Solution of the discrete coagulation equation

Abstract

An approximate analytical solution of the discrete coagulation equation is obtained for an arbitrary initial distribution and a general form of the coagulation coefficient, βᵢⱼ = c₀ + Σ_(q=1)^Q c_q ƒ_(iq)g_(jq) that encompasses most of the forms used in practice. The classic Smoluchowski solution for monodisperse initial distribution and constant βij is thus extended. The approximate nature of the solution arises from the solution for the total number concentration N_∞(t), in which certain moments of the distribution must be assumed constant. In implementing the solution these moments can be updated as a function of time, so that the present solution can be viewed as an alternative to direct numerical solution of the coagulation equation.

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