Swimming and mixing of an ellipsoidal squirmer in a viscoplastic fluid

Abstract

Viscoplastic fluids exhibit yield stress, beyond which they flow viscously, while at lower stress levels they behave as solids. Despite their fundamental biological and medical importance, the hydrodynamics of swimming in viscoplastic environments is still evolving. In this study, we investigate the swimming of an ellipsoidal squirmer and the associated tracer diffusion in a Bingham viscoplastic fluid. The results illustrate that neutral squirmers in viscoplastic fluids experience a reduction in swimming speed and an increase in power dissipation as the Bingham number increases, with swimming efficiency peaking at moderate Bingham numbers. As the aspect ratio of a squirmer increases, ellipsoidal squirmers exhibit significantly higher swimming speeds in viscoplastic fluids. The polar and swirling modes can either enhance or reduce swimming speed, depending on the specific scenarios. These outcomes are closely related to the confinement effects induced by the yield surface surrounding the swimmer, highlighting how both swimmer shape and swimming mode can significantly alter the yield surface and, in turn, modify the swimming hydrodynamics. In addition, this study investigates the influence of viscoplasticity on swimmer-induced diffusion in a dilute suspension. The plasticity enforces the velocity far from the swimmer to be zero, thus breaking the assumptions used in Newtonian fluids. The diffusivity reaches its maximum at intermediate aspect ratios and Bingham numbers, and increases with the magnitude of the squirmer's dipolarity. These findings are important to understand microscale swimming in viscoplastic environments and the suspension properties.