Coupled Self-Organized Hydrodynamics and Stokes models for suspensions of active particles
File(s)Degond2019_Article_CoupledSelf-OrganizedHydrodyna.pdf (989.33 KB)
Published version
Author(s)
Degond, Pierre
Merino Aceituno, Sara
Vergnet, Fabien
Yu, Hui
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.
Date Issued
2019-03-01
Date Acceptance
2019-01-14
Citation
Journal of Mathematical Fluid Mechanics, 2019, 21
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
The Royal Society
Engineering & Physical Science Research Council (EPSRC)
Engineering & Physical Science Research Council (EPSRC)
Grant Number
WM130048
EP/M006883/1
EP/P013651/1
Subjects
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
Date Publish Online
2019-01-31