# Kinetics of Deposition in the Diffusion-Controlled Limit

Source: [Kinetics of Deposition in the Diffusion-Controlled Limit](<https://www.sota2.com/research/paper/68fa38061e209131ce8b6e62>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-24T22:43:25.227Z

Authors: P. L. Krapivsky

Published: 2016-04-15T20:11:48.000Z

## 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.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1604.04633>)

[PDF](<https://arxiv.org/pdf/1604.04633.pdf>)