Dynamics of inertialess sedimentation of a rigid U-shaped disk

Dynamics of inertialess sedimentation of a rigid U-shaped disk

2024 | Tymoteusz Miara, Christian Vaquero-Stainer, Draga Pihler-Puzović, Matthias Heil & Anne Juel
This study investigates the sedimentation of U-shaped rigid disks in a regime where inertia is negligible. Unlike planar disks, which settle in a fixed orientation, U-shaped disks exhibit periodic pitching and rolling motions, leading to complex trajectories such as quasi-periodic spirals and helices. The handedness of these chiral paths is determined by the initial orientation of the disk, not its geometry. The research demonstrates that achiral particles can sediment along chiral paths, providing a framework for interpreting the motion of particles of arbitrary shape. The experiments involved a Perspex tank filled with silicone oil, where U-shaped disks were observed to sediment. The disks were manufactured from polyamide nylon and shaped into a U-form. High-resolution imaging and auto-encoder techniques were used to reconstruct the disk's shape and orientation. The results showed that the disks undergo continuous reorientation, leading to complex motion patterns. The mobility matrix of the disk was determined from experimental data, and simulations were performed to model the disk's long-term behavior in an unbounded fluid. The analysis revealed that the disk's motion is governed by two orientational degrees of freedom, leading to periodic reorientation. The trajectories in the body-fitted coordinate system showed closed orbits, indicating periodic motion. The disk's motion was found to be quasi-periodic, with trajectories ranging from helical to quasi-periodic spirals. The study also showed that the disk's motion is influenced by its initial orientation, with different reorientation sequences observed depending on the starting angles. The disk's motion was modeled using a mobility matrix, and the results were compared with experimental data. The findings highlight the complex dynamics of sedimentation in the Stokes limit, where inertia is negligible, and provide insights into the behavior of particles of arbitrary shape in fluid environments. The research underscores the importance of particle shape in microhydrodynamics and offers a framework for understanding the motion of sedimenting particles.This study investigates the sedimentation of U-shaped rigid disks in a regime where inertia is negligible. Unlike planar disks, which settle in a fixed orientation, U-shaped disks exhibit periodic pitching and rolling motions, leading to complex trajectories such as quasi-periodic spirals and helices. The handedness of these chiral paths is determined by the initial orientation of the disk, not its geometry. The research demonstrates that achiral particles can sediment along chiral paths, providing a framework for interpreting the motion of particles of arbitrary shape. The experiments involved a Perspex tank filled with silicone oil, where U-shaped disks were observed to sediment. The disks were manufactured from polyamide nylon and shaped into a U-form. High-resolution imaging and auto-encoder techniques were used to reconstruct the disk's shape and orientation. The results showed that the disks undergo continuous reorientation, leading to complex motion patterns. The mobility matrix of the disk was determined from experimental data, and simulations were performed to model the disk's long-term behavior in an unbounded fluid. The analysis revealed that the disk's motion is governed by two orientational degrees of freedom, leading to periodic reorientation. The trajectories in the body-fitted coordinate system showed closed orbits, indicating periodic motion. The disk's motion was found to be quasi-periodic, with trajectories ranging from helical to quasi-periodic spirals. The study also showed that the disk's motion is influenced by its initial orientation, with different reorientation sequences observed depending on the starting angles. The disk's motion was modeled using a mobility matrix, and the results were compared with experimental data. The findings highlight the complex dynamics of sedimentation in the Stokes limit, where inertia is negligible, and provide insights into the behavior of particles of arbitrary shape in fluid environments. The research underscores the importance of particle shape in microhydrodynamics and offers a framework for understanding the motion of sedimenting particles.
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