Rotary oscillations of axi-symmetric bodies in an axi-symmetric viscous flow with slip: Numerical solutions for sphere and spheroids

Rotary oscillations of several axi-symmetric bodies in axi-symmetric viscous flows with slip are investigated. A numerical method based on the Greenʹs function technique is used wherein the relevant Helmholtz equation, as obtained from the unsteady Stokes equation, is converted into a surface integral equation. The technique is benchmarked against a known analytical solution, and accurate numerical results for local stress and torque on spheres and spheroids as function of the frequency parameter and the slip coefficients are obtained. It is found that in all cases, slip reduces stress and torque, and increasingly so with the increasing frequency parameter. The method discussed here can be potentially extended to the realistic case of an oscillating disk viscometer.