Interior Stokes "ows with stick-slip boundary conditions

Two-dimensional Stokes "ows generated by line singularities inside a circular cylinder are studied in the presence of stick-slip boundary conditions. For simplicity, line singularities are assumed to be parallel to the cylinder axis, all axes in the same plane. The interior boundary value problem associated with these "ows is solved in terms of a stream function. Analytic solutions are obtained for "ows induced by a rotlet, a potential-source and Stokeslets with axes radial (normal) or tangential to the cylinder by the Fourier expansion method. These solutions are used to plot streamline topologies of these "ows and the "ow patterns are studied as the slip parameter and the locations of the singularities are varied. Eddies of various sizes and shapes appear as the slip parameter is varied. Interesting "ow patterns are observed in "ows generated by a pair of rotlets. In this case, streamline patterns reveal interesting "ow topologies. Some of the "ow patterns observed here are similar to that of vortex mixing "ows. Interior saddle points are found in these "ows for certain values of the slip parameter and locations of the rotlets. The "ows induced by a source and a sink and a pair of Stokeslets also exhibit interesting features. The plots of the "uid velocity on the surface of the cylinder show the locations of surface stagnation points, if they exist. A study of the movement of surface stagnation points as the slip parameter and the locations of the singularities are varied shed some light on the qualitative features of the "ow patterns. The results presented may be relevant for a variety of applications including vortex mixing and journal bearing "ows. c © 2001 Elsevier Science B.V. All rights reserved.