On the growth of a particle coalescing in a Poisson distribution of obstacles

TL;DR

This paper rigorously derives a kinetic equation describing the coalescence dynamics of a tagged particle in a random obstacle field and proves the well-posedness of the particle system for small volume fractions.

Contribution

It provides a rigorous derivation of the kinetic equation for particle coalescence in a Poisson obstacle distribution and establishes well-posedness for small volume fractions.

Findings

Derived a kinetic equation for particle size and position distribution.

Proved well-posedness of the particle system for small volume fractions.

Validated the model for a compactly supported size distribution.

Abstract

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 $\phi$ filled by the background of particles tends to zero. Moreover, we prove that the particle system, i.e. CTP model, is well posed for a small but positive volume fraction with probability one as long as the the distribution of the particle sizes is compactly supported.