Droplets in isotropic turbulence: deformation and breakup statistics

Abstract

The statistics of the deformation and breakup of neutrally buoyant sub-Kolmogorov ellipsoidal drops is investigated via Lagrangian simulations of homogeneous isotropic turbulence. The mean lifetime of a drop is also studied as a function of the initial drop size and the capillary number. A vector model of drop previously introduced by Olbricht, Rallison & Leal [J. Non-Newtonian Fluid Mech. 10, 291-318 (1982)] is used to predict the behaviour of the above quantities analytically.

Polymer scission in turbulent flows

“…Therefore, above the coil-stretch transition, the right-hand tail ofP(R) saturates to the power-law R −1 . An analogous behaviour was found previously for the size distribution of sub-Kolmogorov droplets in isotropic turbulence (Biferale, Meneveau & Verzicco 2014;Ray & Vincenzi 2018). Also note that the exponent α coincides with the one obtained by Balkovsky et al (2000) for the p.d.f.…”

“…The analysis of (3.4 a , b ) to (3.6) closely follows that in Ray & Vincenzi (2018) for the breakup of sub-Kolmogorov droplets in isotropic turbulence. (The results presented here are deduced directly from those in § 3 of Ray & Vincenzi (2018) by setting , , , and .) We therefore skip the details of the derivations and directly present the predictions of scission statistics.…”

“…The former condition ensures that the extension of the polymer stays positive, while the latter describes scission at . The analysis of (3.4 a , b ) to (3.6) closely follows that in Ray & Vincenzi (2018) for the breakup of sub-Kolmogorov droplets in isotropic turbulence. (The results presented here are deduced directly from those in § 3 of Ray & Vincenzi (2018) by setting , , , and .)…”

“…We begin by considering the statistics of the first scission. For passively transported polymers, for which the motion of the polymers does not modify the carrier velocity field, we derive qualitative analytical predictions by restricting ourselves to the Hookean dumbbell model and by using a decorrelated-in-time Gaussian stochastic velocity field (the approach is adapted from a study of droplet breakup conducted in Ray & Vincenzi (2018)). The theoretical predictions are compared with Lagrangian direct numerical simulations (DNS) of the Rouse model in three-dimensional homogeneous isotropic turbulence.…”

Dynamics and fragmentation of small inextensible fibres in turbulence

“…The problem of turbulent fragmentation has been essentially addressed for droplets [19,20], fractal flocs [21] and microscopic polymers [22,23]. The break-up of macroscopic fibres has been essentially addressed in laminar flow [24].…”