Rotation of spheroidal particles in Couette flows

Abstract The rotation of a neutrally buoyant spheroidal particle in a Couette flow is studied by a multi-relaxation-time (MRT) lattice Boltzmann method. We find several new periodic and steady rotation modes for a prolate spheroid for Reynolds numbers ($\mathit{Re}$) exceeding 305. The simulations cover the regime up to $\mathit{Re}\leq 700$. The rotational behaviour of the spheroid appears to be not only sensitive to the Reynolds number but also to its initial orientation. We discuss the effects of initial orientation in detail. For $305\lt \mathit{Re}\lt 345$ we find that the prolate spheroid reaches a periodic mode characterized by precession and nutation around an inclined axis which is located close to the middle plane where the velocity is zero. For $345\lt \mathit{Re}\lt 385$, the prolate spheroid precesses around the vorticity direction with a nutation. For $\mathit{Re}$ close to the critical ${\mathit{Re}}_{c} \approx 345$, a period-doubling phenomenon is observed. We also identify a motionless mode at higher Reynolds numbers ($\mathit{Re}\gt 445$) for the prolate spheroid. For the oblate spheroid the dynamic equilibrium modes found are log rolling, inclined rolling and different steady states for $\mathit{Re}$ increasing from 0 to 520. The initial-orientation effects are studied by simulations of 57 evenly distributed initial orientations for each $\mathit{Re}$ investigated. Only one mode is found for the prolate spheroid for $\mathit{Re}\lt 120$ and $385\lt \mathit{Re}\lt 445$. In other $\mathit{Re}$ regimes, more than one mode is possible and the final mode is sensitive to the initial orientation. However, the oblate spheroid dynamics are insensitive to its initial orientation.