Effects of slippage and permeability of couple stress fluid squeezed between two concentric rotating spheres

Abstract

This study investigates the rotation of two concentric spheres saturated by creeping single-phase couple stress fluid flow under the impacts of permeability and slippage. The slippage conditions are applied on the surfaces of the spheres. In addition, the couple stresses on the boundary are assumed to vanish. Moreover, the analytical solution to the problem is used to obtain the field functions velocity, tangential stress, and couple stresses. The torque experienced by the fluid on the inner solid sphere is evaluated and plotted. The contour lines of fluid velocity are sketched at specific values of the parameters. The results presented that the torque acting on the inside sphere decreases monotonically with the permeability and slippage parameters at certain values of the relevant parameters. Also, the rise of couple stresses inclined the torque.