Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-12-01T00:43:22.689Z Has data issue: false hasContentIssue false
  • English
  • Français

Droplets in isotropic turbulence: deformation and breakup statistics

Published online by Cambridge University Press:  03 August 2018

Samriddhi Sankar Ray  and
Dario Vincenzi Open the ORCID record for Dario Vincenzi [Opens in a new window]
Samriddhi Sankar Ray
Affiliation:
International Centre for Theoretical Sciences, Tata Institute of Fundamental Research, Bangalore 560089, India
Dario Vincenzi*
Affiliation:
Université Côte d’Azur, CNRS, LJAD, 06108 Nice, France
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

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 a drop previously introduced by Olbricht et al. (J. Non-Newtonian Fluid Mech., vol. 10, 1982, pp. 291–318) is used to predict the behaviour of the above quantities analytically.

JFM classification

Drops and Bubbles: Drops Turbulent Flows: Isotropic turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 852 , 10 October 2018 , pp. 313 - 328
Copyright
© 2018 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ayyalasomayajula, S., Collins, L. R. & Warhaft, Z. 2008 Modeling inertial particle acceleration statistics in isotropic turbulence. Phys. Fluids 20, 095104.Google Scholar
Ayyalasomayajula, S., Gylfason, A. & Warhaft, Z. 2008 Lagrangian measurements of fluid and inertial particles in decaying grid generated turbulence. In IUTAM Symposium on Computational Physics and New Perspectives in Turbulence, Nagoya, Japan (ed. Kaneda, Y.), IUTAM Bookseries, vol. IV, pp. 171–175. Springer.Google Scholar
Balkovsky, E., Fouxon, A. & Lebedev, V. 2001 Turbulence of polymer solutions. Phys. Rev. E 64, 056301.Google Scholar
Bec, J., Biferale, L., Boffetta, G., Cencini, M., Lanotte, A., Musacchio, S. & Toschi, F. 2006 Lyapunov exponents of heavy particles in turbulence. Phys. Fluids 18, 091702.Google Scholar
Biferale, L., Meneveau, C. & Verzicco, R. 2014 Deformation statistics of sub-Kolmogorov-scale ellipsoidal neutrally buoyant drops in isotropic turbulence. J. Fluid Mech. 754, 184–207.Google Scholar
Bird, R. B., Hassager, O., Armstrong, R. C. & Curtiss, C. F. 1987 Dynamics of Polymeric Liquids, vol. II. Wiley.Google Scholar
Brunk, B. K. & Koch, D. L. 1997 Hydrodynamic pair diffusion in isotropic random velocity fields with application to turbulent coagulation. Phys. Fluids 9, 2670.Google Scholar
Celani, A., Musacchio, S. & Vincenzi, D. 2005 Polymer transport in random flow. J. Stat. Phys. 118, 531–554.Google Scholar
Cristini, V., Bławzdziewicz, J., Loewenberg, M. & Collins, L. R. 2003 Breakup in stochastic Stokes flows: sub-Kolmogorov drops in isotropic turbulence. J. Fluid Mech. 492, 231–250.Google Scholar
Falkovich, G., Gawȩdzki, K. & Vergassola, M. 2001 Particles and fields in fluid turbulence. Rev. Mod. Phys. 73, 913–975.Google Scholar
Gardiner, C. W. 1983 Handbook of Stochastic Methods. Springer.Google Scholar
Girimaji, S. S. & Pope, S. B. 1990 A diffusion model for velocity gradients in turbulence. Phys. Fluids A 2, 242–256.Google Scholar
Hinze, J. O. 1955 Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AIChE J. 1, 289–295.Google Scholar
James, M. & Ray, S. S. 2017 Enhanced droplet collision rates and impact velocities in turbulent flows: the effect of polydispersity and transient phases. Sci. Rep. 7, 12231.Google Scholar
Kolmogorov, A. N. 1949 On the breakage of drops in a turbulent flow. Dokl. Akad. Nauk SSSR 66, 825–828. For the English translation, see V. M. Tikhomiro (ed.), Selected Works of A. N. Kolmogorov (Kluwer Academic Publishers, 1991), pp. 339–343.Google Scholar
Le Jan, Y. 1984 Exposants de Lyapunov pour les mouvements browniens isotropes. C. R. Acad. Sci. Paris Ser. I 299, 947–949.Google Scholar
Le Jan, Y. 1985 On isotropic Brownian motions. Z. Wahrscheinlichkeitstheor. verw. Gebiete 70, 609–620.Google Scholar
Maffettone, P. L. & Minale, M. 1998 Equation of change for ellipsoidal drops in viscous flow. J. Non-Newtonian Fluid Mech. 78, 227–241.Google Scholar
Milan, F., Sbragaglia, M., Biferale, L. & Toschi, F. 2018 Lattice Boltzmann simulations of droplet dynamics in time-dependent flows. Eur. Phys. J. E 41, 6.Google Scholar
Minale, M. 2010 Models for the deformation of a single ellipsoidal drop: a review. Rheol. Acta 49, 789–806.Google Scholar
Musacchio, S. & Vincenzi, D. 2011 Deformation of a flexible polymer in a random flow with long correlation time. J. Fluid Mech. 670, 326–336.Google Scholar
Muzzio, F. J., Tjahjadi, M. & Ottino, J. M. 1991 Self-similar drop-size distributions produced by breakup in chaotic flows. Phys. Rev. Lett. 67, 54–57.Google Scholar
Olbricht, W. L., Rallison, J. M. & Leal, L. G. 1982 Strong flow criteria based on microstructure deformation. J. Non-Newtonian Fluid Mech. 10, 291–318.Google Scholar
Prabhakaran, P., Weiss, S., Krekhov, A., Pumir, A. & Bodenschatz, E. 2017 Can hail and rain nucleate cloud droplets? Phys. Rev. Lett. 119, 128701.Google Scholar
Perlekar, P., Biferale, L., Sbragaglia, M. & Toschi, F. 2012 Droplet size distribution in homogeneous isotropic turbulence. Phys. Fluids 24, 065101.Google Scholar
Perlekar, P., Mitra, D. & Pandit, R. 2006 Manifestations of drag reduction by polymer additives in decaying, homogeneous, isotropic turbulence. Phys. Rev. Lett. 97, 264501.Google Scholar
Risken, H. 1989 The Fokker–Planck Equation: Methods of Solution and Applications. Springer.Google Scholar
Schuchmann, H. P. & Schubert, H. 2003 Product design in food industry using the example of emulsification. Eng. Life Sci. 3, 67–76.Google Scholar
Spandan, V., Lohse, D. & Verzicco, R. 2016 Deformation and orientation statistics of neutrally buoyant sub-Kolmogorov ellipsoidal droplets in turbulent Taylor–Couette flow. J. Fluid Mech. 809, 480–501.Google Scholar
Tjahjadi, M. & Ottino, J. M. 1991 Stretching and breakup of droplets in chaotic flows. J. Fluid Mech. 232, 191–219.Google Scholar
Vaithianathan, T. & Collins, L. R. 2003 Numerical approach to simulating turbulent flow of a viscoelastic polymer solution. J. Comput. Phys. 187, 1–21.Google Scholar
Vankova, N., Tcholakova, S., Denkov, N. D., Ivanov, I. B., Vulchev, V. D. & Danner, T. 2007 Emulsification in turbulent flow. Part 1. Mean and maximum drop diameters in inertial and viscous regimes. J. Colloid Interface Sci. 312, 363–380.Google Scholar
Vincenzi, D., Perlekar, P., Biferale, L. & Toschi, F. 2015 Impact of the Peterlin approximation on polymer dynamics in turbulent flows. Phys. Rev. E 92, 053004.Google Scholar
Walstra, P. 1993 Principles of emulsion formation. Chem. Engng Sci. 48, 333–349.Google Scholar
Watanabe, T. & Gotoh, T. 2010 Coil-stretch transition in an ensemble of polymers in isotropic turbulence. Phys. Rev. E 81, 066301.Google Scholar
Windhab, E. J., Dressler, M., Feigl, K., Fischer, P. & Megias-Alguacil, D. 2005 Emulsion processing: from single-drop deformation to design of complex processes and products. Chem. Engng Sci. 60, 2101–2113.Google Scholar