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Trapping of an active Brownian particle at a partially absorbing wall
File(s)
ABP(preprint)R.pdf (520.5 KB)
Accepted version
Author(s)
Bressloff, Paul C
Type
Journal Article
Abstract
Active matter concerns the self-organization of energy consuming elements such as motile bacteria or self-propelled colloids. A canonical example is an active Brownian particle (ABP) that moves at a constant speed while its direction of motion undergoes rotational diffusion. When ABPs are confined within a channel, they tend to accumulate at the channel walls, even when inter-particle interactions are ignored. Each particle pushes on the boundary until a tumble event reverses its direction. The wall thus acts as a sticky boundary. In this article, we consider a natural extension of sticky boundaries that allow for a particle to be permanently absorbed (killed) whilst attached to a wall. In particular, we investigate the first passage time (FPT) problem for an ABP in a two-dimensional channel where one of the walls is partially permeable. Calculating the exact FPT statistics requires solving a non-trivial two-way diffusion boundary value problem. We follow a different approach by separating out the dynamics away from the absorbing wall from the dynamics of absorption and escape whilst attached to the wall. By using probabilistic methods, we derive an explicit expression for the mean first passage time of absorption, assuming that the arrival statistics of particles at the wall are known. Our method also allows us to incorporate a more general encounter-based model of absorption.
Date Issued
2023-05
Date Acceptance
2023-05-04
Citation
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2023, 479 (2273)
URI
URL
DOI
ISSN
1364-5021
Publisher
The Royal Society
Journal / Book Title
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume
479
Issue
2273
Copyright Statement
© 2023 The Author(s)

Published by the Royal Society. All rights reserved.
Identifier
http://dx.doi.org/10.1098/rspa.2023.0086
Subjects
01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Publication Status
Published
Date Publish Online
2023-05-31