Wall effects on a sphere translating at constant velocity

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Abstract
We present experimental results on the modified Stokes force F exerted on a sphere in magnetic levitation whose position is kept fixed by an optical feedback system. A Newtonian liquid moves at a constant velocity U relative to the sphere. We consider the motion in two different situations.(i) When the sphere approaches a wall perpendicular to U, the increase in |F| due to lubrication agrees quantitatively with theoretical results such as those of Brenner (1961) and Maude (1961), obtained neglecting the unsteadiness of the flow field.(ii) In the complementary situation of a sphere moving along the axis of a cylindrical tube, our results expressed as a function of the eccentricity of the trajectory and of the ratio of the two radii confirm and extend previous theoretical analyses. They show in particular the existence of a minimum of |F| away from the axis of the cylinder and a sharp increase in |F| when the sphere approaches the sidewall. By comparing with the results for a sphere moving parallel to a flat wall, we analyse the effect of the curvature of the cylindrical tube.