Modeling hydrodynamic self-propulsion with Stokesian Dynamics. Or teaching Stokesian Dynamics to swim

Abstract

We develop a general framework for modeling the hydrodynamic self-propulsion (i.e., swimming) of bodies (e.g., microorganisms) at low Reynolds number via Stokesian Dynamics simulations. The swimming body is composed of many spherical particles constrained to form an assembly that deforms via relative motion of its constituent particles. The resistance tensor describing the hydrodynamic interactions among the individual particles maps directly onto that for the assembly. Specifying a particular swimming gait and imposing the condition that the swimming body is force- and torque-free determine the propulsive speed. The body’s translational and rotational velocities computed via this methodology are identical in form to that from the classical theory for the swimming of arbitrary bodies at low Reynolds number. We illustrate the generality of the method through simulations of a wide array of swimming bodies: pushers and pullers, spinners, the Taylor=Purcell swimming toroid, Taylor’s helical swimmer, Purcell’s three-link swimmer, and an amoeba-like body undergoing large-scale deformation. An open source code is a part of the supplementary material and can be used to simulate the swimming of a body with arbitrary geometry and swimming gait.