THE LIFT FORCE ON A SMALL SPHERE IN THE PRESENCE OF A WALL

The flow of a viscous fluid around a sphere is analysed using a perturbation scheme for a small-sphere Reynolds number when the sphere is sufficiently 'near' a solid wall that the correction due to the wall of the velocity in the inertial region is not negligible. The expansion is used to calculate the transverse force on a small sphere moving in a shearing flow near a wall. The calculation of the force reduced to solving an ordinary differential equation in the transverse direction for the Fourier transform in the other spatial directions of the transverse velocity. The resulting wall-induced lift force is smaller than the force in the same unbounded shear flow, and cannot change the direction of the lift force.