The rotation of a non-spherical particle in simple shear flow

A single particle suspended in a flow with parallel streamlines is typically subject to a simple shear flow, which induces a rotational motion of the particle. The angular dynamics of an ellipsoidal particle in a simple shear flow was analytically derived by Jeffery [1] and shows that the axi-symmetric ellipsoid (i.e. spheroid) is rotating in closed degenerate orbits. However, the derivation of these solutions assumes inertia of both fluid and particle to be negligible, i.e. the particle Reynolds number Re_p equals zero. Here, we will present results of a neutrally buoyant particle in simple shear flow and show how the degeneracy of the Jeffery-orbits is broken due to inertia. Through direct numerical simulations and linear stability analysis, we are able to predict transitions between stable rotational states for spheroids ranging from thin discs to moderately slender fibers [2]. Furthermore, we find that fluid inertia is always dominating over particle inertia for neutrally buoyant particles at low Re_p. At moderate Re_p, particle inertia overcomes viscous damping, which increases the dimensionality of the dynamical system and can lead to chaotic rotational states.
[1] G. B. Jeffery, Proc. R. Soc. A 102, 1922
[2] Rosén et al., Phys. Rev. Fluids 1 (4), 2016