Singularity method for oblate and prolate spheroids in Stokes and linearized oscillatory flow

Abstract

This paper applies the singularity method to obtain analytic solutions for oblate spheroids in Stokes flow, and to obtain numerical results for prolate and oblate spheroids undergoing oscillatory translation, and oscillatory rotation. To apply the method to oblate spheroids, singularities are placed along an imaginary focal length. A novel method is used to determine the hydrodynamic torque by deriving Green’s functions for torque for the unsteady rotlet, stresslet, and potential quadrupole. The results agree with analytic solutions for high and low frequencies, the results of previous studies, and results calculated using the boundary element method.