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Coupled Self-Organized Hydrodynamics and Stokes models for suspensions of active particles

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Title: Coupled Self-Organized Hydrodynamics and Stokes models for suspensions of active particles
Authors: Degond, P
Merino Aceituno, S
Vergnet, F
Yu, H
Item Type: Journal Article
Abstract: We derive macroscopic dynamics for self-propelled particles in a fluid. The starting point is a coupled Vicsek–Stokes system. The Vicsek model describes self-propelled agents interacting through alignment. It provides a phenomenological description of hydrodynamic interactions between agents at high density. Stokes equations describe a low Reynolds number fluid. These two dynamics are coupled by the interaction between the agents and the fluid. The fluid contributes to rotating the particles through Jeffery’s equation. Particle self-propulsion induces a force dipole on the fluid. After coarse-graining we obtain a coupled Self-Organised Hydrodynamics–Stokes system. We perform a linear stability analysis for this system which shows that both pullers and pushers have unstable modes. We conclude by providing extensions of the Vicsek–Stokes model including short-distance repulsion, finite particle inertia and finite Reynolds number fluid regime.
Issue Date: 1-Mar-2019
Date of Acceptance: 14-Jan-2019
URI: http://hdl.handle.net/10044/1/67129
DOI: https://dx.doi.org/10.1007/s00021-019-0406-9
ISSN: 1422-6928
Publisher: Springer (part of Springer Nature)
Journal / Book Title: Journal of Mathematical Fluid Mechanics
Volume: 21
Copyright Statement: © The Author(s) 2019. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
Sponsor/Funder: The Royal Society
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: WM130048
EP/M006883/1
EP/P013651/1
Keywords: Science & Technology
Physical Sciences
Technology
Mathematics, Interdisciplinary Applications
Mechanics
Physics, Fluids & Plasmas
Mathematics
Physics
Collective dynamics
Self-organization
Hydrodynamic limit
Alignment interaction
Vicsek model
Low Reynolds number
Jeffery's equation
Volume exclusion
Stability analysis
Finite inertia
Finite Reynolds number
COLLECTIVE MOTION
FLUID MODEL
LIMIT
DERIVATION
MECHANICS
physics.flu-dyn
math.AP
35L60, 35L65, 35P10, 35Q70, 82C22, 82C70, 82C80, 92D50
01 Mathematical Sciences
09 Engineering
02 Physical Sciences
General Mathematics
Publication Status: Published
Article Number: ARTN 6
Online Publication Date: 2019-01-31
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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