Migration of a micro-swimmer in a channel flow

Abstract

An immersed boundary-lattice Boltzmann (IB-LB) method is employed to investigate the migration of a two-dimensional cylindrical micro-swimmer in a channel flow. The swimming Reynolds numbers (Res), the flow Reynolds numbers (Rep), and the blockage ratios (κ) are respectively set being from 0.05 to 2.0, 40 to 160, and 0.11 to 0.5 in the simulations. A two-dimensional archetypal self-propelled model generating tangential surface waves is employed to mimic a micro-swimmer with different Res swimming in the presence of a channel flow with different Rep and κ, finding four typical locomotion modes, namely, the horizontal mode, the attracted oscillatory mode, the oscillatory mode, and the chaotic mode. At Rep = 100 and κ = 0.25, the squirmer displays an oscillatory motion even though at a lower Res (Res = 0.05), indicating a different migration behavior from that of a passive particle; With increasing Res, the horizontal or the attracted oscillatory mode develops to the oscillatory or the chaotic mode, showing a tendency of motion symmetrical concerning the centreline. On increasing Rep with Res = 0.1 and κ = 0.25, the squirmer with a lower swimming intensity |β| ≤ 1 maintains the attracted oscillatory mode, whereas the pusher (propelled from the rear) with β = −3 and the puller with β = 3 (propelled from the front) develop to the attracted oscillatory mode from the oscillatory and horizontal modes, respectively. At Rep = 100 and Res = 0.1, the squirmers with −3 ≤ β ≤ 0 and the puller with β = 5 respectively maintain the attracted oscillatory and the horizontal modes regardless of κ; On increasing κ, the horizontal mode for the pullers with 1 ≤ β ≤ 3 and the attracted oscillatory mode for the pusher with β = −5 develop to the attracted oscillatory and oscillatory modes, respectively. The transport velocity of the squirmer is also studied with the variations of Res, Rep, and κ, obtaining a maximum value for the neutral squirmer at Res = 1.5, Rep = 100, and κ = 0.25.