Sedimentation of rigid and flexible sheets in a viscous fluid

Most of our everyday experience of objects settling periodically happens in inertia-dominated systems. Examples include a fluttering motion of a leaf falling in air or of a coin falling in water or a spinning motion of maple seeds.

In this experimental study, we first focus on rigid circular sheets bent symmetrically in the shape of U, falling in a viscous liquid (Re<0.02). We show that even such a symmetric and inertia-less system does not have a steady state, but exhibits periodic reorientation.

Our second focus is the fluid-structure interaction of settling flexible sheets, inspired by the process of segregating flakes of 2D materials by centrifugation [1]. We observe that flexible sheets often quickly adopt a U-bent configuration, but as they reorient, the curvature distribution changes. These transients are slow and no steady state is reached within the traversed length of 30 diameters.

We highlight the similarities and differences between flexible and rigid sheets. The behaviours are similar when the sheets are initialised in upright-U-orientations, but if they are initialised upside-down, the rigid sheet rolls, while the flexible sheet bends through and, rather surprisingly, changes the axis of bending in the process.

[1]Khan et al., Carbon 50, 2 (2012)