Inertialess sedimentation of elastic disks

The handling and processing of microscale materials involves a rich variety of sedimentation processes in the Stokes limit of vanishing inertia, where trajectories depend sensitively on particle shape. We study the settling of an elastic disk under its own weight. The sedimentation flow generates viscous loading on the disk which may deform and/or reorient, and thus in turn alter the flow. We find that, unlike a slender flexible fibre, an elastic disk sedimenting in a large tank does not evolve towards a steady state but instead exhibits a myriad of complex reorientation and sedimentation paths depending on its initial orientation. To unravel these complex dynamics, we select a disk whose stiffness is such that it adopts U-bent shapes during settling and study its behaviour by comparison with the settling of a rigid U-shaped disk [1]. We find that in addition to the pitching and rolling motions of the rigid disk, the elastic disk can reconfigure its spine or invert its curvature. We use a neural network to interpolate the experimental data and compare rates of deformation and reorientation of the disk. The model suggests that the elastic disk is likely to exhibit a periodic cycle of rolling to an upright orientation, followed by pitching and subsequent spine reconfiguration.



[1] T. Miara, C. Vaquero-Stainer, D. Pihler-Puzović, M. Heil & A. Juel, Dynamics of inertialess sedimentation of a rigid U-shaped disk, Comms. Phys. 7, 47, 2024.