Influence of interface on nondeformable micropolar drop migration

Abstract In this article, an analytical approach is considered to study the issue of specifying Stokesian motion due to a micropolar sphere drop translating at a concentric instantaneous position within a spherical fluid–fluid interface that divides two immiscible fluids, one of which is bounded and the other is unbounded. Here, the focus is on the situation where there are two microstructure-related fluid phases (micropolar fluids) out of the three. The motion is considered to have low Reynolds numbers; thus, the drop’s surface and fluid–fluid interface have insignificant deformation. General solutions to the slow axisymmetric motion of the micropolar/viscous fluid in a spherical coordinate system are obtained based on a concentric position. Boundary conditions are fulfilled at the drop’s surface and the fluid–fluid interface. Findings indicate that the normalised hydrodynamic force increases monotonically as the droplet-to-interface radius ratio increases, acting on a moving micropolar sphere droplet and becoming unlimited when the drop’s surface touches the fluid–fluid interface. The numerical findings for the normalised force operating on the micropolar sphere droplet at different values of the suitable parameters are introduced in both graphical and tabular form. Our numerical findings are compared with the suitable data for the special cases stated in the literature. The current investigation of the study has practical applications in many domains of industrial, biological, medicinal, and natural processes, for example, liquid crystals, polymeric suspensions, muddy fluids, liquid–liquid extraction, raindrop formation, blood cells moving through a vein or artery, suspension rheology, sedimentation, and coagulation.