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. 2013 Nov;88(5):052120. doi: 10.1103/PhysRevE.88.052120. Epub 2013 Nov 13.
The formation of a gel in a disperse coagulating system, wherein binary coagulation governs the temporal changes of the particle mass spectrum is studied for the coagulation kernel proportional to K(g,l)=gl with g,l being the numbers of monomers in the coalescing pair of particles. This model is known to reveal the sol-gel transition, i.e., the formation of one giant cluster with the mass comparable to the total mass of the whole system. This paper reports on some exact results that are valid for arbitrary initial particle mass spectra. The particle spectrum is shown to be expressed through a contour integral of the exponentiated initial generating function of the particle mass spectrum. The exact formula for the gel mass is derived for the scenario of passive gelation. Two scenarios of gelation, where the gel is either active or passive, are considered.
研究了分散凝聚系统中凝胶的形成，其中二元凝聚控制着粒子质谱的时间变化，所研究的凝聚核与(K(g,l)=gl)成正比，(g)和(l)分别是聚并粒子对中单体的数量。已知该模型揭示了溶胶-凝胶转变，即形成一个质量与整个系统总质量相当的巨型团簇。本文报道了一些对任意初始粒子质谱都有效的精确结果。粒子谱通过粒子质谱的指数化初始生成函数的围道积分来表示。推导了被动凝胶化情况下凝胶质量的精确公式。考虑了两种凝胶化情况，即凝胶是主动的还是被动的。
