  We study the relative velocity of inertial particles suspended in turbulent
flows and discuss implications for dust particle collisions in protoplanetary
disks. We simulate a weakly compressible turbulent flow, evolving 14 particle
species with friction timescale, tau_p, covering the entire range of scales in
the flow. The particle Stokes numbers, St, measuring the ratio of tau_p to the
Kolmogorov timescale, are in the range from ~0.1 to ~800. Using simulation
results, we show that the model by Pan & Padoan (PP10) gives satisfactory
predictions for the rms relative velocity between identical particles. The
probability distribution function (PDF) of the relative velocity is found to be
highly non-Gaussian. The PDF tails are well described by a 4/3 stretched
exponential function for particles with tau_p ~ 1-2 T_L, where T_L is the
Lagrangian correlation timescale, consistent with a prediction based on PP10.
The PDF approaches Gaussian only for very large particles with tau_p >~ 54 T_L.
We split particle pairs at given distances into two types with low and high
relative speeds, referred to as continuous and caustic types, respectively, and
compute their contributions to the collision kernel. Although amplified by the
effect of clustering, the continuous contribution vanishes in the limit of
infinitesimal particle distance, where the caustic contribution dominates. The
caustic kernel per unit cross section rises rapidly as St increases toward ~1,
reaches a maximum at tau_p ~ 2 T_L, and decreases as tau_p^{-1/2} for tau_p >>
T_L.
