Slip-shear and inertial migration of finite-size spheres in plane Poiseuille flow

Abstract

The effect of the slip-shear as well as the rotation on the inertial migration of finite-size spheres with blockage ratio (ratio of the sphere diameter to the channel gap) 0.2 are investigated in a plane Poiseuille flow at Re=100–500 using dissipative particle dynamics simulations, by means of changing the driving force, the sphere density, and the fluid-sphere boundary slip condition, respectively. Neutrally buoyant spheres with equal density with the fluid and with no-slip boundary condition are observed to equilibrated at lateral positions around midway between the channel centerline and the wall, and the positions move closer to the channel centerline with increasing Re. The spheres always lag behind the surrounding fluid. A correction to the slip is proposed by considering the effect of the distance between the sphere and the wall. A forward driving force or a larger density facilitates the forward motion of the spheres and leads to their leading relative to the surrounding fluid, which drives the spheres to lateral equilibrium positions close to the wall; and vice versa. All spheres rotate with angular velocities approximate to but a bit less than the half of the local fluid shear rate at the sphere centroid, no mater the spheres are neutrally or non-neutrally buoyant, expect the spheres much close to the wall. The lift induced by rotation is found one to two orders of magnitude less than the lift induced by slip-shear due to the small angular slip velocity between the sphere and the surrounding fluid; while the slip-shear-induced lift is found critical to determine the lateral equilibrium positions of finite-size spheres cooperating with the wall-induced lift and the shear-gradient-induced lift as Re varies. An empirical theory considering the last three lifts above mentioned is built, which interprets the relation between the slip-shear and the equilibrium positions of the spheres. Above relation holds for spheres with no-slip boundary condition, whilst for neutrally buoyant spheres with full-slip boundary condition, though they always lag behind the surrounding fluid, they migrate towards the wall as Re increases, as their hydrodynamic interactions with the fluid are changed.