Finite Element Methods for Active Particles in Fluids

Abstract

The dynamics of active microparticles, such as phoretic or biological squirmers, results from the imposition of velocities and/or surface forces at the interface of the fluid-solid interaction problem. This allows the squirmer, which could be a ciliated microorganism or a Janus particle for example, to attain net displacements in low Reynolds number regimes. This problem involves large geometrical deformations of the domain, since the rigid-body motions of each squirmer are unknowns of the problem. We present a finite element method that admits general interface conditions for these particles and, contrary to popular boundary-element methods, works for both linear and nonlinear rheological models. Numerical examples are presented showing the effect of nonlinearities in the fluid rheology and in the dependence of the tangential force with the slip velocity at the interface.