Resonance type flow due to rectilinear oscillations of a sphere in a micropolar fluid

Abstract

The flow of an incompressible micro-polar fluid generated due to rectilinear oscillations of a sphere about a diameter of the sphere is considered. The flow is so slow that oscillations Reynolds number is less than unity and hence nonlinear convective terms in the equations of motion are neglected. A rare but distinct special case in which material constants satisfy a resonance condition is considered. The stream function and drag acting on cylinder are obtained. The effect of physical parameters like micro-polarity and couple stress parameter on the drag due to oscillations is shown through graphs.