Evolution of coagulating systems

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 co(t) and t, where co(t) is the concentration of coagulating particles consisting of g monomers and t is a dimensionless time, new variables τ = f0tc1(t′)dt′ and νg(τ) = cgc1 are introduced. These ν9 are then expanded in powers of τ. This expansion has the convergence radius τ1 ⩾ τ0 = f0∞c1(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.