Tumbling of small axisymmetric particles in random and turbulent flows

TL;DR

This paper investigates how small axisymmetric particles tumble in random and turbulent flows, revealing the influence of flow structures, particle shape, and inertia on their rotational dynamics through theoretical analysis and simulations.

Contribution

It introduces a perturbation expansion approach to analyze particle tumbling rates and highlights the effects of flow type, particle shape, and inertia on tumbling behavior.

Findings

Disks tumble faster than rods in turbulent flows due to vorticity regions.

Preferential sampling affects tumbling rates, especially in turbulent flows.

Inertia influences tumbling angles and collision dynamics for larger particles.

Abstract

We analyse the tumbling of small non-spherical, 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 [Parsa et al., Phys. Rev. Lett. 109 (2012) 134501]. 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.