  We calculate the relative grain-grain motions arising from interstellar
magnetohydrodynamic (MHD) turbulence. The MHD turbulence includes both fluid
motions and magnetic fluctuations. While the fluid motions accelerate grains
through hydro-drag, the electromagnetic fluctuations accelerate grains through
resonant interactions. We consider both incompressive (Alfv\'{e}n) and
compressive (fast and slow) MHD modes and use descriptions of MHD turbulence
obtained in Cho & Lazarian (2002). Calculations of grain relative motion are
made for realistic grain charging and interstellar turbulence that is
consistent with the velocity dispersions observed in diffuse gas, including
cutoff of the turbulence from various damping processes. We show that fast
modes dominate grain acceleration, and can drive grains to supersonic
velocities. Grains are also scattered by gyroresonance interactions, but the
scattering is less important than acceleration for grains moving with
sub-Alfv\'{e}nic velocities. Since the grains are preferentially accelerated
with large pitch angles, the supersonic grains will be aligned with long axes
perpendicular to the magnetic field. We compare grain velocities arising from
MHD turbulence with those arising from photoelectric emission, radiation
pressure and H$_{2}$ thrust. We show that for typical interstellar conditions
turbulence should prevent these mechanisms from segregating small and large
grains. Finally, gyroresonant acceleration is bound to preaccelerate grains
that are further accelerated in shocks. Grain-grain collisions in the shock may
then contribute to the overabundance of refractory elements in the composition
of galactic cosmic rays.

Astrophysics