A Lattice Boltzmann Model for Squirmers

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.

9 pages, 7 figures

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• Frequency-dependent higher-order Stokes singularities near a planar elastic boundary: implications for the hydrodynamics of an active microswimmer near an elastic interface
• Noisy Pursuit and Pattern Formation of Self-Steering Active Particles
• Simulating active agents under confinement with Dissipative Particles (hydro)Dynamics
• Gravity induced formation of spinners and polar order of spherical microswimmers on a surface