Oscillatory flow in a cone-and-plate bioreactor

Motivated by biometric applications, we analyze oscillatory flow in a cone-and-plate geometry. The cone is rotated in a simple harmonic way on a stationary plate. Based on assuming that the angle between the cone and plate is small, we describe the flow analytically by a perturbation method in terms of two small parameters, the Womersley number and the Reynolds number, which account for the influences of the local acceleration and centripetal force, respectively. Working equations for the shear stresses induced both by laminar primary and secondary flows on the plate surface are presented.