Inertial migration and self-assembly of staggered spheroidal particle pairs in square duct flows

In this paper, a staggered spheroidal particle pair inside a three-dimensional duct Poiseuille flow with Reynolds number (Re) up to 120 is investigated via the lattice Boltzmann method. Validation tests show excellent agreement with numerical and experimental results obtained by other groups. The entire migration dynamics and the final equilibrium state of the oblate and prolate particle pairs are analyzed and compared to those of the spherical particle pairs. The effects of initial axial spacing, particle aspect ratio, and Re are explored herein. Simulation results indicate that spheroidal particles tend to distribute orderly in the streamwise direction after they reach the corresponding face equilibrium positions. A key finding is that the prolate particle pairs eventually tumble with periodic oscillating axial spacing. Present results reveal that the initial axial spacing does not influence the equilibrium positions and interparticle spacings of spheroidal particle pairs. However, it does affect the migration process from the initial to the final stable or dynamic stable state. As Re increases from 20 to 120, spheroidal particles in the staggered pair gradually migrate toward the lower and upper walls, and the dimensionless average axial spacing between the adjacent prolate particles increases from 3.49 to 5.05 and collapses onto a single curve as a linear function of the particle Re. Compared to the oblate particle pair, the prolate particles are closer to the duct wall, and the corresponding axial spacing is larger at the same Re. For a staggered spheroidal particle pair, particles reach the equilibrium state under the attractive and repulsive forces. A second spheroidal particle prefers to occupy the eddy center generated by the first focusing particle. For the prolate particles with the tumbling mode, the distance between the particle and the eddy center gradually changes, and the axial spacing of the prolate particle pair also fluctuates periodically.