Wall effects on a rigid sphere moving perpendicular to a plane wall in a couple stress fluid filling a half-space

In this work, we investigate the slow motion of a rigid sphere in an incompressible couple stress fluid filling a half-space along a direction perpendicular to an infinite plane wall. The fluid flow is assumed to be steady and the Stokesian assumption is applied. An analytical technique based on the superposition principle is employed to construct the general solution in the form of an infinite series. A numerical approach, namely boundary collocation technique, is utilized to satisfy the imposed boundary conditions on the surface of the spherical object. The drag force experienced by the fluid flow on the spherical particle is obtained in terms of one of the coefficients of the infinite series. Numerical values of the normalized drag force are tabulated and graphed. The numerical results show that the presence of the plane wall has an apparent effect on the drag force experienced by the fluid flow on the sphere. It is found that the drag force increases monotonically as the sphere approaches the wall. In addition, it is observed that the couple stress viscosity coefficient has a considerable effect on the drag force. (C) 2018 Elsevier Masson SAS. All rights reserved.