Kinetics of Deposition in the Diffusion-Controlled Limit

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.

8 pages, 2 figures

References in corpus (5)

• Entropic transport: Kinetics, scaling and control mechanisms
• Survival of a static target in a gas of diffusing particles with exclusion
• Narrow escape of interacting diffusing particles
• Boundary conditions in random sequential adsorption
• Survival of interacting diffusing particles inside a domain with absorbing boundary

Cited by in corpus (1)

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