Effect of neutrally buoyant oblate spheroid's aspect ratio on its equilibrium position in a square duct

Abstract

The inertial migration of a neutrally buoyant oblate spheroid in a square duct is numerically simulated via the multiple-relaxation-time lattice Boltzmann method. This study aims to investigate the effect of a particle's aspect ratio $(AR)$ on its equilibrium position at different initial positions, orientations, and Reynolds numbers $(Re)$. The spheroid's equatorial radius remains unchanged here, and its $AR$ is adjusted by changing its polar radius, which is distinct from previous studies. Therefore, the particle's volume and mass increase with the $AR$. At a low $Re$ $(Re~=~80)$, the particle's initial position and orientation affect its final motion. There are three possible motion modes, tumbling, log-rolling and inclined log-rolling. Although the oblate spheroids with different $ARs$ may experience different motion modes at their final equilibrium states, their rotational diameters are constant. For the tumbling mode, the $AR$ affects the equilibrium position, and the particle gradually approaches the duct center as the $AR$ increases. For the inclined log-rolling mode, the $AR$ partially affects the equilibrium position, where the corresponding equilibrium positions remain unchanged for the spheroids with $AR~=~0.5$ and $0.75$, approaching closer to the duct center for the spherical particle with $AR~=~1$. Finally, for the log-rolling mode, $AR$ has a negligible effect on the equilibrium positions. Furthermore, in the same motion mode, the particle's equilibrium position approaches the wall as the $Re$ increases from 40 to 160.