Relative velocities in bidisperse turbulent suspensions

We investigate the distribution of relative velocities between small heavy particles of different sizes in turbulence by analysing a statistical model for bidisperse turbulent suspensions, containing particles with two different Stokes numbers. This number, $\mathrm{S}\mathrm{t}$, 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 $\mathrm{S}\mathrm{t}$. The power-law exponent is a non-analytic function of the mean Stokes number $\overline{\mathrm{S}\mathrm{t}}$, 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 $\overline{\mathrm{S}\mathrm{t}}$ is large enough.