Inertial migration of oblate spheroids in a plane channel

We study the inertial migration of neutrally buoyant oblate spheroids in a plane channel at moderate Reynolds numbers using lattice Boltzmann simulations. Spheroids reorient to perform a log-rolling motion with their minor axis in the vorticity direction. We demonstrate that, for moderate aspect ratios, the equilibrium positions relative to the channel walls for such a stable motion depend only on the equatorial radius $a$ of the spheroid, and the inertial lift force on the spheroid is proportional to $a^3b$, where $b$ is the polar radius. Therefore, the lift force on the spheroid can be expressed in terms of that for the sphere of the same $a$.