Slow viscous flow due to motion of an annular disk; pressure-driven extrusion through an annular hole in a wall

Abstract

The description of the slow viscous flow due to the axisymmetric or asymmetric translation of an annular disk involves the solution of respectively one or two sets of triple integral equations involving Bessel functions. An efficient method is presented for transforming each set into a Fredholm integral equation of the second kind. Simple, regular kernels are obtained and the required physical constants are readily available. The method is also applied to the pressure-driven extrusion flow through an annular hole in a wall. The velocity profiles in the holes are found to be flatter than expected with correspondingly sharper variation near a rim. For the sideways motion of a disk, an exact solution is given with bounded velocities and both components of the rim pressure singularity minimized. The additional drag experienced by this disk when the fluid is bounded by walls parallel to the motion is then determined by solving a pair of integral equations, according to methods given in an earlier paper.