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Stirring by periodic arrays of microswimmers

de Graaf, Joost and Stenhammar, Joakim LU (2017) In Journal of Fluid Mechanics 811. p.487-498
Abstract

The interaction between swimming micro-organisms or artificial self-propelled colloids and passive (tracer) particles in a fluid leads to enhanced diffusion of the tracers. This enhancement has attracted strong interest, as it could lead to new strategies to tackle the difficult problem of mixing on a microfluidic scale. Most of the theoretical work on this topic has focused on hydrodynamic interactions between the tracers and swimmers in a bulk fluid. However, in simulations, periodic boundary conditions (PBCs) are often imposed on the sample and the fluid. Here, we theoretically analyse the effect of PBCs on the hydrodynamic interactions between tracer particles and microswimmers. We formulate an Ewald sum for the leading-order... (More)

The interaction between swimming micro-organisms or artificial self-propelled colloids and passive (tracer) particles in a fluid leads to enhanced diffusion of the tracers. This enhancement has attracted strong interest, as it could lead to new strategies to tackle the difficult problem of mixing on a microfluidic scale. Most of the theoretical work on this topic has focused on hydrodynamic interactions between the tracers and swimmers in a bulk fluid. However, in simulations, periodic boundary conditions (PBCs) are often imposed on the sample and the fluid. Here, we theoretically analyse the effect of PBCs on the hydrodynamic interactions between tracer particles and microswimmers. We formulate an Ewald sum for the leading-order stresslet singularity produced by a swimmer to probe the effect of PBCs on tracer trajectories. We find that introducing periodicity into the system has a surprisingly significant effect, even for relatively small swimmer–tracer separations. We also find that the bulk limit is only reached for very large system sizes, which are challenging to simulate with most hydrodynamic solvers.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
computational methods, micro-organism dynamics, Navier–Stokes equations
in
Journal of Fluid Mechanics
volume
811
pages
12 pages
publisher
Cambridge University Press
external identifiers
  • scopus:85027917816
  • scopus:85004097291
  • wos:000390352200024
ISSN
0022-1120
DOI
10.1017/jfm.2016.797
language
English
LU publication?
yes
id
796c9e57-2dc7-41b0-b1a7-bb9d453d79ea
date added to LUP
2016-12-23 08:03:15
date last changed
2018-01-07 11:42:25
@article{796c9e57-2dc7-41b0-b1a7-bb9d453d79ea,
  abstract     = {<p>The interaction between swimming micro-organisms or artificial self-propelled colloids and passive (tracer) particles in a fluid leads to enhanced diffusion of the tracers. This enhancement has attracted strong interest, as it could lead to new strategies to tackle the difficult problem of mixing on a microfluidic scale. Most of the theoretical work on this topic has focused on hydrodynamic interactions between the tracers and swimmers in a bulk fluid. However, in simulations, periodic boundary conditions (PBCs) are often imposed on the sample and the fluid. Here, we theoretically analyse the effect of PBCs on the hydrodynamic interactions between tracer particles and microswimmers. We formulate an Ewald sum for the leading-order stresslet singularity produced by a swimmer to probe the effect of PBCs on tracer trajectories. We find that introducing periodicity into the system has a surprisingly significant effect, even for relatively small swimmer–tracer separations. We also find that the bulk limit is only reached for very large system sizes, which are challenging to simulate with most hydrodynamic solvers.</p>},
  author       = {de Graaf, Joost and Stenhammar, Joakim},
  issn         = {0022-1120},
  keyword      = {computational methods,micro-organism dynamics,Navier–Stokes equations},
  language     = {eng},
  pages        = {487--498},
  publisher    = {Cambridge University Press},
  series       = {Journal of Fluid Mechanics},
  title        = {Stirring by periodic arrays of microswimmers},
  url          = {http://dx.doi.org/10.1017/jfm.2016.797},
  volume       = {811},
  year         = {2017},
}