Hostname: page-component-848d4c4894-mwx4w Total loading time: 0 Render date: 2024-06-19T17:46:57.744Z Has data issue: false hasContentIssue false
  • English
  • Français

Intermittency in turbulent emulsions

Published online by Cambridge University Press:  06 October 2023

M. Crialesi-Esposito Open the ORCID record for M. Crialesi-Esposito [Opens in a new window] ,
G. Boffetta Open the ORCID record for G. Boffetta [Opens in a new window] ,
L. Brandt Open the ORCID record for L. Brandt [Opens in a new window] ,
S. Chibbaro Open the ORCID record for S. Chibbaro [Opens in a new window]  and
S. Musacchio Open the ORCID record for S. Musacchio [Opens in a new window]
M. Crialesi-Esposito*
Affiliation:
INFN, Sezione di Torino, via Pietro Giuria 1, 10125 Torino, Italy
G. Boffetta
Affiliation:
Dipartimento di Fisica and INFN, Università degli Studi di Torino, via P. Giuria 1, 10125 Torino, Italy
L. Brandt
Affiliation:
FLOW Centre, KTH Royal Institute of Technology, Stockholm, Sweden Department of Energy and Process Engineering, Norwegian University of Science and Technology (NTNU), Trondheim, Norway
S. Chibbaro
Affiliation:
Université Paris-Saclay, CNRS, LISN, 91400 Orsay, France
S. Musacchio
Affiliation:
Dipartimento di Fisica and INFN, Università degli Studi di Torino, via P. Giuria 1, 10125 Torino, Italy
*
†Email address for correspondence: mcrialesi@unimore.it
Get access Rights & Permissions [Opens in a new window]

Abstract

We investigate the statistics of turbulence in emulsions of two immiscible fluids of the same density. We compute velocity increments between points conditioned to be located in the same phase or in different phases, and examine their probability density functions (PDFs) and the associated structure functions (SFs). This enables us to demonstrate that the presence of the interface reduces the skewness of the PDF at small scales and therefore the magnitude of the energy flux towards the dissipative scales, which is quantified by the third-order SF. The analysis of the higher-order SFs shows that multiphase turbulence is more intermittent than single-phase turbulence. In particular, the local scaling exponents of the SFs display a saturation below the Kolmogorov–Hinze scale, which indicates the presence of large velocity gradients across the interface. Interestingly, the statistics of the velocity differences in the carrier phase recovers that of single-phase turbulence when the viscosity of the dispersed phase is high.

JFM classification

Multiphase and Particle-laden Flows: Multiphase flow Turbulent Flows: Intermittency
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 972 , 10 October 2023 , A37
Check for updates
Copyright
© The Author(s), 2023. Published by 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

Begemann, A., Trummler, T., Trautner, E., Hasslberger, J. & Klein, M. 2022 Effect of turbulence intensity and surface tension on the emulsification process and its stationary state – a numerical study. Can. J. Chem. Engng 100 (12), 3548–3561.CrossRefGoogle Scholar
Benzi, R., Ciliberto, S., Tripiccione, R., Baudet, C., Massaioli, F. & Succi, S. 1993 Extended self-similarity in turbulent flows. Phys. Rev. E 48 (1), R29.CrossRefGoogle ScholarPubMed
Benzi, R., Paladin, G., Parisi, G. & Vulpiani, A. 1984 On the multifractal nature of fully developed turbulence and chaotic systems. J. Phys. A: Math. Gen. 17 (18), 3521.CrossRefGoogle Scholar
Crialesi-Esposito, M., Chibbaro, S. & Brandt, L. 2023 a The interaction of droplet dynamics and turbulence cascade. Commun. Phys. 6 (1), 5.CrossRefGoogle Scholar
Crialesi-Esposito, M., Rosti, M.E., Chibbaro, S. & Brandt, L. 2022 Modulation of homogeneous and isotropic turbulence in emulsions. J. Fluid Mech. 940, A19.CrossRefGoogle Scholar
Crialesi-Esposito, M., Scapin, N., Demou, A.D., Rosti, M.E., Costa, P., Spiga, F. & Brandt, L. 2023 b FluTAS: a GPU-accelerated finite difference code for multiphase flows. Comput. Phys. Commun. 284, 108602.CrossRefGoogle Scholar
Deane, G.B. & Stokes, M.D. 2002 Scale dependence of bubble creation mechanisms in breaking waves. Nature 418 (6900), 839–844.CrossRefGoogle ScholarPubMed
Deike, L., Melville, W.K. & Popinet, S. 2016 Air entrainment and bubble statistics in breaking waves. J. Fluid Mech. 801, 91–129.CrossRefGoogle Scholar
Dodd, M.S. & Ferrante, A. 2014 A fast pressure-correction method for incompressible two-fluid flows. J. Comput. Phys. 273, 416–434.CrossRefGoogle Scholar
Dodd, M.S. & Ferrante, A. 2016 On the interaction of Taylor length scale size droplets and isotropic turbulence. J. Fluid Mech. 806, 356–412.CrossRefGoogle Scholar
French-McCay, D.P. 2004 Oil spill impact modeling: development and validation. Environ. Toxic. Chem. Intl J. 23 (10), 2441–2456.CrossRefGoogle ScholarPubMed
Freund, A. & Ferrante, A. 2019 Wavelet-spectral analysis of droplet-laden isotropic turbulence. J. Fluid Mech. 875, 914–928.CrossRefGoogle Scholar
Frisch, U. 1995 Turbulence. Cambridge University Press.CrossRefGoogle Scholar
Frisch, U. & Parisi, G. 1985 Turbulence and Predictability of Geophysical Fluid Dynamics and Climate Dynamics. North-Holland.Google Scholar
Garrett, C., Li, M. & Farmer, D. 2000 The connection between bubble size spectra and energy dissipation rates in the upper ocean. J. Phys. Oceanogr. 30 (9), 2163–2171.2.0.CO;2>CrossRefGoogle Scholar
Girotto, I., Benzi, R., Di Staso, G., Scagliarini, A., Schifano, S.F. & Toschi, F. 2022 Build up of yield stress fluids via chaotic emulsification. J. Turbul. 23 (6), 265–275.CrossRefGoogle Scholar
Gopalan, B. & Katz, J. 2010 Turbulent shearing of crude oil mixed with dispersants generates long microthreads and microdroplets. Phys. Rev. Lett. 104 (5), 054501.CrossRefGoogle ScholarPubMed
Hinze, J.O. 1955 Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AIChE J. 1 (3), 289–295.CrossRefGoogle Scholar
Ii, S., Sugiyama, K., Takeuchi, S., Takagi, S., Matsumoto, Y. & Xiao, F. 2012 An interface capturing method with a continuous function: the THINC method with multi-dimensional reconstruction. J. Comput. Phys. 231 (5), 2328–2358.CrossRefGoogle 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.CrossRefGoogle Scholar
Kaneda, Y. & Morishita, K. 2012 Small-scale statistics and structure of turbulence – in the light of high resolution direct numerical simulation. In Ten Chapters in Turbulence (ed. P. Davidson, Y. Kaneda & K. Sreenivasan), p. 1–42. Cambridge University Press.CrossRefGoogle Scholar
Kilpatrick, P.K. 2012 Water-in-crude oil emulsion stabilization: review and unanswered questions. Energy Fuels 26 (7), 4017–4026.CrossRefGoogle Scholar
Kokal, S.L. 2005 Crude oil emulsions: a state-of-the-art review. SPE Prod. Facil. 20 (1), 5–13.CrossRefGoogle Scholar
Kolmogorov, A. 1949 On the breakage of drops in a turbulent flow. Dokl. Akad. Nauk SSSR 66, 825–828.Google Scholar
Li, M. & Garrett, C. 1998 The relationship between oil droplet size and upper ocean turbulence. Mar. Pollut. Bull. 36 (12), 961–970.CrossRefGoogle Scholar
Ma, T., Ott, B., Frohlich, J. & Bragg, A.D. 2021 Scale-dependent anisotropy, energy transfer and intermittency in bubble-laden turbulent flows. J. Fluid Mech. 927, A16.CrossRefGoogle Scholar
Mandal, A., Samanta, A., Bera, A. & Ojha, K. 2010 Characterization of oil–water emulsion and its use in enhanced oil recovery. Ind. Engng Chem. Res. 49 (24), 12756–12761.CrossRefGoogle Scholar
McClements, D.J. 2015 Food Emulsions: Principles, Practices, and Techniques. CRC Press.CrossRefGoogle Scholar
Meneveau, C. & Sreenivasan, K.R. 1991 The multifractal nature of turbulent energy dissipation. J. Fluid Mech. 224, 429–484.CrossRefGoogle Scholar
Mininni, P.D., Alexakis, A. & Pouquet, A. 2006 Large-scale flow effects, energy transfer, and self-similarity on turbulence. Phys. Rev. E – Stat. Nonlinear Soft Matt. Phys. 74 (1), 1–13.Google ScholarPubMed
Mukherjee, S., Safdari, A., Shardt, O., Kenjereš, S. & Van den Akker, H.E.A. 2019 Droplet-turbulence interactions and quasi-equilibrium dynamics in turbulent emulsions. J. Fluid Mech. 878, 221–276.CrossRefGoogle Scholar
Nielloud, F. 2000 Pharmaceutical Emulsions and Suspensions: Revised and Expanded. CRC Press.Google Scholar
Olivieri, S., Cannon, I. & Rosti, M.E. 2022 The effect of particle anisotropy on the modulation of turbulent flows. J. Fluid Mech. 950, R2.CrossRefGoogle Scholar
Pandey, V., Ramadugu, R. & Perlekar, P. 2020 Liquid velocity fluctuations and energy spectra in three-dimensional buoyancy-driven bubbly flows. J. Fluid Mech. 884, R6.CrossRefGoogle Scholar
Perlekar, P. 2019 Kinetic energy spectra and flux in turbulent phase-separating symmetric binary-fluid mixtures. J. Fluid Mech. 873, 459–474.CrossRefGoogle 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 (1), 1–5.CrossRefGoogle ScholarPubMed
Qi, Y., Tan, S., Corbitt, N., Urbanik, C., Salibindla, A.K.R. & Ni, R. 2022 Fragmentation in turbulence by small eddies. Nat. Commun. 13 (1), 1–8.CrossRefGoogle ScholarPubMed
Rivière, A., Mostert, W., Perrard, S. & Deike, L. 2021 a Sub-Hinze scale bubble production in turbulent bubble break-up. J. Fluid Mech. 917, A40.CrossRefGoogle Scholar
Rivière, A., Ruth, D., Mostert, W., Deike, L. & Perrard, S. 2021 b Capillary driven fragmentation of large gas bubbles in turbulence. Preprint, arXiv:2112.06480.Google Scholar
Rosti, M.E., Ge, Z., Jain, S.S., Dodd, M.S. & Brandt, L. 2020 Droplets in homogeneous shear turbulence. J. Fluid Mech. 876, 962–984.CrossRefGoogle Scholar
Schumacher, J., Sreenivasan, K.R. & Yakhot, V. 2007 Asymptotic exponents from low-Reynolds-number flows. New J. Phys. 9 (4), 89.CrossRefGoogle Scholar
She, Z.-S. & Leveque, E. 1994 Universal scaling laws in fully developed turbulence. Phys. Rev. Lett. 72 (3), 336.CrossRefGoogle ScholarPubMed
Siggia, E.D. 1981 Numerical study of small-scale intermittency in three-dimensional turbulence. J. Fluid Mech. 107, 375–406.CrossRefGoogle Scholar
Spernath, A. & Aserin, A. 2006 Microemulsions as carriers for drugs and nutraceuticals. Adv. Colloid Interface Sci. 128, 47–64.CrossRefGoogle ScholarPubMed
Sreenivasan, K.R. & Antonia, R.A. 1997 The phenomenology of small-scale turbulence. Annu. Rev. Fluid Mech. 29 (1), 435–472.CrossRefGoogle Scholar
Tryggvason, G., Scardovelli, R. & Zaleski, S. 2011 Direct Numerical Simulations of Gas–Liquid Multiphase Flows. Cambridge University Press.Google Scholar
Vela-Martín, A. & Avila, M. 2021 Deformation of drops by outer eddies in turbulence. J. Fluid Mech. 929, A38.CrossRefGoogle Scholar
Vela-Martín, A. & Avila, M. 2022 Memoryless drop breakup in turbulence. Sci. Adv. 8 (50), eabp9561.CrossRefGoogle ScholarPubMed
Wang, C., Yi, L., Jiang, L. & Sun, C. 2022 Turbulence drag modulation by dispersed droplets in Taylor–Couette flow: the effects of the dispersed phase viscosity. Preprint, arXiv:2210.04500.CrossRefGoogle Scholar
Watanabe, T. & Gotoh, T. 2007 Inertial-range intermittency and accuracy of direct numerical simulation for turbulence and passive scalar turbulence. J. Fluid Mech. 590, 117–146.CrossRefGoogle Scholar
Yi, L., Toschi, F. & Sun, C. 2021 Global and local statistics in turbulent emulsions. J. Fluid Mech. 912, A13.CrossRefGoogle Scholar
Yousefi, A. 2022 Transport and mixing by finite-size particles in turbulent flows. PhD thesis, KTH Royal Institute of Technology.Google Scholar