INERTIAL LIFT ON A MOVING SPHERE IN CONTACT WITH A PLANE WALL IN A SHEAR-FLOW

In this paper we calculate the Lift force on a smooth sphere rotating and translating in a simple shear flow in contact with a rigid wall. The calculation involves only known creeping flow solutions and is presented in terms of six different coefficients, each arising as a result of a pairwise combination of the translational velocity, rotational velocity, and the imposed shear flow. The results obtained agree well with those of Cherukat and McLaughlin [J. Fluid Mech. 263, 1 (1994a); and (personal communication, 19946)], extrapolated for the case of zero separation distance. The calculated lift is further integrated into a force and torque balance on a non-neutrally buoyant rough sphere moving in contact with a plane. It is found that if the shear Reynolds number Re is sufficiently large, the lift force exceeds the gravitational force and the sphere separates from the plane. The increased separation is accompanied by an increase in the translational velocity U of the sphere and a corresponding decrease in the lift force due to the negative shear-translation coefficient, ultimately resulting in the sphere acquiring some steady separation distance. The equilibrium separation distance and velocity are plotted as a function of the parameter Re-2/Re-s, where Re-s is the sedimentation Reynolds number. (C) 1995 American Institute of Physics.