THE SLOW MOTION OF A CYLINDER NEXT TO A PLANE WALL

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Abstract
The two-dimensional flow around a cylinder that is near a plane wall is calculated assuming that the Reynolds number for the flow is small. For a cylinder translating parallel to the wall, the torque on the cylinder is zero; similarly, for a rotating cylinder the force is zero. These results, which are surprising when compared with corresponding ones for a sphere, are proved and then examined further using lubrication theory. We also consider motion perpendicular to the wall, allowing us to discuss the behaviour of a cylinder falling down an inclined plane. In addition streamline patterns are described.

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