A Lattice Boltzmann Model for Squirmers

TL;DR

This paper develops a lattice Boltzmann model for simulating microswimmers called squirmers, demonstrating its accuracy and resolution requirements through various hydrodynamic tests and comparing it with other solvers.

Contribution

The paper introduces a lattice Boltzmann approach for modeling squirmers, highlighting the necessary grid resolution and validating it against established hydrodynamic results.

Findings

LB method accurately captures far-field flow and interactions.

High grid resolution is essential for near-field accuracy.

The model aligns well with other hydrodynamic solvers.

Abstract

The squirmer is a simple yet instructive model for microswimmers, which employs an effective slip velocity on the surface of a spherical swimmer to describe its self-propulsion. We solve the hydrodynamic flow problem with the lattice Boltzmann (LB) method, which is well-suited for time-dependent problems involving complex boundary conditions. Incorporating the squirmer into LB is relatively straight-forward, but requires an unexpectedly fine grid resolution to capture the physical flow fields and behaviors accurately. We demonstrate this using four basic hydrodynamic tests: Two for the far-field flow---accuracy of the hydrodynamic moments and squirmer-squirmer interactions---and two that require the near field to be accurately resolved---a squirmer confined to a tube and one scattering off a spherical obstacle---which LB is capable of doing down to the grid resolution. We find good agreement with (numerical) results obtained using other hydrodynamic solvers in the same geometries and identify a minimum required resolution to achieve this reproduction. We discuss our algorithm in the context of other hydrodynamic solvers and present an outlook on its application to multi-squirmer problems.