Sedimentation of an oblate ellipsoid in narrow tubes

Sedimentation behaviors of an oblate ellipsoidal particle inside narrow $[R/a\in (1.2,2.0\left)\right]$ infinitely long circular tubes are studied by the lattice Boltzmann method, where $R$ and $a$ are the radius of the tube and the length of the semimajor axis of the ellipsoid, respectively. The Archimedes numbers (Ar) up to 70 are considered. Four periodic and two steady sedimentation modes are identified. It is the first time that the anomalous mode has been found in a circular tube for an ellipsoidal particle. The phase diagram of the modes as a function of Ar and $R/a$ is obtained. The anomalous mode is observed in the larger $R/a$ and lower-Ar regime. Through comparisons between the anomalous and oscillatory modes, it is found that $\frac{R}{a}$ plays a critical role for the anomalous mode. Some constrained cases with two steady modes are simulated. It is found that the particle settles faster in the unconstrained modes than in the corresponding constrained modes. This might inspire further study on why the particle adopts a specific mode under a certain circumstance.