Inertial swimming in a channel filled with a power-law fluid

Abstract

We employ an immersed boundary-lattice Boltzmann (IB-LB) scheme to simulate a cylindrical (a classical self-propelled model) and a rod-shaped squirmer swimming in a channel filled with power-law fluids. The power-law index n, the channel blocking ratio κ (squirmer diameter/channel width), and the swimming Reynolds number Re are, respectively, set at 0.8 ≤ n ≤ 1.2, 0.2 ≤ κ ≤ 0.5 and 0.05 ≤ Re ≤ 5 to investigate the microswimmer' swimming speed, its power expenditure (P), and its hydrodynamic efficiency (η). The results show that increasing n yields a faster squirmer at a low Re (Re ≤ 0.5). On further increasing Re (Re ≥ 1), a larger n results in a slower pusher (a squirmer propelled from the rear), or a faster puller (a squirmer propelled from the front). Increasing the channel's width (decreasing κ) can lead to a slower puller or a puller rod squirmer. A definition of puller/pusher will be provided later. It is also found that, with shear-thinning, it is easier to unstabilize a puller than with shear-thickening, when increasing Re. Swimming in a shear-thinning fluid expends more power P than in a shear-thickening fluid, and P is scaled with Re according to P ∼ Ren-1 (0.05 ≤ Re ≤ 1). In addition, a stronger channel constraint (κ = 0.5) yields a higher η for the puller and the weak inertial pusher, whereas a weaker channel constraint (κ = 0.2) results in a higher η for the pusher with the increased fluid inertia.

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