Abstract
The coagulation equation with kernelK ij =A+B(i+j)+C ij and arbitrary initial conditions is studied analytically and a simple expression for the solution is found. For monodisperse initial conditions, we recover the known size distribution expressed in terms of a degeneracy factorN k, which is determined by a recursion relation. For polydisperse initial conditions, a similar solution form is found, which includes a degeneracy factorN kl, also determined by a recursion relation. The physical meaning ofN kl and the recursion relation is given. A method to get explicit expressions forN k andN kl is illustrated. Finally, the pre-gel solution is given explicitly and a general method to get the post-gel solution is proposed.
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Lu, B. The evolution of the cluster size distribution in a coagulation system. J Stat Phys 49, 669–684 (1987). https://doi.org/10.1007/BF01009352
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DOI: https://doi.org/10.1007/BF01009352