Abstract
This study deals with axisymmetric steady rotational movement of an incompressible couple stress fluid between two non-concentric objects. Two spherical boundaries are revolving axially with different angular velocities. At low Reynolds numbers, the solution is obtained semi-analytically utilizing the superposition guideline and the collocation approach. The hydrodynamic couple exerted by the fluid on the internal particle is considered. The results obtained in the study are compared with the corresponding results of the classical viscous fluids available in the literature.