Inertial Focusing of a Large Particle in Square-Duct Flow at Low Reynolds Numbers

Spherical particles that are neutrally buoyant in a square-duct flow are known to undergo cross-sectional motion due to inertial lift forces while being transported downstream. Far downstream, this lateral migration converges, and particles focus near the midpoints of the duct walls, as demonstrated by experiments, numerical simulations, and theoretical analyses. In contrast, numerical studies have predicted that relatively large particles at low Reynolds numbers can focus not near the wall midpoints but rather near the duct corners along the diagonals. In this study, we reproduce this diagonal focusing pattern numerically and confirm its occurrence experimentally. Numerical computations of the lift forces acting on a particle reveal the equilibrium points that appear within the cross-section and clarify their stability. Front-view observation experiments are conducted under corresponding parameter conditions, and the distributions of particle positions in the downstream cross-section are measured. Both numerical and experimental results confirm that particles indeed focus near the corners along the diagonals for specific parameter ranges. Furthermore, we show that this diagonal pattern transitions, with increasing Reynolds number, to a bistable focusing pattern in which focusing occurs on both the diagonals and the midlines, and finally to the standard midline-focused pattern. This sequence of transitions is explained by changes in the stability of the particle equilibrium points.