Unsteady axisymmetric slow viscous flow due to the oscillating motion of a circular disk parallel to a plane wall is studied on the basis of the Stokes' approximation. The problem is formulated as a system of linear integral equations of the first kind for a distribution of unsteady Stokeslets over the circular disk and the plane wall. The unknown density of Stokeslets is obtained numerically by reducing the integral equations to a system of linear algebraic equations. Pressure and shear stress distributions on the disk and wall are calculated and the drag exerted on the disk is determined. Instantaneous velocity fields and streamlines are determined, and their features are discussed.
The effect of the wall is studied by examining the surface stress and the streamline patterns for various h. The results reveal that the stress on the disk surface facing toward the wall increases significantly as the disk comes close to the wall, whereas the stress on opposite side is little affected by the wall. It is shown that when h is small as compared with viscous penetration length $O(|α|^{-1})$, drag force on disk approaches to steady Stokes drag, and when h is higher than $|α|^{-1}$, the wall effect disappears. In the case where the disk oscillates in an unbounded fluid without the wall, the results show qualitative agreements with those for oblate spheroid, biconcave disk, and sphere.
