Entrance flows of a dispersion and particles migration towards the vessel center

Abstract We investigate the entrance flow of a suspension modeled as a single inhomogeneous fluid. The inhomogeneity is due to non-uniform distribution on the vessel cross section. The aim of our study aims is indeed to show that the particles migration towards the duct axis can also be explained as an entrance effect. The analysis is performed generalizing the classical inertial terms linearization, getting an autonomous system of two ODEs whose numerical solution is validated considering, as benchmark, the homogeneous flow. The results obtained indicates that the flow asymptotically reaches a core-annulus structure and that the particles migration towards the center essentially occurs in the entrance region. The drift is in fact essentially governed by the transverse velocity which vanishes outside the entrance region. In particular, the migration away from the walls is substantially independent of the Reynolds number but inversely proportional to the viscosity of the suspension and therefore to the particles concentration. The Reynolds number affects the length of the entrance region.