Optimizing numerical performance of enzymatic coagulation models: Insight into proteolysis and gelation dynamics

Cheese manufacturing from milk is a meticulous process that transforms casein micelles into various cheeses through enzymatic action and controlled steps. During enzymatic milk coagulation, three key processes occur: enzymatic proteolysis, coagulation, and gelation. Enzymatic proteolysis breaks down milk proteins, leading to coagulation, where the milk thickens. Gelation then forms a gel-like structure that separates curds from whey, essential for cheese production. To model the enzymatic coagulation of milk, a new mathematical framework is derived based on the conservative formulation of the coagulation equation. To solve this nonlinear complex model, an efficient numerical approach utilizing the finite volume scheme is developed. This method features a straightforward mathematical formulation and robustness for implementation on both uniform and nonuniform grids, enhancing its applicability across various scenarios compared to existing approaches [M. Tsagkaridis et al., “Analysis of turbulent coagulation in a jet with discretised population balance and DNS,” J. Fluid Mech. 937, A25 (2022)]. We also discuss the stability condition for the time step to ensure a positive solution. The validation of this new approach involves analyzing number density functions and their integral moments for different gelling and non-gelling kernels. Results indicate that the method captures zeroth and first-order moments with high precision while also computing second-order moments and average micelle sizes formed in the system. Additionally, the impact of the proteolysis constant on gelation is thoroughly examined. This comprehensive capability and detailed analysis provide deeper insight into the enzymatic coagulation process, facilitating its efficient optimization.