The coagulation of casein micelles caused by enzymes is a critical step in the dairy industry for cheese manufacture. During enzymatic coagulation of milk, three processes occur: enzymic proteolysis, coagulation, and gelation. This study presents the first numerical approach based on a finite volume scheme for describing the enzyme-induced coagulation of casein micelles. The finite volume scheme is mainly concerned with ensuring mass conservation and developed on the assumption that the particles are concentrated on the mean of each cell of the discretization. The key advantages of the new technique are its simple mathematical formulation and its robustness that allow it to be implemented on any type of grid and tailored to different coagulation kernels. The accuracy of the new approach is compared with newly derived analytical results for several gelling and non-gelling coagulation kernels. The comparison demonstrates that the new approach closely matches the exact results. In order to analyse the convergence behaviour of different order moments, various refined non-uniform grids have been taken into consideration.

中文翻译：

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用于凝乳酶诱导凝固方程的高效保质有限体积方法

由酶引起的酪蛋白胶束的凝固是乳制品工业中奶酪制造的关键步骤。在牛奶的酶促凝固过程中，发生三个过程：酶促蛋白水解、凝固和凝胶化。这项研究提出了第一个基于有限体积方案的数值方法，用于描述酶诱导的酪蛋白胶束凝固。有限体积方案主要涉及确保质量守恒，并基于粒子集中在离散化的每个单元的平均值上的假设而开发。这项新技术的主要优点是其简单的数学公式和鲁棒性，使其可以在任何类型的网格上实施并针对不同的凝固内核进行定制。将新方法的准确性与新得出的几种胶凝和非胶凝凝结颗粒的分析结果进行了比较。比较表明新方法与实际结果非常吻合。为了分析不同阶矩的收敛行为，考虑了各种细化的非均匀网格。