A stochastic approach to colloidal particle collision/agglomeration

TL;DR

This paper introduces a stochastic modeling approach for colloidal particle collisions using Langevin processes, proposing a discretisation scheme and analyzing convergence, with numerical confirmation for both elastic and agglomeration scenarios.

Contribution

It presents a novel discretisation scheme for Langevin processes with specular reflection and absorption, along with a conjecture on convergence rates, validated numerically.

Findings

Numerical results confirm the conjectured convergence rates.

The scheme effectively models elastic and agglomeration collisions.

The approach advances stochastic simulation of colloidal interactions.

Abstract

Colloidal particles that experience perfectly elastic collisions can be modelled using Langevin processes with specular reflection conditions. The article presents a discretisation scheme and offers a conjecture for the rate of convergence of the bias produced. Numerically, these conjectures are confirmed for the specular reflection scheme but also for the absorption scheme, which models perfect agglomeration.