Draga Pihler-Puzovic: Sedimentation of thin rigid disks in a viscous fluid

When thinking of everyday examples of sedimenting objects, we often imagine a periodic motion, be that a fluttering motion of a leaf falling in the air, a coin falling in the water or a spinning motion of maple seeds. Inertia dominates in these system, while the sedimentation on the other end of the Reynolds number (Re) spectrum is typically less exciting – a flat disk sedimenting in a viscous fluid maintains its initial orientation and its centre of mass follows a straight trajectory. In this talk we will consider disks which are bent symmetrically in the shape of U, or with one plane of symmetry, so that one side of the U shape is more tightly curved than the other (i.e. disked are of pinched U shape). We have conducted experiments and performed numerical simulations to build long-term predictions of the behaviour of such disks using the resistance matrix formalism by Happel&Brenner [1]. We find that the disks with one plane of symmetry tend to well-defined equilibrium orientations (so that the tightly curved end point of the disk is pointing downwards). However, they also exhibits transient dynamics of increasing complexity as their asymmetry tends to zero. In the limiting case corresponding to the U-shaped disk, we demonstrate that this inertia-less system has no steady states, but exhibits periodic reorientation in ever-repeating sequence of pitching and rolling motions, mimicking leaf flutter at Re=0.