Stirring by periodic arrays of microswimmers

Joost de Graaf*, Joakim Stenhammar

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)487-498
Number of pages12
JournalJournal of Fluid Mechanics
Early online date13 Dec 2016
Publication statusE-pub ahead of print - 13 Dec 2016


  • computational methods
  • micro-organism dynamics
  • Navier–Stokes equations

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