Coagulation with product kernel and arbitrary initial conditions: Exact kinetics within the Marcus-Lushnikov framework

TL;DR

This paper derives exact kinetic equations for coagulating particles with the product kernel from arbitrary initial conditions using an improved Marcus-Lushnikov approach, validated by numerical simulations.

Contribution

It provides an exact solution for the average particle number distribution over time for the coagulation process with arbitrary initial conditions.

Findings

Exact expression for average particle number derived

Validation through numerical simulations

Applicable to arbitrary initial mass spectra

Abstract

The time evolution of a system of coagulating particles under the product kernel and arbitrary initial conditions is studied. Using the improved Marcus-Lushnikov approach, the master equation is solved for the probability $W(Q,t)$ to find the system in a given mass spectrum $Q=\{n_1,n_2,\dots,n_g\dots\}$, with $n_g$ being the number of particles of size $g$. The exact expression for the average number of particles, $\langle n_g(t)\rangle$, at arbitrary time $t$ is derived and its validity is confirmed in numerical simulations of several selected initial mass spectra.