Lift on a sphere near a plane wall in a second-order fluid

Abstract

In this paper, we examine the lift on a sphere moving very close to an infinite plane wall in a shear flow of a second-order fluid. The sphere is allowed to both translate and rotate along the plane. We focus on the limit when the sphere touches the wall. We found that due to the normal stress effect, the flow gives rise to a positive elastic lift force on the sphere when the gap between the sphere and the wall is small. For a moving particle driven by shear flow, the ratio of the elastic lift to the buoyant weight of the particle is inversely proportional to the particle radius, such that smaller particles will be easier to suspend, in contrast to the result that the ratio of the inertial lift to the buoyant weight of the particle is proportional to the particle radius, such that the inertial lift does not suspend small particles. Furthermore, the elastic lift force is singular when the minimum gap between the sphere and the wall approaches zero. Consequently, a moving particle in a viscoelastic fluid will always be suspended from a smooth surface.