Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-23T18:38:36.416Z Has data issue: false hasContentIssue false
  • English
  • Français

Kinetic energy spectra and flux in turbulent phase-separating symmetric binary-fluid mixtures

Published online by Cambridge University Press:  24 June 2019

Prasad Perlekar Open the ORCID record for Prasad Perlekar [Opens in a new window]
Get access Rights & Permissions [Opens in a new window]

Abstract

We conduct direct numerical simulations (DNS) of the Cahn–Hilliard–Navier–Stokes (CHNS) equations to investigate the statistical properties of a turbulent phase-separating symmetric binary-fluid mixture. Turbulence causes an arrest of the phase separation which leads to the formation of a statistically steady emulsion. We characterise turbulent velocity fluctuations in an emulsion for different values of the Reynolds number and the Weber number. Our scale-by-scale kinetic energy budget analysis shows that the interfacial terms in the CHNS equations provide an alternative route for the kinetic energy transfer. By studying the probability distribution function (p.d.f.) of the energy dissipation rate, the vorticity magnitude and the joint-p.d.f. of the velocity-gradient invariants we show that the statistics of the turbulent fluctuations do not change with the Weber number.

JFM classification

Drops and Bubbles: Breakup/coalescence Turbulent Flows: Isotropic turbulence Turbulent Flows: Turbulence simulation
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 873 , 25 August 2019 , pp. 459 - 474
Check for updates
Copyright
© 2019 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

Aronovitz, J. A. & Nelson, D. R. 1984 Turbulence in phase-separating binary mixtures. Phys. Rev. A 29, 2012–2016.Google Scholar
Balkovsky, E., Fouxon, A. & Lebedev, V. 2001 Turbulence in polymer solutions. Phys. Rev. E 64, 056301.Google Scholar
Berti, S., Boffetta, G., Cencini, M. & Vulpiani, A. 2005 Turbulence and coarsening in active and passive binary mixtures. Phys. Rev. Lett. 95, 224501.Google Scholar
Bray, A. J. 1994 Theory of phase-ordering kinetics. Adv. Phys. 43, 357–459.Google Scholar
Cahn, J. 1968 Spinodal decomposition. Trans. Metall. Soc. AIME 242, 166–180.Google Scholar
Cantwell, B. J. 1992 Exact solution of a restricted Euler equation for the velocity gradient tensor. Phys. Fluids A 4, 782–793.Google Scholar
Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. A. 1988 Spectral Methods in Fluid Dynamics. Springer.Google Scholar
Cates, M. E. & Tjhung, E. 2018 Theories of binary fluid mixtures: from phase-separation kinetics to active emulsions. J. Fluid Mech. 836, 1–68.Google Scholar
Celani, A., Mazzino, A., Muratore-Ginanneschi, P. & Vozella, L. 2009 Phase-field model for the Rayleigh–Taylor instability of immisible fluids. J. Fluid Mech. 622, 115–134.Google Scholar
Chaikin, P. M. & Lubensky, T. C. 1998 Principles of Condensed Matter Physics. Cambridge University Press.Google Scholar
Cox, S. M. & Matthews, P. C. 2002 Exponential time differencing for stiff systems. J. Comput. Phys. 176, 430–455.Google Scholar
Datt, C., Thampi, S. P. & Govindarajan, R. 2015 Morphological evolution of domains in spinodal decomposition. Phys. Rev. E 91, 010101.Google Scholar
Easwar, N. 1992 Effect of continuous stirring on off-critical and critical samples of a phase-separating binary liquid mixture. Phys. Rev. Lett. 68, 186–189.Google Scholar
Fan, X., Diamond, P. H. & Chacon, L. 2018 Chns: a case study of turbulence in elastic media. Phys. Plasmas 25, 055702.Google Scholar
Fan, X., Diamond, P. H., Cahcon, L. & Hui, L. 2016 Cascades and spectra of a turbulent spinodal decomposition in two-dimensional symmetric binary liquid mixtures. Phys. Rev. Fluids 1, 054403.Google Scholar
Frisch, U. 1996 Turbulence the Legacy of A.N. Kolmogorov. Cambridge University Press.Google Scholar
Furukawa, H. 1985 Effect of inertia on droplet growth in a fluid. Phys. Rev. A 31, 1103–1108.Google Scholar
Furukawa, H. 2000 Spinodal decomposition of two-dimensional fluid mixtures: a spectral analysis of droplet growth. Phys. Rev. E 61, 1423–1431.Google Scholar
Goldenfeld, N. 2005 Lectures on Phase Transitions and the Renormalization Group. Levant Books.Google Scholar
Hashimoto, T., Matsuzaka, K., Moses, E. & Onuki, A. 1995 String phase in phase-separating fluids under shear flow. Phys. Rev. Lett. 74, 126–129.Google Scholar
Hinze, J. O. 1955 Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AIChE J. 1, 289–295.Google Scholar
Hohenburg, P. & Halperin, B. 1977 Theory of dynamic critical phenomena. Rev. Mod. Phys. 49, 435–479.Google Scholar
Ishihara, T., Gotoh, T. & Kaneda, Y. 2009 Study of high-Reynolds number isotropic turbulence by direct numerical simulation. Annu. Rev. Fluid Mech. 41, 165–180.Google Scholar
Jacqmin, D. 1999 Calculation of two-phase navier-stokes flows using phase-field modeling. J. Comput. Phys. 155, 96–127.Google Scholar
Kendon, V. M. 2000 Scaling theory of three-dimensional spinodal turbulence. Phys. Rev. E 61, R6071.Google Scholar
Kendon, V. M., Cates, M. E., Paganobarraga, I., Desplat, J. C. & Bladon, P. 2001 Inertial effects in three-dimensional spindoal decomposition of a symmetric binary fluid mixture: a lattice Boltzmann study. J. Fluid Mech. 440, 147–203.Google Scholar
Kolmogorov, A. N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk USSR 30, 9–13.Google Scholar
Lifshitz, I. M. & Slyozov, V. V. 1961 The kinetics of precipitation from supersaturated solid solutions. J. Phys. Chem. Solids 19, 35–50.Google Scholar
Magaletti, F., Picano, F., Chinappi, M., Marino, L. & Casciola, C. M. 2013 The sharp-interface limit of the Cahn–Hilliard/Navier–Stokes model for binary fluids. J. Fluid Mech. 714, 95–126.Google Scholar
Onuki, A. 2002 Phase Transition Dynamics. Cambridge University Press.Google Scholar
Pandit, R., Banerjee, D., Bhatnagar, A., Brachet, M., Gupta, A., Mitra, D., Pal, N., Perlekar, P., Ray, S. S., Shukla, V. et al. 2017 An overview of the statistical properties of two-dimensional turbulence in fluids with particles, conducting fluids, fluids with polymer additives, binary-fluid mixtures, and superfluids. Phys. Fluids 29, 111112.Google Scholar
Pandit, R., Perlekar, P. & Ray, S. S. 2009 Statistical properties of turbulence: an overview. Pramana 73, 179–213.Google Scholar
Perlekar, P., Benzi, R., Clercx, H. J. H., Nelson, D. R. & Toschi, F. 2014 Spinodal decomposition in homogeneous and isotropic turbulence. Phys. Rev. Lett. 112, 014502.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
Perlekar, P., Mitra, D. & Pandit, R. 2010 Direct numerical simulations of statistically steady, homogeneous, isotropic fluid turbulence with polymer additives. Phys. Rev. E 82, 066313.Google Scholar
Perlekar, P., Pal, N. & Pandit, R. 2017 Two-dimensional turbulence in symmetric binary-fluid mixtures: coarsening arrest by the inverse cascade. Sci. Rep. 7, 44589.Google Scholar
Perry, A. E. & Chong, M. S. 1987 A description of eddying motions and flow patterns using critical-point concepts. Annu. Rev. Fluid Mech. 19, 125–155.Google Scholar
Pine, D. J., Easwar, N., Maher, J. V. & Goldburg, W. I. 1984 Turbulent suppression of spinodal decomposition. Phys. Rev. A 29, 308–313.Google Scholar
Popinet, S. & Jones, T.2004 Gts: Gnu triangulated surface library. http://gts.sourceforge.net.Google Scholar
Puri, S. 2009 Kinetics of phase transitions. In Kinetics of Phase Transitions (ed. Puri, S. & Wadhawan, V.), vol. 6, p. 437. CRC Press.Google Scholar
Scarbolo, L., Molin, D., Perlekar, P., Sbragaglia, M., Soldati, A. & Toschi, F. 2013 Unified framework for a side-by-side comparison of different multicomponent algorithms: lattice Boltzmann versus phase filed model. J. Comput. Phys. 234, 263–279.Google Scholar
Siggia, E. D. 1979 Late stages of spinodal decomposition in binary mixtures. Phys. Rev. A 20, 595–605.Google Scholar
Stansell, P., Stratford, K., Desplat, J. C., Adhikari, R. & Cates, M. E. 2006 Nonequilibrium steady states in sheared binary fluids. Phys. Rev. Lett. 96, 085701.Google Scholar
Stratford, K., Desplat, J. C., Stansell, P. & Cates, M. E. 2007 Binary fluids under steady shear in three dimensions. Phys. Rev. E 76, 030501(R).Google Scholar
Valente, P. C., Silva, d. C. B. & Pinho, F. T. 2014 The effect of viscoelasticity on the turbulent kinetic energy cascade. J. Fluid Mech. 760, 39–62.Google Scholar
Vincent, A. & Meneguzzi, M. 1991 The spatial structure and statistical properties of homogeneous turbulence. J. Fluid. Mech. 225, 1–20.Google Scholar
Wims, A. M., Sengers, J. V., McIntyre, D. & Shereshefsky, J. 1970 Interfacial tension of 3-methylpentane-nitroethane near the critical point. J. Chem. Phys. 52, 3042–3049.Google Scholar
Yue, P., Zhou, C. & Feng, J. J. 2010 Sharp-interface limit of the Cahn–Hilliard model for moving contact lines. J. Fluid Mech. 645, 279–294.Google Scholar