Simulating squirmers with volumetric solvers

TL;DR

This paper introduces a volumetric simulation approach for squirmers, enabling the modeling of nonlinear fluid effects and complex interface conditions, advancing the study of microswimmer dynamics.

Contribution

It presents a novel volumetric numerical method for simulating squirmers, overcoming limitations of boundary-element methods and incorporating nonlinear fluid behaviors.

Findings

Successful 2D simulation of hydrodynamic interactions between Opalina ranarum individuals.

Generalized interface conditions for squirmers in volumetric methods.

Procedures for implementing the methodology in fluid solvers, including surface wave treatment.

Abstract

Squirmers are models of a class of microswimmers, such as ciliated organisms and phoretic particles, that self-propel in fluids without significant deformation of their body shape. Available techniques for their simulation are based on the boundary-element method and do not contemplate nonlinearities such as those arising from the fluid's inertia or non-Newtonian rheology. This article describes a methodology to simulate squirmers that overcomes these limitations by using volumetric numerical methods, such as finite elements or finite volumes. It deals with interface conditions at the squirmer's surface that generalize those in the published literature. The actual procedures to be performed on a fluid solver to implement the proposed methodology are provided, including the treatment of metachronal surface waves. Among the several numerical examples, a two-dimensional simulation is shown of the hydrodynamic interaction of two individuals of Opalina ranarum.