Relative velocities in bidisperse turbulent suspensions

Abstract

We investigate the distribution of relative velocities between small heavy particles of different sizes in turbulence by analyzing a statistical model for bidisperse turbulent suspensions, containing particles with two different Stokes numbers. This number, St, is a measure of particle inertia which in turn depends on particle size. When the Stokes numbers are similar, the distribution exhibits power-law tails, just as in the case of equal St. The power-law exponent is a nonanalytic function of the mean Stokes number St, so that the exponent cannot be calculated in perturbation theory around the advective limit. When the Stokes-number difference is larger, the power law disappears, but the tails of the distribution still dominate the relative-velocity moments, if St is large enough.