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    Turbulence-Induced Relative Velocity Of Dust Particles. III. The Probability Distribution

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    2014_09_velocitydustparticlesiii.pdf (612.2Kb)
    Date
    2014-09
    Author
    Pan, Lubin B.
    Padoan, Paolo
    Scalo, John
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    Abstract
    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.
    Department
    Astronomy
    Subject
    minor planets, asteroids: general
    planets and satellites: formation
    protoplanetary disks
    turbulence
    bidisperse inertial particles
    isotropic turbulence
    protoplanetary
    disks
    growth pebbles
    planetesimal formation
    bouncing barrier
    collision
    statistics
    grains
    simulations
    astronomy & astrophysics
    URI
    http://hdl.handle.net/2152/34926
    xmlui.dri2xhtml.METS-1.0.item-citation
    Pan, Liubin, Paolo Padoan, and John Scalo. "Turbulence-Induced Relative Velocity of Dust Particles III: The Probability Distribution." arXiv preprint arXiv:1407.1101 (2014).
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