Migration of nondeformable droplets in a circular tube filled with micropolar fluids

Abstract

In the case of low Reynolds numbers, nothing is known on the significance of migration of nondeformable droplets in a circular tube filled with micropolar fluids. The report presents the outcome of a study on the quasi-steady flow caused by a droplet translating in a micropolar fluid along the centreline of an impermeable circular tube. A general solution for the micropolar fluid is constructed from the superposition of the basic solutions in both cylindrical and spherical coordinates; the boundary conditions are satisfied first at the tube wall by the Fourier transforms and then at the surface of the droplet by boundary collocation techniques. The aim of this article is to study and find out the effect of cylindrical wall on the drag force acting on the droplet due its presence in a microstructure fluid of micropolar type. It is found that the normalized drag force is a monotonic increasing function of the ratio of particle-to-tube radii, and approaches to infinity in the limit. The findings also demonstrate that the normalized drag force increases as the micropolarity parameter increases. The present study is of much important in the fields of biomedical and industrial processes such as sedimentation, coagulation, suspension rheology, and motion of blood cells in an artery or vein.