On the Growth of a Particle Coalescing in a Poisson Distribution of Obstacles

In this paper we consider the coalescence dynamics of a tagged particle moving in a random distribution of particles with volumes independently distributed according to a probability distribution (CTP model). We provide a rigorous derivation of a kinetic equation for the probability density for the size and position of the tagged particle in the kinetic limit where the volume fraction ϕ filled by the background of particles tends to zero. Moreover, we prove that the particle system, i.e., the CTP model, is well posed for a small but positive volume fraction with probability one as long as the distribution of the particle sizes is compactly supported.