Abstract
We analyze the tumbling of small nonspherical, axisymmetric particles in random and turbulent flows. We compute the orientational dynamics in terms of a perturbation expansion in the Kubo number, and obtain the tumbling rate in terms of Lagrangian correlation functions. These capture preferential sampling of the fluid gradients, which in turn can give rise to differences in the tumbling rates of disks and rods. We show that this is a weak effect in Gaussian random flows. But in turbulent flows persistent regions of high vorticity cause disks to tumble much faster than rods, as observed in direct numerical simulations [S. Parsa, E. Calzavarini, F. Toschi, and G. A. Voth, Phys. Rev. Lett. 109, 134501 (2012)]. For larger particles (at finite Stokes numbers), rotational and translational inertia affects the tumbling rate and the angle at which particles collide, due to the formation of rotational caustics.
Highlights
The orientational dynamics of axisymmetric particles in random and turbulent flows is of great significance in many areas of the natural sciences and in technology
A last example concerns plankton in the upper ocean layer. Their tumbling may influence their nutrient uptake and light scattering [9]. In all of these cases the particles are smaller than the smallest turbulent eddies in the suspending flow, and the orientational dynamics of such small particles is driven by the local flow gradients: the difference in flow velocity over the particle leads to a hydrodynamic torque
Understanding how small nonspherical particles respond to flow gradients is a necessary step in describing the collision dynamics of turbulent suspensions of axisymmetric particles
Summary
The orientational dynamics of axisymmetric particles in random and turbulent flows is of great significance in many areas of the natural sciences and in technology. Understanding how small nonspherical particles respond to flow gradients is a necessary step in describing the collision dynamics of turbulent suspensions of axisymmetric particles. The orientational dynamics of small nonspherical particles is of fundamental interest in turbulence research, because it reflects the statistics of the velocity gradients in turbulent flows [10].
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