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Upstream swimming and Taylor dispersion of active Brownian particles

Peng, Zhiwei and Brady, John F. (2020) Upstream swimming and Taylor dispersion of active Brownian particles. Physical Review Fluids, 5 (7). Art. No. 073102. ISSN 2469-990X. https://resolver.caltech.edu/CaltechAUTHORS:20200708-093747683

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Abstract

Locomotion of self-propelled particles such as motile bacteria or phoretic swimmers often takes place in the presence of applied flows and confining boundaries. Interactions of these active swimmers with the flow environment are important for the understanding of many biological processes, including infection by motile bacteria and the formation of biofilms. Recent experimental and theoretical works have shown that active particles in a Poiseuille flow exhibit interesting dynamics including accumulation at the wall and upstream swimming. Compared to the well-studied Taylor dispersion of passive Brownian particles, a theoretical understanding of the transport of active Brownian particles (ABPs) in a pressure-driven flow is relatively less developed. In this paper, employing a small wave-number expansion of the Smoluchowski equation describing the particle distribution, we explicitly derive an effective advection-diffusion equation for the cross-sectional average of the particle number density in Fourier space. We characterize the average drift (specifically upstream swimming) and effective longitudinal dispersion coefficient of active particles in relation to the flow speed, the intrinsic swimming speed of the active particles, their Brownian diffusion, and the degree of confinement. In contrast to passive Brownian particles, both the average drift and the longitudinal dispersivity of ABPs exhibit a nonmonotonic variation as a function of the flow speed. In particular, the dispersion of ABPs includes the classical shear-enhanced (Taylor) dispersion and an active contribution called the swim diffusivity. In the absence of translational diffusion, the classical Taylor dispersion is absent and we observe a giant longitudinal dispersion in the strong flow limit. Our continuum theory is corroborated by a direct Brownian dynamics simulation of the Langevin equations governing the motion of each ABP.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevFluids.5.073102DOIArticle
https://journals.aps.org/prfluids/abstract/10.1103/PhysRevFluids.5.073102PublisherArticle
ORCID:
AuthorORCID
Peng, Zhiwei0000-0002-9486-2837
Brady, John F.0000-0001-5817-9128
Additional Information:© 2020 American Physical Society. Received 10 October 2019; accepted 1 June 2020; published 8 July 2020. This work is funded by NSF under Grant No. CBET 1803662.
Funders:
Funding AgencyGrant Number
NSFCBET-1803662
Issue or Number:7
Record Number:CaltechAUTHORS:20200708-093747683
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20200708-093747683
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:104270
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:08 Jul 2020 16:56
Last Modified:08 Jul 2020 16:56

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