**Bharath Ganapathisubramani's**

**Experimental Fluid Mechanics**

**Research Laboratory**

**Edge effects on the fluttering characteristics of freely falling planar particles.**

The effect of particle edge geometry on the descent motion of freely falling planar particles is examined through experiments. Various planar particles, such as disk and polygons, with identical frontal areas (Ap ) and different number of edges (or perimeter) are used. All particles are designed such that their values of Galileo number (G ) and dimensionless moment of inertia (I∗ ) correspond to the previously identified fluttering regime of particle motion. Several modes of secondary motion are observed for the same particle and conditions, and these are not equally probable. This probability depends on the particle shape. Disks and heptagons were found to prefer a “planar zig-zag” behavior. These planar motions are composed of gliding sweeps and turning sections. As the number of sides in the polygon decreases, i.e., for hexagons and pentagons, the trajectory transitions to a more three-dimensional form. These trajectories were found to be restricted to one plane per swing, but the subsequent swings are in other planes. Further decrease in number of sides to a square results in the trajectories having a severe out-of-plane motion. These subregimes of particle motion within the fluttering regime are consistent with those reported for disks in previous studies. Based on this information, a length scale that accounts for the frontal area of the particles and its edge geometry (i.e., perimeter) is proposed. This length scale represents an approach to determine an equivalent disk for planar particles such that the phase diagram in the Reynolds number (Re ) and dimensionless moment of inertia (I∗ ) domain can be used to characterize the motion of planar particles with different frontal geometries. However, further experiments covering other domains of the regime map are needed to verify its universality.

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