Publications

Particles whose shapes couple translation to rotation display a rich array of behaviors as they sediment at low Reynolds number. We introduce a unifying perspective in which the possible dynamical regimes and bifurcations between them can be understood. We use experimental measurements of helical ribbons, with controlled center of mass offsets, to identify the key bifurcation from complex dynamics to a single attracting state as the magnitude of the offset increases. The sedimentation dynamics are very sensitive to small center of mass offsets, with the bifurcation occurring for offsets less than one percent of the particle length. Using mobility tensors obtained from immersed boundary method simulations, we simulate helical particle sedimentation and identify an alignment bifurcation surface, defined in the three dimensional space of center of mass offsets, that separates simple from complex sedimentation dynamics. Inside this surface we find limit cycles which emerge through Hopf and homoclinic bifurcations. Cocentered particles with coincident centers of force and mobility provide a reference case at the center of the bifurcation surface. We show how the geometric and dynamical symmetries of sedimenting cocentered particles are broken as the center of force offset moves away from the cocentered case. Three parity time-reversal (PT) symmetries exist for all cocentered particles under reflections normal to the eigenvectors of its translation-rotation coupling tensor. When a center of force offset preserves at least one of these PT symmetries, then there are closed orbits for particles inside the alignment bifurcation surface.

We experimentally measure the full set of mobility tensors for helical particles from 3D tracking of sedimentation at low-Reynolds-number. This includes the rotational mobility tensor which is rarely measured because it requires precise control of applied torque. By introducing a known center of mass offset in the geometry and tracking position and orientation during sedimentation, we can experimentally resolve the a, b, and c mobility tensors, which can be inverted to obtain the A, B, and C resistance tensors. The availability of accurate measurements of full sets of resistance and mobility tensors allows experimental measurement of the centers of mobility and resistance as well as validation of computational methods for predicting mobility tensors from particle geometry.

Sedimenting complex shaped chiral particles in turbulence are widely understood to experience preferential rotation due to translation-rotation coupling. However, recent research has concluded that the effects of chirality disappear as the Reynolds number becomes large. We perform experimental measurements in a turbulent vertical water tunnel to measure the dynamics of sedimenting chiral particles. We find that the effects of translation-rotation coupling due to chiral particle shape persist to high turbulence intensities. To observe these effects, measured rotation rates must be conditioned on particle orientation since translation-rotation coupling is right-handed for some orientations but left-handed for others. The measured translation and rotation are accurately modeled using mobility tensors that depend on particle Reynolds number. The Reynolds number dependence of the translation-rotation coupling tensor is much weaker than that of the translation mobility tensor. These results highlight an extension that is needed to existing models of orientation dependent drag, lift, and pitching torque on particles. When particle shape couples translation to rotation, a more complete approach is needed that includes full mobility tensors that depend on particle Reynolds number with additional contributions from inertial torques.

We study the dynamics of chiral particles sedimenting in 3D homogeneous turbulence and how the dynamics depend on particle shape. We perform experimental measurements in a vertical water tunnel under influence of gravity and turbulence. In 3D turbulence that is approximately homogeneous and isotropic, we measure the translational and rotational dynamics of three-bladed propellers. We investigate key aspects of propeller dynamics, including position, velocity, rotation rate and the coupling between rotational and translational motion. The mean vertical component of the rotation rate of the chiral particles is nearly zero because of a cancellation between orientations with right and left handed translation-rotation coupling. However, when we condition the rotation rate on orientation, we find strong chiral coupling that depends on the orientation of the particle with respect to the relative velocity. We then compare the results with equivalent achiral particles.