Slow motion of spherical droplet in a micropolar fluid flow perpendicular to a planar solid surface

The Stokes axisymmetrical flow problem of a viscous fluid sphere moving perpendicular to an impermeable bounding surface within a micropolar stagnant fluid as well as the related problem of a micropolar fluid sphere moving perpendicular to an impermeable planar surface within a stagnant viscous fluid are considered. The fluids are considered to be incompressible, and the deformation of the fluid particle is neglected. A general solution is constructed from fundamental solutions in both cylindrical and spherical coordinate systems. As boundary conditions, continuity of velocity, continuity of shear stress and the spin–vorticity relation at the droplet surface are applied. Also the no-slip and no-spin boundary conditions are used at the impermeable plane surface. A combined analytical-numerical procedure based on collocation technique is used. The drag acting, in each case, on the fluid particle is evaluated with good convergence. Numerical results for the normalized hydrodynamic drag force versus the relative viscosity, relative separation distance between the particle and wall, micropolarity parameter (a viscosity ratio characterizing micropolar fluids) and spin parameter (a non-dimensional scalar factor relating the microrotation and vorticity at the droplet surface) are presented both in tabular and graphical forms. The results for the drag coefficient are in good agreement with the available solutions in the literature for the limiting cases.