Abstract
The time evolution of a coagulating mixture in which binary coagulation governs the temporal changes to the particle mass and composition spectra is studied under the assumption that the coagulation kernel is proportional to the product of masses of the first and the second components in the coalescing particles. This model is shown to reveal the sol–gel transition, i.e., the formation of a cluster with mass comparable to the total mass of the whole system. This letter reports on the exact solution of this model. The evolution equation for the generating functional defining all properties of coagulating systems is solved exactly for this particular kernel. The single-particle mass spectrum is analysed in the thermodynamic limit and it is demonstrated how the gel appears in this mixed system.
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