Browsing by Subject "minor planets, asteroids: general"

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Turbulence-Induced Relative Velocity Of Dust Particles. II. The Bidisperse Case
(2014-08) Pan, Lubin B.; Padoan, Paolo; Scalo, John; Scalo, John
We extend our earlier work on turbulence-induced relative velocity between equal-size particles ( Paper I, in this series) to particles of arbitrarily different sizes. The Pan & 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, < w(2)>(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, < w(2)>(1/2) as a function of tau(p2) shows a dip at tau(p2) similar or equal to tau(p1), indicating tighter velocity correlation between similar particles. Defining a ratio f equivalent to tau(p,1)/tau(p,h), with tau(p,1) and tau(p,h) the friction times of the smaller and larger particles, we find that < w(2)>(1/2) increases with decreasing f due to the generalized acceleration contribution, which dominates at f less than or similar to 1/4. At a fixed f, our model predicts that < w(2)>(1/2) scales as tau(1/2)(p,h) tau(p,h) for in the inertial range of the flow, stays roughly constant for T-L less than or similar to tau(p,h) less than or similar to T-L/f, and finally decreases as tau(-1/2)(p,h) p, h for tau(p,h) >> T-L/f. The acceleration term is independent of the particle distance, r, and reduces the r dependence of < w(2)>(1/2) in the bidisperse case.
Turbulence-Induced Relative Velocity Of Dust Particles. III. The Probability Distribution
(2014-09) Pan, Lubin B.; Padoan, Paolo; Scalo, John; Scalo, John
Motivated by its important role in the collisional growth of dust particles in protoplanetary disks, we investigate the probability distribution function (PDF) of the relative velocity of inertial particles suspended in turbulent flows. Using the simulation from our previous work, we compute the relative velocity PDF as a function of the friction timescales, tau(p1) and tau(p2), of two particles of arbitrary sizes. The friction time of the particles included in the simulation ranges from 0.1 tau(eta) to 54T(L), where tau(eta) and T-L are the Kolmogorov time and the Lagrangian correlation time of the flow, respectively. The relative velocity PDF is generically non-Gaussian, exhibiting fat tails. For a fixed value of tau(p1), the PDF shape is the fattest for equal-size particles (tau(p2) = tau(p1)), and becomes thinner at both tau(p2) < tau(p1) and tau(p2) > tau(p1). Defining f as the friction time ratio of the smaller particle to the larger one, we find that, at a given f in (1/2) less than or similar to f less than or similar to 1, the PDF fatness first increases with the friction time tau(p,h) of the larger particle, peaks at tau(p,h) similar or equal to tau(eta), and then decreases as tp, h increases further. For 0 <= f less than or similar to (1/4), the PDF becomes continuously thinner with increasing tau(p,h). The PDF is nearly Gaussian only if tau(p,h) is sufficiently large (>> T-L). These features are successfully explained by the Pan & Padoan model. Using our simulation data and some simplifying assumptions, we estimated the fractions of collisions resulting in sticking, bouncing, and fragmentation as a function of the dust size in protoplanetary disks, and argued that accounting for non-Gaussianity of the collision velocity may help further alleviate the bouncing barrier problem.