Lift on a Moving Sphere Near a Plane Wall in a Second Order Fluid

In this paper we examine the lift on a sphere moving very close to an infinite plane wall in 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 gap between the sphere and the wall is small. For a moving particle in a shear flow, the ratio of the elastic lift to the buoyant weight of the particle is proportional to the particle radius, such that smaller particles will be easier to be suspended. We also found that the ratio of the inertial lift to the elastic lift is proportional to the square of the particle radius. 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 be always suspended from a smooth surface.