On the orientation dependence of the pressure and frictional drag experienced by spheroids in creeping flow

Abstract

The present work deals with the creeping flow past a single oblate or prolate spheroid. On the basis of the investigations by Aoi [J. Phys. Soc. Jpn. 10, 119 (1955)] on the contributions of pressure and frictional drag to the total drag experienced by spheroids when the fluid streams with a speed parallel to the axis of symmetry, we find that the pressure contribution corresponds to half of the dimensionless shape factor γ0 provided by Happel and Brenner, Low Reynolds Number Hydrodynamics (Prentice-Hall Inc. Englewood Cliffs, NJ, 1965). Accordingly, we conjecture the validity of this finding when the fluid streams with a speed perpendicular to the axis of symmetry. Therefore, the formulations of dimensionless shape factors α0/2 and β0/2 are confronted with the numerical results at particle Reynolds number of 0.1. Furthermore, the formulations of the pressure and the frictional drag are deduced and extended to any orientation relative to the flow direction. These results give physical insight into the total drag experienced by spheroids in creeping flow and can be helpful for the validation of simulations of the flow past an obstacle.