We extend our earlier work on turbulence-induced relative velocity between
equal-size particles (Pan and Padoan, Paper I) to particles of arbitrarily
different sizes. The Pan and Padoan (PP10) model shows that the relative
velocity between different particles has two contributions, named the
generalized shear and acceleration terms, respectively. The generalized shear
term represents the particles' memory of the spatial flow velocity difference
across the particle distance in the past, while the acceleration term is
associated with the temporal flow velocity difference on individual particle
trajectories. Using the simulation of Paper I, we compute the root-mean-square
relative velocity, ^1/2, as a function of the friction times, tau_p1 and
tau_p2, of the two particles, and show that the PP10 prediction is in
satisfactory agreement with the data, confirming its physical picture. For a
given tau_p1 below the Lagrangian correlation time of the flow, T_L, ^1/2
as a function of tau_p2 shows a dip at tau_p2~tau_p1, indicating tighter
velocity correlation between similar particles. Defining a ratio
f=tau_pl/tau_ph, with tau_pl and tau_ph the friction times of the smaller and
larger particles, we find that ^1/2 increases with decreasing f due to the
generalized acceleration contribution, which dominates at f<1/4. At a fixed f,
our model predicts that ^1/2 scales as tau_ph^1/2 for tau_p,h in the
inertial range of the flow, stays roughly constant for T_L <tau_ph < T_L/f, and
finally decreases as tau_ph^-1/2 for tau_ph>>T_L/f. The acceleration term is
independent of the particle distance, r, and thus reduces the r-dependence of
^1/2 in the bidisperse case.Comment: 23 pages, 12 figures, Accepted to Ap