Drag reduction of a sphere with oscillation in pseudo-plastic fluid

A force acting on a spherical particle or bubble moving in pseudo-plastic fluid is numerically investigated. The sphere motion is characterized by prescribed translational and oscillating velocities. The unsteady Stokes equation together with the power-law viscosity $\mu=K\dot{\gamma}^{n-1}$ (here, $K$ is the consistency factor, $\dot{\gamma}$ is the shear rate, and $n$ is the power index) is solved by a finite-difference approach with varying $n$ and the oscillation amplitude $A$. With increasing $A$, the time-averaged drag force reduces due to the enhanced shear-thinning effect. Such a drag reduction is more remarkable with decreasing $n$, and is arranged by two scaling relations for small $A$ and for large $A$. Examining the instantaneous and time-averaged velocity distributions, we discuss the relevance of the Stokes boundary layer near the sphere surface and the nearly irrotational velocity in the bulk.