Collision rates of bidisperse inertial particles in isotropic turbulence

Zaichik, L. I.; Simonin, Olivier; Alipchenkov, V. M.

doi:10.1063/1.2187548

Cited by 42 publications

(71 citation statements)

References 35 publications

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“…In the limit of vanishing τ p (i.e., passive tracers), this correlation tensor would approach the Lagrangian correlation tensor, B Lij , of the flow, which has been extensively studied (e.g., Yeung & Pope 1989). A common approximation is to set B Tij equal to B Lij for particles with any τ p (e.g., Zaichik et al , 2006Ayala et al 2008). Physically, it corresponds to the assumption that the trajectory of any inertial particle is not far away from that of a tracer particle starting from the same initial condition.…”

Section: The General Formulationmentioning

confidence: 99%

“…A detailed discussion of the qualitative differences between these models and their problems will be given in §4. An important reason for the problems in most of the previous models is that they did not clearly recognize or carefully consider the effect of the particle pair separation backward in time (except for the differential model by Zaichik et al ( , 2006 to be discussed below, which we think has the particle backward separation implicitly included). The role of this backward separation will be revealed along the formulation of our model.…”

Section: Introductionmentioning

confidence: 99%

“…The existing models have very different predictions for the relative speed in the inertial range for the monodisperse case (Volk et al 1980;Williams & Crane 1983;Yuu 1984;Kruis & Kusters 1997;Zaichik et al , 2006Ayala et al 2008). A detailed discussion of the qualitative differences between these models and their problems will be given in §4.…”

Section: Introductionmentioning

confidence: 99%

“…In the previous studies that cover a whole range of Stokes numbers, the differential model by Zaichik and collaborators Zaichik et al , 2006 is perhaps the most complete one, as it examines the effect of preferential clustering and the relative speed simultaneously. We will refer to this model as Zaichik et al's model or the model by Zaichik et al Assuming Gaussian statistics for the flow velocity, the model first sets up an equation for the joint probability distribution function (pdf) of the particle separation and the relative velocity.…”

Section: Introductionmentioning

confidence: 99%

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Relative velocity of inertial particles in turbulent flows

Pan

Padoan

2010

J. Fluid Mech.

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We present a model for the relative velocity of inertial particles in turbulent flows that provides new physical insight into this problem. Our general formulation shows that the relative velocity has contributions from two terms, referred to as the generalized acceleration and generalized shear terms, because they reduce to the well known acceleration and shear terms in the Saffman-Turner limit. The generalized shear term represents particles' memory of the flow velocity difference along their trajectories and depends on the inertial particle pair dispersion backward in time. The importance of this backward dispersion in determining the particle relative velocity is emphasized. We find that our model with a two-phase separation behavior, an early ballistic phase and a later tracer-like phase, as found by recent simulations for the forward (in time) dispersion of inertial particle pairs, gives good fits to the measured relative speeds from simulations at low Reynolds numbers. In the monodisperse case with identical particles, the generalized acceleration term vanishes and the relative velocity is determined by the generalized shear term. At large Reynolds numbers, our model gives a St 1/2 dependence of the relative velocity on the Stokes number St in the inertial range for both the ballistic behavior and the Richardson separation law. This leads to the same inertial-range scaling for the two-phase separation that well fits the simulation results. Our calculations for the bidisperse case show that, with the friction timescale of one particle fixed, the relative speed as a function of the other particle's friction time has a dip when the two timescales are similar. This indicates that similar-size particles tend to have stronger velocity correlation than different ones. We find that the primary contribution at the dip, i.e., for similar particles, is from the generalized shear term, while the generalized acceleration term is dominant for particles of very different sizes. Future numerical studies are motivated to check the accuracy of the assumptions made in our model and to investigate the backward-in-time dispersion of inertial particle pairs in turbulent flows.

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Section: The General Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Relative velocity of inertial particles in turbulent flows

Pan

Padoan

2010

J. Fluid Mech.

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“…The dashed line is the expected structure function in an incompressible turbulent flow with Re λ = 300. It is obtained from a bridging formula given in Zaichik et al (2006), which connects the established scaling behaviors of the structure function in different scale ranges. Clearly, the data points are in good agreement with the dashed line.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Turbulent Clustering of Protoplanetary Dust and Planetesimal Formation

Pan

Padoan

Scalo

et al. 2011

ApJ

120

109

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We study the clustering of inertial particles in turbulent flows and discuss its applications to dust particles in protoplanetary disks. Using numerical simulations, we compute the radial distribution function (RDF), which measures the probability of finding particle pairs at given distances, and the probability density function of the particle concentration. The clustering statistics depend on the Stokes number, St, defined as the ratio of the particle friction timescale, τ p , to the Kolmogorov timescale in the flow. In agreement with previous studies, we find that, in the dissipation range, the clustering intensity strongly peaks at St 1, and the RDF for St ∼ 1 shows a fast power-law increase toward small scales, suggesting that turbulent clustering may considerably enhance the particle collision rate. Clustering at inertial-range scales is of particular interest to the problem of planetesimal formation. At these large scales, the strongest clustering is from particles with τ p in the inertial range. Clustering of these particles occurs primarily around a scale where the eddy turnover time is ∼τ p . We find that particles of different sizes tend to cluster at different locations, leading to flat RDFs between different particles at small scales. In the presence of multiple particle sizes, the overall clustering strength decreases as the particle size distribution broadens. We discuss particle clustering in two recent models for planetesimal formation. We argue that, in the model based on turbulent clustering of chondrule-size particles, the probability of finding strong clusters that can seed planetesimals may have been significantly overestimated. We discuss various clustering mechanisms in simulations of planetesimal formation by gravitational collapse of dense clumps of meter-size particles, in particular the contribution from turbulent clustering due to the limited numerical resolution.

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References

2008

Particles in Turbulent Flows

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Collision rates of bidisperse inertial particles in isotropic turbulence

Cited by 42 publications

References 35 publications

Relative velocity of inertial particles in turbulent flows

Relative velocity of inertial particles in turbulent flows

Turbulent Clustering of Protoplanetary Dust and Planetesimal Formation

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