On the transport of a suspended particle in flow through the entrance region of a tube

Abstract

The motion of a single, spherical particle, released at different radial positions at the inlet of the entrance region of a straight circular laminar flow tube (Re = 260), was studied theoretically. Radial migration of the particle, either toward the tube center or toward the tube wall, was predicted. Based on the hypothesis that the particle experienced a lift force which was produced by the vorticity in the boundary layer and a velocity difference between the center of the suspended particle and the fluid medium, an inertia-vorticity fluid dynamic model was formulated to analyze the particle radial motions. Computational flow dynamics (CFD) solutions obtained from a 9.8 mm diameter tube model included the resulting particle loci for three particle radii (a = 0.1 cm, 0.085 cm, 0.050 cm), with the particle entry at various radial positions. The computation also covered a range of different particle entry speeds. The results showed that the particle migrates toward the tube center if it lags behind the medium in the core region; otherwise, it migrates toward the tube wall. Additional flow experiments were conducted in a circular (2R = 10.2 mm), 300 mm long straight tube. A small polystyrene sphere (2a = 1.72 mm, density ${\mathit{\rho }}_{\mathrm{p}}=1.014\text{g}·{\text{cm}}^{-3}$ ) was released at the inlet (X = 0, $\mathit{\eta }\mathrm{/}\mathrm{R}=0.48$ ) with two dimensionless release velocities ( ${\mathit{\omega }}_{\mathrm{p}}=0$ , and ${\mathit{\omega }}_{\mathrm{p}}\mathrm{>}1.0$ ). The recorded particle traces agree well with the computational model.