Clustering of settling charged particles in turbulence: theory and experiments

Atmospheric clouds, electrosprays and protoplanetary nebula (dusty plasma) contain electrically charged particles embedded in turbulent flows, often under the influence of an externally imposed, approximately uniform gravitational or electric force. We have developed a theoretical description of the dynamics of such systems of charged, sedimenting particles in turbulence, allowing radial distribution functions (RDFs) to be predicted for both monodisperse and bidisperse particle size distributions. The governing parameters are the particle Stokes number (particle inertial time scale relative to turbulence dissipation time scale), the Coulomb-turbulence parameter (ratio of Coulomb 'terminal' speed to the turbulence dissipation velocity scale) and the settling parameter (the ratio of the gravitational terminal speed to the turbulence dissipation velocity scale). The theory is compared to measured RDFs for water particles in homogeneous, isotropic air turbulence. The RDFs are obtained from particle positions measured in three dimensions using digital holography. The measurements verify the general theoretical expression, consisting of a power law increase in particle clustering due to particle response to dissipative turbulent eddies, modulated by an exponential electrostatic interaction term. Both terms are modified as a result of the gravitational diffusion-like term, and the role of 'gravity' is explored by imposing a macroscopic uniform electric field to create an enhanced, effective gravity.