Lushnikov A A
Geophysical Center of Russian Academy of Science, 3, Molodezhnaya Street, 119296 Moscow, Russia and Karpov Institute of Physical Chemistry, 10 Vorontsovo Pole, 105064 Moscow, Russia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Mar;89(3):032121. doi: 10.1103/PhysRevE.89.032121. Epub 2014 Mar 19.
Gelation in a two component disperse system wherein binary coagulation governs the temporal changes of particle composition spectra is studied for the crossproduct coagulation kernel proportional to m1n2+m2n1, with m,n being the numbers of monomers of the first and the second component in the coalescing pair of particles. This model reveals the sol-gel transition, i.e., after a finite interval of time the conservation of the total particle mass concentration violates because of the formation of giant particles (the gel). This paper reports on the exact solution of this model for arbitrary initial particle composition spectra. Exact expressions for the particle composition spectrum, the gel mass, and the second moments of the composition distribution are derived. Two scenarios of gelation, where the gel is either active or passive, are considered.
研究了双组分分散体系中的凝胶化现象，其中二元凝聚控制着颗粒组成谱的时间变化，针对与m1n2 + m2n1成正比的交叉产物凝聚核进行研究，m、n分别为聚并颗粒对中第一和第二组分的单体数量。该模型揭示了溶胶-凝胶转变，即经过有限的时间间隔后，由于巨型颗粒（凝胶）的形成，总颗粒质量浓度的守恒被打破。本文报道了该模型对于任意初始颗粒组成谱的精确解。推导了颗粒组成谱、凝胶质量和组成分布二阶矩的精确表达式。考虑了凝胶化的两种情况，即凝胶是活性的还是非活性的。
