Abstract
This paper is devoted to the study of some properties of solutions to the kinetic equation of coagulation. A simple transformation of the equation is proposed. Instead of c o ( t) and t, where c o ( t) is the concentration of coagulating particles consisting of g monomers and t is a dimensionless time, new variables τ = f 0 t c 1( t′) dt′ and ν g(τ) = c g c 1 are introduced. These ν 9 are then expanded in powers of τ. This expansion has the convergence radius τ 1 ⩾ τ 0 = f 0 ∞ c 1( t) dt and therefore determines the behavior of the size distribution in the interval 0 ⩽ t < ∞. Simple recurrence relations are obtained for the determination of the coefficients of the expansion. A scaling hypothesis adopted from the modern theory of second-order phase transitions is applied to establish the asymptotic form of size distributions at large g and t. Three exactly soluble models are used to demonstrate the possibilities of the proposed method.
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