Impact of permeability and fluid parameters in couple stress media on rotating eccentric spheres - Al-Hanaya Amal; El-Sapa Shreen (Open Physics)
This study elucidates the axisymmetric rotation of two eccentric spheres immersed in an incompressible couple stress fluid within a porous annular region. The investigation incorporates boundary conditions applied to the surfaces of both spheres, which rotate axially at differing angular velocities. Utilizing a collocation scheme alongside a semi-analytical approach under the assumption of low Reynolds numbers, this research delves into the hydrodynamic couple force (torque) exerted by the Brinkman couple stress fluid on the interior sphere. The analysis reveals that the dimensionless torque becomes increasingly significant as permeability enhances the size ratio, couple stress fluid parameters, and separation distance. The computed torque values due to stress and couple stress are presented graphically, providing visual clarity to the findings. Additionally, all the results align closely with the numerical analysis of two eccentric rigid spheres in conventional couple stress fluids, devoid of permeability effects or slip conditions, as demonstrated in previous studies (Al-Hanaya and El-Sapa (Effects of slippage and permeability of couple stress fluid squeezed between two concentric rotating spheres. Phys Fluids. 2023;35:103112); Al-Hanaya et al. (Axisymmetric motion of an incompressible couple stress fluid between two eccentric rotating spheres. J Appl Mech Tech Phys. 2022;63(5):1–9)).