Gelation time in the discrete coagulation–fragmentation equations with a bilinear coagulation kernel
Gelation time in the discrete coagulation–fragmentation equations with a bilinear coagulation kernel
复制标题
具有双线性凝固核的离散凝固-破碎方程中的胶凝时间
DOI：
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发表时间：
2007
期刊：
影响因子：
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通讯作者：
H. V. Van Roessel
中科院分区：
文献类型：
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作者：
É. Brunelle;R. G. Owens;H. V. Van Roessel
本文研究了离散的双线性凝聚核凝聚-碎裂方程，该方程描述了经历二元反应的粒子团的演化。我们计算了纯凝聚方程的凝胶时间和凝胶后质量。提出了一种特征线法，数值求解了凝聚核和破碎速率为常数时矩母函数所满足的偏微分方程。数值方法的准确性进行了验证，通过比较的数值结果与一个精确的解决方案的单体数密度。对于一个给定的凝固率，破碎率的临界值，值大于导致质量守恒，确定。
The discrete coagulation–fragmentation equations with a bilinear coagulation kernel, describing the evolution of clusters of particles undergoing binary reactions, are studied. We compute the gelation time and post-gelation mass for the pure coagulation equation. A method of characteristics is developed to solve numerically the partial differential equation satisfied by a moment generating function for a product coagulation kernel and a constant fragmentation rate. The accuracy of the numerical method is verified by comparison of the numerical results with an exact solution for the number density of monomers. For a given coagulation rate, a critical value of the fragmentation rate, values greater than which lead to mass conservation, is identified.