Interaction of toroidal swimmers in Stokes flow.

A doughnut-shaped object supporting surface rotations was a hypothetical construct proposed by both Taylor and Purcell as a swimmer that would be able to propel itself in a Stokesian fluid because of the irreversibility of its stroke. Here we numerically examine the hydrodynamic interaction of pairs and trios of these free toroidal swimmers. First, we study the axisymmetric case of two toroidal swimmers placed in tandem, and show that a single torus of a corotating pair is more efficient than when it swims alone, but less efficient when paired with a counterrotating partner. Using a regularized Stokeslet framework, we study the nonaxisymmetric case of toroidal swimmers whose axes are initially parallel, but not collinear. These perturbed in tandem swimmers can exhibit qualitatively different trajectories that may, for instance, repel the swimmers or have them settle into a periodic state. We also illustrate interesting dynamics that occur for different initial configurations of three tori.