The hydrodynamics of an inertial squirmer rod

Abstract

The hydrodynamic behavior of a two-dimensional elongated micro-swimmer (squirmer rod) in a bulk fluid is studied numerically with an immersed boundary-lattice Boltzmann method. The swimming Reynolds numbers, the number of the squirmers (squirmer is a self-propelled model to assemble the elongated micro-swimmer), and the relative distance between two adjacent squirmers' centers are, respectively, set being 0.05 ≤ Res ≤ 5, 2 ≤ i ≤ 8, and 0.75d ≤ s ≤ 1.5d (d is the diameter of the squirmer) to investigate the swimming speed, the power expenditure, and the hydrodynamic efficiency of the micro-swimmer. The results show that the swimming speed of the puller rod (a type of elongated micro-swimmers propelled from the front) increases monotonically with enhancing i. The pusher rod (a type of elongated micro-swimmers propelled from the rear) with more pushers i swims faster at Res ≤ 0.1, whereas it swims slower at Res > 0.1. The speed of the pusher rod increases monotonously with the decrease in the distance s, whereas a non-monotonous variation is found for the puller rod. Meanwhile, the more i or smaller s for the puller and pusher rods, the more power P they expend, and no appreciable distinction is found for their P at 0.05 ≤ Res ≤ 1. By continuing to increase Res (Res > 1), P increases monotonically for both the puller and pusher rods, and it is more appreciably for the pusher rods. Finally, the hydrodynamic efficiency η of the pusher rods increases monotonically with the translational Reynolds number ReU, in contrast to that of the puller rods, which decreases (ReU ≤ 1) and then increases (ReU > 1) with ReU. For the pusher rods at ReU > 1, the increasing ratio of η is proportional to ReU0.7. The higher η is found for the squirmer rods with smaller i or greater s.