Relative velocities in bidisperse turbulent suspensions

We investigate the distribution of relative velocities between small heavy particles of different Stokes numbers in turbulence by analysing a statistical model for turbulent suspensions of particles with two different Stokes numbers. When the Stokes numbers are similar, the distribution exhibits power-law tails, just as in the case of equal Stokes numbers. We show that the power-law exponent is a non-analytic function of the mean $\overline{\text{St}}$ of the two Stokes numbers. This means that the exponent cannot be calculated in perturbation theory around the advective limit. When the difference between the Stokes numbers is larger, the power law disappears, but the tails of the distribution still dominate the relative-velocity moments, if $\overline{\text{St}}$ is large enough.