Motion of a slip spherical particle near a planar micropolar-viscous interface

Abstract

An analytical–numerical method based on collocation techniques is presented to investigate the problem of determining Stokes flow caused by a spherical particle moving perpendicularly to a plane interface separating two semi-infinite immiscible fluid phases. Attention is focused on the case when one of the two fluid phases is of a microstructure nature (micropolar fluid). A linear slip boundary conditions, of Basset type, is used on the surface of the particle. The motion is considered in the limit of small Reynolds and capillary numbers where in this case the interface is of insignificant deformation. To solve the axisymmetric creeping motion of the micropolar fluid for velocity and microrotation components, a general solution is constructed from the superposition of some basic solutions in both cylindrical and spherical coordinate systems. Boundary conditions are satisfied first at the fluid–fluid interface using the Fourier Bessel transforms and then on the surface of the particle by the collocation scheme. Numerical results of the normalized drag force acting on the particle are obtained with good convergence for various values of the relevant parameters and presented both in graphical and tabular. Our results of the normalized drag force are compared with the available data in the literature for the limiting cases.