Inertial self-propulsion of spherical microswimmers by rotation-translation coupling

We study swimming of small spherical particles that regulate fluid flow on their surface by applying tangential squirming strokes. We derive translational and rotational velocities for any given stroke which is not restricted by axial symmetry as assumed usually. The formulation includes inertia of both the fluid and the swimmer, motivated by inertia's relevance for large Volvox colonies. We show that inertial contribution to mean speed comes from dynamic coupling between translation and rotation, which occurs only for strokes that break axial symmetry. Remarkably, this effect enables overcoming the scallop theorem on impossibility of propulsion by time-reversible strokes. We study examples of tangential strokes of an axisymmetric traveling wave and of asymmetric time-reversible flapping. In the latter case, we find that the inertia-driven mean speed is optimized for flapping frequency and the swimmer's size, which fall well within the range of realistic physical values for Volvox colonies. We conjecture that similarly to Paramecia, large Volvox could use time-reversible strokes for inertia-driven swimming coupled with their rotations.