Preferential Rotation of Chiral Dipoles in Isotropic Turbulence

Abstract

Particles in the shape of chiral dipoles show a preferential rotation in three dimensional homogeneous isotropic turbulence. A chiral dipole consists of a rod with two helices of opposite handedness, one at each end. We can use 3d printing to fabricate these particles with length in the inertial range and track their rotations in a turbulent flow between oscillating grids. High aspect ratio chiral dipoles will align with the extensional eigenvectors of the strain rate tensor and the helical ends will respond to the strain field by spinning around its long axis. The mean of the measured spinning rate is non-zero and reflects the average stretching the particles experience. We use Stokesian dynamics simulations of chiral dipoles in pure strain flow to quantify the dependence of spinning on particle shape. Based on the known response to pure strain, we build a model that gives the spinning rate of small chiral dipoles using Lagrangian velocity gradients from high resolution direct numerical simulations. The statistics of chiral dipole spinning determined with this model show surprisingly good agreement with the measured spinning of much larger chiral dipoles in the experiments.

Helicoidal particles and swimmers in a flow at low Reynolds number

“…Further extensions for an object with discrete symmetry have been performed by Fries et al (2017). A helical object with a fore-aft symmetry, such as a rod-like object with two connected helices of opposite chirality (Kramel et al 2015), is included in the symmetry group of helicoidal objects with reflectional symmetry with respect to a plane perpendicular to the axis of helicoidal symmetry (figures 2c, 3c), and we have proved in a general manner that such an object needs a constant α in the generalized Jeffery equations, though no drift velocity is generated. A rod-like helicoidal object considered in Chen & Zhang (2011) belongs to the class of helicoidal objects with additional π-rotational symmetry around an axis perpendicular to the axis of helicoidal symmetry, as illustrated in figures 2(d), 3(d), and our generalized version of the Jeffery equations is reduced to the usual Jeffery equation as obtained by Chen & Zhang (2011).…”

“…If α 2 + β 2 > 1, α = 0, the object orientation is attracted to one of the two stable fixed points in the phase space, whereas nonlinear periodic orbits are obtained when α = 0. These non-trivial fixed points are possible by the nonlinearity of the director equation (1.1), which suggests complicated dynamics in a general background flow such as Kolmogorov flow, ABC flow and isotropic turbulence (Gustavsson & Biferale 2016;Kramel et al 2015;Clifton et al 2018).…”

Angular dynamics of small crystals in viscous flow

“…1 and 2 are not chiral. Other authors have studied the translational and angular dynamics of chiral particles in steady and turbulent flows, see for instance [30][31][32].…”

Scale-dependent alignment, tumbling and stretching of slender rods in isotropic turbulence

“…We aim to add to this knowledge of inertial-range dynamics by investigating rods that naturally respond to features in the flow and become aligned by fluid motions whose scale is near the rod length. We also build on the previous results from laboratory experiments which investigated the rod tumbling rate (rate of change of rod orientation (Parsa & Voth 2014)) and the rod stretching rate (longitudinal velocity increment across the rod (Kramel et al 2016)) for rods with lengths in the inertial range. To do so, we use direct numerical simulation (DNS) data of isotropic turbulence in which we compute the motion of long rods (or, equivalently, rigid material lines).…”