Eur. Phys. J. Plus (2016) 131: 175
https://doi.org/10.1140/epjp/i2016-16175-6

Regular Article

Unsteady Stokes flow of a couple stress fluid around a rotating sphere with slip

¹ Department of Mathematics and Computer Science, Faculty of Science, Beirut Arab University, Beirut, Lebanon
² Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Alexandria, Egypt

^* e-mail: emad.ashmawy@bau.edu.lb

Received: 19 February 2016
Revised: 20 April 2016
Accepted: 22 April 2016
Published online: 27 May 2016

Abstract

In this paper, the unsteady Stokes flow of an incompressible couple stress fluid around a rotating sphere is investigated. The non-classical slip condition is applied on the spherical boundary. In addition, the couple stresses on the boundary are assumed to vanish. The analytical solution of the problem is obtained using the technique of Laplace transform. The torque experienced by the fluid on the sphere is evaluated and the inversion of the Laplace transform is implemented numerically. The results showed that the torque acting on the sphere increases monotonically with the slip parameter at a fixed time. They also showed that the presence of couple stresses increases the torque.