Stokes drag on a disc with a Navier slip condition near a plane wall

Abstract

The Stokes drag and couple acting on a disc moving through incompressible Newtonian fluid are investigated for the case when the fluid obeys a Navier slip condition, with slip length b, on the surface of the disc. The fluid is bounded by an infinite plane wall on which there is no slip. The disc, of zero thickness and radius a, is parallel to the wall and distance h from it. Analyses are presented for the limits h ≫ a and h ≪ a; results for intermediate values of the separation h are obtained numerically by means of Tranter's method. The resistance coefficients for translation normal to the disc surface, and for rotation about a diameter, are unaffected by slip when the disc lies in unbounded fluid, but all resistance coefficients depend upon the slip length b when the disc is close to the wall. Their dependence on h becomes weak when b ≫ a.