical formulation, robust enough to be implemented on any type of grid and can be tailored for different coagulation kernels. Due to the non-availability of the exact (analytical) results of number density functions, the accuracy of the new approach is tested and verified against the newly derived analytical results for numerous gelling and non-gelling coagulation kernels. The comparison demonstrates that the new approach predicts the results with high precision and closely matches with the exact results. In order to analyse the convergence behaviour of different order moments, various refined non-uniform grids have been taken into consideration.