Evolution of coagulating systems: III. Coagulating mixtures

Abstract Coagulation is considered of particles consisting of monomers of two kinds. Assuming the collision frequency to be dependent on the total masses of the colliding particles only, the complete solution to the kinetic equation describing time evolution of the composition distribution c(m, n;t) (m, n are numbers of monomers of the first and the second constituent) in terms of the generating function F(z,t) = ∑ g=1 ∞ C g (t)z g for the size distribution cg(t) and the initial generating function T o (x,y)=T(x,y;t=O) = ∑ m,n c(m,n;t=O)x m y n for the composition distribution is given. The result is F(x, y; t) = F(F0−1(F0(x, y)),t) with F0−1(z) being the inversion of F0(z) = F(z, t = 0). Expressions for the composition distribution, the total particle number, and the total mass with fixed concentration of the first constituent, are derived in terms of contour integrals of F(x, y; t). The results obtained are illustrated by two examples.