  We report experimental results on the relative motion of pairs of solid
spheric particles with initial separations in the inertial range of fully
developed turbulence in water. The particle densities were in the range of $1
\lessapprox \rho_{p}/\rho_{f} \lessapprox 8$, \textit{i.e.}, from neutrally
buoyant to highly inertial; and their sizes were of the Kolmogorov scale. For
all particles, we observed a Batchelor like regime, in which particles
separated ballistically. Similar to the Batchelor regime for tracers, this
regime was observed in the early stages of the relative separation for times $t
\lessapprox 0.1 t_0$ with $t_0$ determined by the turbulence energy dissipation
rate and the initial separation between particle pairs. In this time interval
heavier particles separated faster than fluid tracers. The second order
Eulerian velocity structure functions was found to increase with density. In
other words, both observations show that the relative velocity between inertial
particles was larger than that between tracers. Based on the widely used,
simplified equation of motion for inertial point-particles, we derived a model
that shows an increase in relative velocity between inertial particles. In its
scale dependence, however, it disagrees quantitatively with the experimental
results. This we attribute to the preferential sampling of the flow field by
inertial particles, which is not captured by the model.
