Hydrodynamics of an Elliptical Squirmer

Abstract

In this paper the propulsion of elliptical objects (called squirmers) by imposed tangential velocity along the surface is studied. For a symmetric velocity distribution (a neutral squirmer), pushers (increased tangential velocity on the downstream side of the ellipse) and pullers (increased tangential velocity on the upstream side of the ellipse), the hydrodynamic characteristics, are simulated numerically using the immersed boundary-lattice Boltzmann method. The accuracy of the numerical scheme and code are validated. The effects of Reynolds number (Re) and squirmer aspect ratio (AR) on the velocity u*, power expenditure P* and hydrodynamic efficiency η of the squirmer are explored. The results show that the change of u* along radial direction r* shows the relation of u*~r*−2 for the neutral squirmer, and u*~r*−1 for the pusher and puller. With the increase of Re, u* of the pusher increases monotonically, but u* of the puller decreases from Re = 0.01 to 0.3, and then increases from Re = 0.3 to 3. The values of P* of the pusher and puller are the same for 0.01 ≤ Re ≤ 0.3; P* of the pusher is larger than that of the puller when Re > 0.3. η of the pusher and puller increases with increasing Re, but the pusher has a larger η than the puller at the same Re. u* and P* decrease with increasing AR, and the pusher and puller have the largest and least u*, respectively. The values of P* of the pusher and puller are almost the same and are much larger than those of the neutral squirmer. With the increase of AR, η increases for the neutral squirmer, but changes non-monotonically for the pusher and puller.