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Stirring by periodic arrays of microswimmers

Published online by Cambridge University Press:  13 December 2016

Joost de Graaf*
Affiliation:
Department of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, UK
Joakim Stenhammar
Affiliation:
Division of Physical Chemistry, Lund University, P.O. Box 124, S-221 00 Lund, Sweden
*
Email address for correspondence: j.degraaf@ed.ac.uk

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 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.

Type
Papers
Copyright
© 2016 Cambridge University Press 

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