Kinetics of Deposition in the Diffusion-Controlled Limit

TL;DR

This paper investigates the kinetics of particle deposition on substrates in diffusion-controlled limits, deriving asymptotic behaviors for different particle shapes and substrate dimensions, with implications for understanding adsorption processes.

Contribution

It provides a detailed analysis of the asymptotic deposition kinetics for various particle shapes and substrate dimensions in diffusion-controlled adsorption.

Findings

Coverage approaches saturation as t^{-1} for planar disks in 3D.

Different asymptotic behaviors for spherical and square particles.

Generalized results for substrates of various dimensions.

Abstract

The adsorption of particles diffusing in a half-space bounded by the substrate and irreversibly sticking to the substrate upon contacts is investigated. We show that when absorbing particles are planar disks diffusing in the three-dimensional half-space, the coverage approaches its saturated jamming value as $t^{-1}$ in the large time limit [generally as $t^{-1/(d-1)}$ when the substrate is $d$ dimensional and $d>1$, and as $e^{-t/\ln(t)}$ when $d=1$]. We also analyze the asymptotic behavior when particles are spherical and when particles are planar aligned squares.