A Squirmer Across Reynolds Numbers

The self-propulsion of a spherical squirmer – a model swimming organism that achieves locomotion via steady tangential movement of its surface – is quantified across small to large Reynolds numbers (Re) via numerical solution of the Navier-Stokes equations.  A fixed swimming stroke is considered.  We show that fluid inertia leads to profound differences in the locomotion of so-called pusher versus puller squirmers.  The swimming speed of a pusher increases monotonically with increasing Re.  In contrast, a puller first slows down with increasing Re and then speeds up. We show that the large Re flow around a pusher is essentially irrotational (akin to a spherical bubble), while a large vortical structure develops at the rear of a puller (akin to a no-slip sphere under an external force). Consequently, it is found that the steady axisymmetric locomotion of a pusher is stable to Re that far exceed that of a puller or even a no-slip sphere.  Additionally, we quantify fluid mixing at finite Re by a dilute collection of squirmers via the mechanism of drift diffusion. Here, we show that pullers, while less efficient swimmers, achieve a greater degree of mixing than pushers.