Time-dependent rotational motion of a solid sphere in a Jeffrey fluid with velocity slip

This study investigates the time-dependent rotational motion of a solid sphere in an incompressible Jeffrey fluid, governed by the unsteady Stokes equation. The Laplace transform technique is employed to solve the governing equation, and the velocity slip boundary condition is utilized. The torque acting on the sphere's surface is derived in the Laplace domain. Analytical expressions are explored for various cases, including damped oscillations, accelerating rotation, and impulsive motion. The influence of slip condition, Jeffrey parameters, and time-dependent effects on the torque are illustrated and analyzed through graphical results. It is observed that both the slip parameter and the Deborah number (De) enhance the torque, whereas the Jeffrey parameter λ1 tends to reduce it. The results obtained are in agreement with existing solution for Newtonian fluid in the limiting case.