Unsteady rotation of a solid sphere in a couple stress Brinkman medium with spin slip and velocity slip

This study investigates the unsteady rotational dynamics of a solid spherical particle immersed in an incompressible couple stress fluid. The flow dynamics are governed by the unsteady Brinkman equation. The Laplace transform technique is employed to convert the governing equation. The velocity slip and spin slip boundary conditions at the surface of the sphere are applied. The torque acting on the sphere is evaluated in the Laplace domain. The effects of key parameters—namely, the permeability parameter, slip parameter, spin slip parameter, couple stress viscosity ratio parameter, and couple stress parameter on the torque are analyzed for both oscillatory and sudden motion in time-dependent flow. Graphical representations of the torque are provided as functions of these parameters over time. The results are consistent with the corresponding limiting cases available in the existing literature.