An analysis of slippage effects on a solid sphere enclosed by a non-concentric cavity filled with a couple stress fluids

This investigation shows the effect of slippage on the slow spinning of a rigid sphere covered by a non-concentric spherical hollow full of an incompressible couple stress fluid. Moreover, the velocity slip conditions are employed on surfaces of both the rigid sphere and the cavity. In addition, the solid sphere and the cavity are rotating axially at various angular speeds. The solution is obtained semi-analytically at low Reynolds numbers utilizing the superposition with the numerical collocation approach. This paper discusses the hydrodynamic couple exerted by the fluid on the internal particle. The dimensionless torque increases as the slip and spin slip increase by 99%, the couple stress parameter by 49%, and the separation parameter by 79%. Additionally, the non-dimensional torque decreases with the increase of the size ratio by 89%. Consequently, it is found that all the results agreed with the corresponding numerical analysis in the traditional viscous liquids and the revolving of two eccentric rigid spheres with no slippage (Al-Hanaya et al. in J. Appl Mech Tech Phys 63(5):1–9, 2022).