Simulating squirmers with volumetric solvers
This work provides a more general simulation tool for microswimmers, enabling studies of nonlinear fluid effects that were previously inaccessible.
The authors developed a volumetric simulation methodology for squirmers that overcomes limitations of boundary-element methods by handling fluid inertia and non-Newtonian rheology. They demonstrated its effectiveness with a 2D simulation of two Opalina ranarum individuals.
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.