Inertial migration of spherical particles in circular Poiseuille flow at moderately high Reynolds numbers

Abstract

The inertial migration of spherical particles in a circular Poiseuille flow is numerically investigated for the tube Reynolds number up to 2200. The periodic boundary condition is imposed in the streamwise direction. The equilibrium positions, the migration velocity, and the angular velocity of a single particle in a tube cell are examined at different Reynolds numbers, particle-tube size ratios, and tube lengths. Inner equilibrium positions are observed as the Reynolds number exceeds a critical value, in qualitatively agreement with the previous experimental observations [J.-P. Matas, J. F. Morris, and E. Guazzelli, J. Fluid Mech. 515, 171 (2004)]. Our results indicate that the hydrodynamic interactions between the particles in different periodic cells have significant effects on the migration of the particles at the tube length being even as large as 6.7 particle diameters and they tend to stabilize the particles at the outer Segré–Silberberg equilibrium positions and to suppress the emergence of the inner equilibrium positions. A mirror-symmetric traveling-wave-like structure is observed when the particle Reynolds number is large enough. A pair of counter-rotating streamwise vortices exists at both upstream and downstream of the particle but with different rotating directions. The fluids in the half of the pipe without the particle flow more slowly and most fluids in the other half with the particle move faster with respect to the parabolic profile. The intensity of the structure is influenced by the local particle Reynolds number, the particle motion, and the tube length. In addition, the migration of multiple particles in a periodic tube cell is examined. We attribute the disparity in the critical particle Reynolds number for the occurrence of the inner particle annulus for the experiments and our simulations to the effect of the tube length or the periodic boundary condition in our numerical model.