Lattice-Boltzmann Simulations of Microswimmer-Tracer Interactions

TL;DR

This paper validates an efficient lattice-Boltzmann simulation method for modeling hydrodynamic interactions between microswimmers and tracers, highlighting its accuracy and limitations in low-Reynolds-number systems.

Contribution

It demonstrates the effectiveness of a force/counter-force lattice-Boltzmann algorithm in capturing swimmer-tracer hydrodynamics and discusses its limitations due to finite momentum transport.

Findings

LB algorithm reproduces far-field theoretical results accurately

Flow field smearing affects close swimmer-tracer interactions

Finite momentum transport time causes deviations from Stokes flow predictions

Abstract

Hydrodynamic interactions in systems comprised of self-propelled particles, such as swimming microorganisms, and passive tracers have a significant impact on the tracer dynamics compared to the equivalent "dry" sample. However, such interactions are often difficult to take into account in simulations due to their computational cost. Here, we perform a systematic investigation of swimmer-tracer interaction using an efficient force/counter-force based lattice-Boltzmann (LB) algorithm [J. de Graaf~\textit{et al.}, J. Chem. Phys.~\textbf{144}, 134106 (2016)] in order to validate its ability to capture the relevant low-Reynolds-number physics. We show that the LB algorithm reproduces far-field theoretical results well, both in a system with periodic boundary conditions and in a spherical cavity with no-slip walls, for which we derive expressions here. The force-lattice coupling of the LB algorithm leads to a "smearing out" of the flow field, which strongly perturbs the tracer trajectories at close swimmer-tracer separations, and we analyze how this effect can be accurately captured using a simple renormalized hydrodynamic theory. Finally, we show that care must be taken when using LB algorithms to simulate systems of self-propelled particles, since its finite momentum transport time can lead to significant deviations from theoretical predictions based on Stokes flow. These insights should prove relevant to the future study of large-scale microswimmer suspensions using these methods.