Enhanced droplet collision rates and impact velocities in turbulent flows: The effect of poly-dispersity and transient phases

Abstract

We compare the collision rates and the typical collisional velocities amongst droplets of different sizes in a poly-disperse suspension advected by two- and three-dimensional turbulent flows. We show that the collision rate is enhanced in the transient phase for droplets for which the size-ratios between the colliding pairs is large as well as obtain precise theoretical estimates of the dependence of the impact velocity of particles-pairs on their relative sizes. These analytical results are validated against data from our direct numerical simulations. Our results suggest that an explanation of the rapid growth of droplets, e.g., in warm clouds, may well lie in the dynamics of particles in transient phases where increased collision rates between large and small particles could result in runaway process. Our results are also important to model coalescence or fragmentation (depending on the impact velocities) and will be crucial, for example, in obtaining precise coalescence kernels in such systems.

Experimental study of the effects of droplet number density on turbulence-driven polydisperse droplet size growth

“…The dynamics across different droplet sizes in a polydisperse droplet field may introduce non-trivial effects that are absent in monodisperse droplets. For polydisperse droplet fields, studies on droplet collisions have focused either on preferential concentration (Reade & Collins 2000;Aliseda et al 2002) or particle decorrelation (James & Ray 2017). Preferential concentration and particle decorrelation are, however, physically coupled (Bec et al 2005).…”

Polymer stretching in laminar and random flows: entropic characterization

“…To this end, we use a database of Lagrangian trajectories from a direct numerical simulation (DNS) of the Navier-Stokes equations in a periodic cube at Taylor-microscale Reynolds number R λ = 111 (see Refs. [30,31] for the details). The velocity gradient κ(t) is evaluated along 10 4 trajectories and is then inserted in Eq.…”

Effect of long-range Coulomb repulsion on adhesive particle agglomeration in homogeneous isotropic turbulence

“…More details about particle dispersion can be found in several reviews and the references therein (Falkovich, Gawedzki & Vergassola 2001;Balachandar & Eaton 2009;Toschi & Bodenschatz 2009;Mathai, Lohse & Sun 2020). With regard to the radial relative velocity, both numerical simulations (Gustavsson & Mehlig 2014;Ireland, Bragg & Collins 2016a,b;James & Ray 2017;Bhatnagar et al 2018a;Bhatnagar, Gustavsson & Mitra 2018b) and experimental studies (de Jong et al 2010;Saw et al 2014;Dou et al 2018) have been conducted to systematically investigate the relative velocity statistics. The impacts of particle inertia and Taylor Reynolds number are further elaborated.…”