Impact of Couple Stresses on Slow Rotation of a Slip Sphere: Brinkman’s Medium

The impact of couple stresses on the rotation of solid sphere in Brinkman’s model with slip influence is analytically solved. The tangential slip and vanishing of couple stress conditions are used on a spherical boundary. A solution for the rotation of sphere in Brinkman’s medium is obtained. The torque experienced by the couple stress fluid is determined, and it is a function of the couple stress viscosity ratio, couple stress, slip, and permeability parameters, and the impacts of these parameters on the torque are represented graphically and tabulated. We have also considered consistent couple stress fluid, and the effects of different parameters are discussed in graphs and table. We concluded that the torque on a sphere decreases with an increase in permeability and increases with an increase in slip parameter. The torque effect on rotation of a solid sphere is weaker than on translation of a solid sphere embedded in Newtonian fluid and couple stress fluid. The particular cases of rotation of a solid sphere embedded in a porous medium (Newtonian fluid) with slip and no-slip conditions are deduced.