Motion characteristics of squirmers in linear shear flow

Abstract

In this study, the two-dimensional lattice Boltzmann method was employed to simulate the motions and distributions of a circular squirmer in a linear shear flow. The objective was to systematically investigate the dynamics of microorganisms or engineered squirmers in a flowing environment. We conducted multiple simulations across a range of self-propelled strengths (0.08 ⩽ α ⩽ 0.8) and squirmer type parameters (−5 ⩽ β ⩽ 5). Initially, we analyzed the swimming motions of the neutral squirmer (β = 0) in the shear flow. Our analysis revealed two distinct distributions depending on α, i.e. near the bottom or the top plate, which differs from conventional particle behavior. Moreover, we observed that the separation point of these two distributions occurs at α_c = 0.41. The puller and pusher exhibit similarities and differences, with both showing a periodic oscillation pattern. Additionally, both types reach a steady inclined pattern near the plate, with the distinction that the low-pressure region of the puller’s head is captured by the plate, whereas the pusher is captured by the low-pressure region on the side of the body. The limit cycle pattern (LCP) is unique to the pusher because the response of the pressure distribution around the pusher to the flow field is different from that of a puller. The pusher starts from the initial motion and asymptotes to a closed limit cycle under the influence of flow-solid interaction. The frequency St of LCP is inversely proportional to the amplitude h ^* because the pusher takes longer to complete a larger limit cycle. Finally, an open limit cycle is shown, representing a swimming pattern that crosses the width of the channel.