Migration and rheotaxis of elliptical squirmers in a Poiseuille flow

Abstract

The migration and rheotaxis of elliptical squirmers (a swimmer self-propels by imposing a given tangential velocity at its surface) in a Poiseuille flow are simulated numerically. The phase diagrams are employed to illustrate the effect of the aspect ratio ([Formula: see text]) and the Reynolds number of the squirmer ([Formula: see text]), the self-propelling strength ([Formula: see text]), and the blockage ratio ([Formula: see text]) on the stable movement and orientation evolution of the elliptical squirmers. Five typical migration modes (including the stable sliding, periodic tumbling, damped swinging, periodic swimming, and chaotic migrating modes) and three rheotaxis states (including the stable, sub-stable, and unstable states) are identified. This pattern also exists for the locomotion of a pair of squirmers. It is found that, with increasing [Formula: see text] and [Formula: see text] or [Formula: see text] and [Formula: see text], the squirmers migrate in the more stable modes and rheotaxis states. With increasing Rep ([Formula: see text]), this pattern can also be found when the locomotion of two squirmers is considered, but it shows the opposite effect for an individual squirmer. In addition, a squirmer with a smaller AR is more easily to be trapped by the sidewall with [Formula: see text] because it is difficult to orient. Accordingly, a larger AR yields a migration, which is more easily along the centerline of the flow with [Formula: see text]. It is interesting that the squirmers with AR = 0.2 almost maintain upstream oriented as they are usually attracted by the sidewall.

Motion characteristics of squirmers in linear shear flow

“…Additionally, the fluid dynamics of squirmers have been studied in various fluidic conditions, including under gravitational influence at low Reynolds numbers (Rühle and Stark 2020), at intermediate Reynolds numbers (Dombrowski et al 2022), and in proximity to surfaces (Shen et al 2018). In a recent study, Liu et al (2022) utilized the lattice Boltzmann method (LBM) to examine the migration and rheology of elliptical swimmers in Poiseuille flow, identifying five distinct migration modes and three rheological states. Collectively, these studies affirm that swimmers demonstrate a rich array of complex behaviors across different fluid environments.…”

Study of sedimentation characteristics of an elliptical squirmer in a vertical channel

“…This is especially true for lattice Boltzmann method, where, after all, it is a relatively straightforward task to modify the 2D code to handle 3D simulations. In addition, previous studies [38,39,42,43,45,46] have shown that the essence of the phenomenon remains unchanged even when the dimensionality is reduced. Moreover, comparing 2D simulation results with 3D simulation results can also help us to understand the effect of dimensionality.…”

“…In addition, as the aspect ratio of the elliptical squirmer increases, the hydrodynamic efficiency of the neutral squirmer increases, whereas the variations of the pusher and puller are not monotonic. Subsequently, Liu et al [43] numerically simulated the migration and rheological properties of elliptical squirmer in a Poiseuille flow and identified five typical migration modes and three rheological states. The migration modes were stable sliding, periodic tumbling, damped swinging, periodic swimming, and chaotic migrating, and the rheological states were stable, sub-stable, and unstable.…”