On the angular velocity of a swirling spheroidal squirmer in a viscous fluid

The propulsion speed of spheroidal squirmers was obtained by Keller & Wu ( J. Fluid Mech. , 1977, vol. 80, p. A31). It has become the benchmark to investigate the effect of shape on the propulsion of ciliated microorganisms. However, their study focused on translational motion whereas many biologically relevant organisms also experience rotational (or swirling) motion. We derive an analytical expression for the angular velocity of a swirling spheroidal squirmer. Our analysis reveals that spheroidal squirmers rotate faster than their spherical counterparts in Newtonian fluids. We also determine the contribution of the second azimuthal mode to the power dissipation generated by a spheroidal squirmer, and uncover a behaviour uniquely distinct from the power dissipation of a strictly translating swimmer.