Dynamics of small heavy particles in homogeneous turbulence: a Lagrangian experimental study

Abstract

We investigate the behavior of microscopic heavy particles settling in homogeneous air turbulence. The regimes are relevant to the airborne transport of dust and droplets: the Taylor-microscale Reynolds number is Re = 289 - 462, the Kolmogorov-scale Stokes number is St = 1.2 - 13, and the Kolmogorov acceleration is comparable to the gravitational acceleration (i.e., the Froude number Fr = O(1)). We use high-speed laser imaging to track the particles and simultaneously characterize the air velocity field, resolving all relevant spatio-temporal scales. The role of the flow sampled by the particles is spotlighted. In the present range of parameters, the particle settling velocity is enhanced proportionally to the velocity scale of the turbulence. Both gravity and inertia reduce the velocity fluctuations of the particles compared to the fluid; while they have competing effect on the particle acceleration, through the crossing trajectories and inertial filtering mechanisms, respectively. The preferential sampling of high-strain/low-vorticity regions is measurable, but its impact on the global statistics is moderate. The inertial particles have large relative velocity at small separations, which increases their pair dispersion; however, gravity offsets this effect by causing them to experience fluid velocities that decorrelate faster in time compared to tracers. Based on the observations, we derive an analytical model to predict the particle velocity and acceleration variances for arbitrary St, Fr, and Re. This agrees well with the present observations and previous simulations and captures the respective effects of inertia and gravity, both of which play crucial roles in the transport.