Application of Bipolar Coordinates to the Two-Dimensional Creeping Motion of a Liquid. III. Separation in Stokes Flows

Abstract

When there is a linear shear flow along a plane wall with a cylindrical depression, flow penetrating into the cavity separates from the wall, if the ratio of the depth of the cavity to the width of its mouth exceeds a critical value which is about 0.32. The pressure becomes infinite at the sharp edges of the cavity, while for the flow over a projection the pressure is a continuous function which on the boundary has two extremum values symmetrically about the cylindrical portion. As another example of separation in Stokes flows, the flow generated by the rotation of a circular cylinder which is eccentrically encircled with a larger cylinder or placed near a plane is considered.