Hydrodynamical characteristics of a pair of elliptical squirmers in a channel flow of power-law fluids

The locomotion state and motion type of elliptical squirmers in a channel flow of power-law fluids are simulated numerically. Three locomotion states (independent, coupled, related) and three types of motions (upstream, intermediate, downstream) for pairs of squirmers are found and identified. The effect of height difference (0.5 ~ 10) between the initial positions of two squirmers, aspect ratio (0.3 ~ 1.0), particle Reynolds numbers (0.5 ~ 10), self-propelling strength of the squirmers (− 9 to 9), and power-law index (0.4 ~ 1.5) of the fluid on the locomotion state and motion type of a pair of squirmers are explored, and the corresponding hydrodynamical characteristics are analyzed in detail. Head-to-head coupled structures and body-to-body coupled structures are observed for a pair of pullers and a pair of pushers, respectively. It is found that coupled structures are easy to be broken for squirmers with larger aspect ratio or larger particle Reynolds number and self-propelling strength. The movement characteristics of squirmers are closely related to the initial positions of squirmers in strong shear-thinning fluid, but not to the initial positions in strong shear-thickening fluid. The dependence of viscosity on shear will also significantly affect the flow velocity, thus changing the motion type of squirmers. Graphical Abstract