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 (A R = 0.2 - 1.0) and the Reynolds number of the squirmer (R e p = 0.05 - 4.0), the self-propelling strength (β = - 11 to 9), and the blockage ratio (κ = 0.09 - 0.25) 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 | β | and β ≥ 5 or β ≤ - 11 and κ ≥ 0.21, the squirmers migrate in the more stable modes and rheotaxis states. With increasing Rep (R e p ≥ 2.5), 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 y e q / H = 0.18, θ e q / π = 1.5 because it is difficult to orient. Accordingly, a larger AR yields a migration, which is more easily along the centerline of the flow with y e q / H = 0.5, θ e q / π = 1.0. It is interesting that the squirmers with AR = 0.2 almost maintain upstream oriented as they are usually attracted by the sidewall.