Analytic model for the ballistic adsorption of polydisperse mixtures

TL;DR

This paper develops an analytical mean-field model for the ballistic adsorption of polydisperse sphere mixtures onto a line, providing solutions that match simulations and extend understanding of adsorption processes.

Contribution

It introduces an analytical kinetic equation approach for polydisperse mixtures, simplifying the substrate as effective particles of average size, and validates it against simulations.

Findings

Analytical solution agrees quantitatively with Monte Carlo simulations for binary mixtures.

Model captures qualitative behavior observed in higher-dimensional simulations.

Mean-field approximation effectively describes the adsorption process for polydisperse mixtures.

Abstract

We study the ballistic adsorption of a polydisperse mixture of spheres onto a line. Within a mean-field approximation, the problem can be analytically solved by means of a kinetic equation for the gap distribution. In the mean-field approach, the adsorbed substrate as approximated as composed by {\em effective} particles with the {\em same} size, equal to the average diameter of the spheres in the original mixture. The analytic solution in the case of binary mixtures agrees quantitatively with direct Monte Carlo simulations of the model, and qualitatively with previous simulations of a related model in $d=2$.