The hydrodynamic behavior of a squirmer swimming in power-law fluid

Abstract

The hydrodynamic behavior of a squirmer swimming in the flow of power-law fluid is studied numerically with an immersed boundary-lattice Boltzmann method. The power-law fluids with three typical power-law indexes (n = 0.5, 1, and 1.5) are selected for embodying the characteristics of non-Newtonian fluid. The results show that, at zero Reynolds number, the squirmers swim slower in the shear-thinning fluid (n = 0.5) than in the Newtonian fluid (n = 1). The speed of squirmer swimming increases monotonically with the Reynolds number in the shear-thickening fluid (n = 1.5). When the fluid inertia is taken into account, the speed of a pusher (a kind of swimmer type) increases monotonically with the Reynolds number, while the speed of a puller (another kind of swimmer type) shows a non-monotonic increasing tendency. Some critical points, beyond which the pullers swim with lateral displacement, are obtained. The flow field and force distribution around the squirmer are calculated and analyzed. The power expenditure of squirmers in different kinds of flow is also studied. It is found that, as the Reynolds number increases, the power expenditure generally decreases in shear-thinning fluid, which is different from the case in Newtonian fluid and shear-thickening fluid. Finally, the hydrodynamic efficiency is introduced to compare the power expenditure of squirmers with that of a counterpart particle towing in the same type of fluid. Results show that the hydrodynamic efficiency of pushers increases with the Reynolds number, while the hydrodynamic efficiency of pullers shows non-monotonic behavior when the Reynolds number is varied.