Measurement of the inertial lift on a moving sphere in contact with a plane wall in a shear flow

Abstract

The translational and rotational velocities of a positively buoyant sphere suspended in a parallel plate device are measured, and related to the inertial lift of the sphere from the upper plate. The experimental results obtained agree well with the corrected theoretical predictions of Krishnan and Leighton [Phys. Fluids 7, 11 (1995)]. The motion of the sphere principally depends on the shear Reynolds number Re≡γ̇a2/ν, where γ̇ is the shear rate, a is the particle radius and ν the kinematic viscosity, and the sedimentation Reynolds number Res≡Usa/ν where Us is the Stokes sedimentation velocity of the sphere. The transition from translation without slip to translation with slip along the plane is observed to scale as Re/Res, and occurs at order 10−1. The separation of the sphere from the plane due to inertial lift at low Reynolds number is found to have the scaling Re2/Res, as predicted by theory. In experiments with two particles of diameter 1.5 and 2 mm in two glycerin/water solutions of different densities, the particles were found to lift off the plane at Re2/Res≈4. This value is consistent with measurements of the particle surface roughness.