Analytical solutions for composition-dependent coagulation (Q1792752)

Summary: Exact solutions of the bicomponent Smoluchowski's equation with a composition-dependent additive kernel \(K(v_a, v_b; v_a', v_b') = \alpha(v_a + v_a') +(v_b + v_b')\) are derived by using the Laplace transform for any initial particle size distribution. The exact solution for an exponential initial distribution is then used to analyse the effects of parameter \(\alpha\) on mixing degree of such bicomponent mixtures and the conditional distribution of the first component for particles with given mass. The main finding is that the conditional distribution of large particles at larger time is a Gaussian function which is independent of the parameter \(\alpha\).