As a simple model of MEMS device, the oscillatory Stokes flow due to an oscillating plate with arbitrary planform parallel to an infinite plane wall is considered, when the gap between the plate and the plane is much smaller than the characteristic dimension of the plate.
By means of the method of matched asymptotic expansion, the region occupied by fluid is divided into three regions: the interior region, the rim region and the exterior region. The interior solution is the parallel flows between two parallel infinite plates. The rim solution is the oscillatory Stokes flow in the region of the semi-infinite plate parallel to an infinite plane wall, which is considered by a numerical methods adopting the vorticity-stream function formulation. The exterior solution is the oscillatory Stokes flow in the upper region above the infinite plane wall, which is obtained by a double Fourier transfom.
After matching the solutions obtained in each region, the hydrodynamic force and torque exerted on the plate is presented. For a circular disk parallel to an infinite plate, the results are in good agreement with those obtained by the dual integral equation approach.
Viscous force on the plate in an oscillating flow consists of the damping force related with energy dissipation in an interior region and the restoring force in an exterior region. Since the unsteady effect of the fluid flow depends on the spatial region, to estimate the unsteadiness only the dimensionless frequency is not adequate and new measure is proposed.
