Relative velocities in bidisperse turbulent aerosols: Simulations and theory

We perform direct numerical simulations of a bidisperse suspension of heavy spherical particles in forced, homogeneous, and isotropic three-dimensional turbulence. We compute the joint distribution of relative particle distances and longitudinal relative velocities between particles of different inertia. For a pair of particles with small difference in their inertias we compare our results with recent theoretical predictions [Meibohm et al., Phys. Rev. E 96, 061102 (2017)] for the shape of this distribution. We also compute the moments of relative velocities as a function of particle separation and compare with the theoretical predictions. We observe good agreement. For a pair of particles that are very different from each other-one is heavy and the other one has negligible inertia-we give a theory to calculate their root-mean-square relative velocity. This theory also agrees well with the results of our simulations.