Inertial squirmer

Although the propulsion of micro-organisms has been extensively studied in the literature, current studies have mainly focused on their propulsion in the absence of inertia. Here in this paper, we quantify the effects of convective inertial forces in the limit of small, but nonzero, Reynolds number regime. We analytically quantify the role of inertia on swimming speed, energy expenditure, and flow signature of an archetypal swimming model “squirmer”. Our results suggest that pushers, generating thrust behind their body, have a competitive advantage in swimming due to higher motility in the inertial regime. In contrast, those organisms that generate thrust in front of their body, pullers, have more efficient foraging in the inertial regime compared to their counterparts in the Stokes regime. Inertia enhances the swimming speed of a pusher swimmer and hinders it for a puller, potentially affecting a broad range of abundant millimeter- to centimeter-size organisms living in oceans and lakes.