The Slow Motion of a Cylinder Next to a Plane Wall

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.