Resistance coefficients for Stokes flow around a disk with a Navier slip condition

Abstract

The Stokes drag and couple acting on a disk of zero thickness as it moves through Newtonian fluid are investigated for the case when slip can occur at the surface of the disk. It is shown that when the disk translates parallel to its axis, the well-known velocity field for a no-slip boundary condition exerts zero shear stress on the surface of the disk. The flow is therefore unchanged if the boundary condition on the disk is modified to a stress-free or to a Navier slip boundary condition. This invariance also holds for a disk that rotates about a diameter. However, flow around a disk that rotates about its axis, or that translates in its own plane (edgewise), is modified when the no-slip boundary condition is changed to a Navier slip condition. The fluid velocity can be expressed in terms of Hankel transforms, and the resulting dual integral equations are solved numerically. Results for the torque and drag on the disk are presented as functions of the slip length in the Navier boundary condition.