Orientation dynamics of spheroids in linear flows

We study the orientation dynamics of a neutrally buoyant spheroid suspended in the one-parameter family of planar linear flows, in the presence of weak fluid and particle inertia, as characterized by the Reynolds (Re) and Stokes numbers (St). Recent numerical studies have shown a rich dynamical behavior for finite Re and St. In particular, an intricate sequence of bifurcations mediates the transition from a closed to an open trajectory topology, on the unit sphere of orientations, with increasing inertia; although, these studies are for restricted values of the spheroid aspect ratio and for simple shear flow. We demonstrate that the sequence of bifurcations can be reproduced within the small-Re, St framework. An examination of the governing two-dimensional system of equations, obtained from earlier efforts, allows us to organize the possible bifurcation scenarios in a parameter space consisting of the spheroid aspect ratio (κ) , the planar linear flow parameter (λ) and the ratio St/Re.