Study on the interaction and motion patterns of squirmers swimming in a shear flow

Abstract

In order to study the dynamic characteristics of micro-organisms or engineered swimmers, the simulations of the motion and interaction of a pair of squirmers in a shear flow are conducted using the lattice Boltzmann method (LBM) in the range of squirmer-type factor −5 ≤ β ≤ 5, self-propulsion strength 0.1 ≤ α ≤ 0.8, initial spacing between two squirmers 0.5d ≤ d′ ≤ 3d (d is the diameter of the squirmers). The interactions and motion mechanisms of squirmers in puller–puller, pusher–pusher, puller–pusher, and pusher–puller configurations are analyzed. The results show that there are three typical motion patterns in the puller–puller configuration, i.e., steady tilting motion (STM), large-amplitude oscillation motion (LAO), and small-amplitude oscillation motion (SAO). The motion of pullers has a large vertical range, and the swimming angle continues to increase in the LAO, while the pullers oscillate near the plate and have a small range of changes in swimming angles in the SAO. The situation is more complex in the pusher–pusher configuration, and there are five motion patterns, i.e., STM, LAO, SAO, limit cycle motion (LCM), and open limit cycle motion (OLCM). Three different STMs are found according to the pressure distribution around the pushers. d′ is an important parameter affecting the interaction of squirmers. In the puller–puller configuration, the backflow area on the right side of puller 1 is completely suppressed when d′ = 0.5d, but this suppression gradually weakens as d′ increases. Changes in d′ result in the differences in the final motion patterns of pullers on the upper and low plates. In the pusher–pusher configuration, changes in d′ result in transitions between different motion patterns. There exist a critical swimming angle θc when d′ changes, and the pattern changes from the STM to the LCM when θ > θc. At d′ = 0.5d, in the puller–pusher configuration, there exists a stable structure formed by the mutual repulsion caused by the high pressure area between the puller and pusher. In the pusher–puller configuration, there is a low-pressure area on one side of the pusher, which attracts the low-pressure area on the head of the puller and affects their subsequent motion patterns.