Stirring by Periodic Arrays of Microswimmers

TL;DR

This paper investigates how periodic boundary conditions influence hydrodynamic interactions between microswimmers and tracers, revealing significant effects even at small separations and highlighting challenges in simulating large systems.

Contribution

It provides a theoretical analysis and Ewald sum formulation of the stresslet interactions under periodic boundary conditions, a topic less explored in prior work.

Findings

Periodic boundary conditions significantly affect tracer-swimmer interactions.

Bulk behavior only emerges at very large system sizes.

Simulating large systems with hydrodynamic solvers is computationally challenging.

Abstract

The interaction between swimming microorganisms 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 analyze 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.