Kinetics of Deposition in the Diffusion-Controlled Limit

P. L. Krapivsky

doi:10.1103/physreve.98.012119

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arXiv · 1604.04633

Kinetics of Deposition in the Diffusion-Controlled Limit

P. L. Krapivsky

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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.

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P. L. Krapivsky. 2018-07-12. Kinetics of Deposition in the Diffusion-Controlled Limit. https://doi.org/10.1103/physreve.98.012119

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