Abstract
We investigate the distribution of relative velocities between small heavy particles of different sizes in turbulence by analyzing a statistical model for bidisperse turbulent suspensions, containing particles with two different Stokes numbers. This number, St, is a measure of particle inertia which in turn depends on particle size. When the Stokes numbers are similar, the distribution exhibits power-law tails, just as in the case of equal St. The power-law exponent is a nonanalytic function of the mean Stokes number St[over ¯], so that the exponent cannot be calculated in perturbation theory around the advective limit. When the Stokes-number difference is larger, the power law disappears, but the tails of the distribution still dominate the relative-velocity moments, if St[over ¯] is large enough.
Highlights
The dynamics of small heavy particles in turbulence plays a crucial role in many scientific problems and technological applications
We analyzed the distribution of relative velocities in turbulence between small, heavy particles with different Stokes numbers St
We demonstrated that the difference in St causes diffusive relative motion at small separations, giving rise to a plateau in the distribution for relative velocities smaller than a cut off vc. This is in qualitative agreement with direct numerical simulation (DNS) [51]
Summary
The dynamics of small heavy particles in turbulence plays a crucial role in many scientific problems and technological applications. This analysis has offered fundamental insights about how caustics shape the distribution of relative velocities of nearby particles [2,3,4,5,6,7,8,9,10]. These results apply only to “monodisperse” suspensions of identical particles. An important question is how particles of different sizes cluster and move relative to each other Spatial clustering of such “bidisperse” suspensions was analyzed in Refs. The dimensionless parameters of the model are the Stokes number St ≡ 1/(γ τ ), a measure of particle inertia, and the Kubo number, Ku ≡ u0τ/η, measuring the persistence of the flow
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
