Power efficiency of stress-driven squirmers: Influence of inertia and confinement on a swimmer in a conduit's centerline

In recent years, the study of self-propelled microorganisms has attracted attention from disciplines like physics, biology, and mathematics, among others. The squirmer was one of the first models proposed to describe the hydrodynamics of microswimmers, where the micro-organism is represented as a mobile sphere with an imposed tangential velocity on its surface. Originally devised for the Stokes regime—due to the size of microorganisms—this model has also been used to study the motion of larger swimmers under inertial conditions. In this work, we use the original squirmer model (called type I) and a variant in which the imposed velocity profile at the swimmer boundary is replaced by a tangential stress (type II model) to study the propulsion of a swimmer along the centerline of a cylindrical conduit. We led our study by solving numerically the axisymmetric Navier–Stokes and continuity equations, along with the equations accounting for the conservation of linear momentum of the squirmer. When unconfined, our results show that a type II squirmer is more power-efficient compared to the traditional squirmer model. Besides, inertialess squirmers of type II decrease their power expenditure with increasing confinement, in contrast to the increase observed in type I squirmers. Under inertial flow conditions, the power expenditure of strong pushers of either type is unaffected by confinement, while strong pullers of type I spend more power in keeping a given speed as they become more confined, while strong pullers of type II spend less power.