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We study the collision rates and velocities for point-particles of differentsizes in turbulent flows. We construct fits for the collision rates atspecified velocities (effectively a collisional velocity probabilitydistribution) for particle stopping time ratios up to four; already by thatpoint the collisional partners are very poorly correlated and so the resultsshould be robust for even larger stopping time ratios. Significantly, we findthat while particles of very different masses have approximately Maxwelliancollisional statistics, as the mass ratio shrinks the distribution changesdramatically. At small stopping time ratios, the collisional partners arehighly correlated and we find a population of high number density (clustered),low relative-velocity particle pairs. Unlike in the case of identical stoppingtime collisional partners, this low relative-velocity clustered population iscollisional, but the clustering is barely adequate to trigger bulk effects suchas the streaming instability. We conclude our analysis by constructing a masterfit to the collisional statistics as a function only of the stopping timeratio. Together with our previous work for identical stopping time particlepairs, this provides a recipe for including collisional velocity probabilitydistributions in dust coagulation models for protoplanetary disks. We alsoinclude our recipe for determining particle collisional diagnostics fromnumerical simulations.

Turbulence Induced Collision Velocities and Rates between Different Sized Dust Grains