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Global and local statistics in turbulent emulsions

Published online by Cambridge University Press:  05 February 2021

Lei Yi Open the ORCID record for Lei Yi [Opens in a new window] ,
Federico Toschi Open the ORCID record for Federico Toschi [Opens in a new window]  and
Chao Sun Open the ORCID record for Chao Sun [Opens in a new window]
Lei Yi
Affiliation:
Center for Combustion Energy, Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing100084, PR China
Federico Toschi
Affiliation:
Department of Physics and Department of Mathematics and Computer Science, Eindhoven University of Technology, 5600 MBEindhoven, The Netherlands CNR-IAC, Via dei Taurini 19, 00185Roma, Italy
Chao Sun*
Affiliation:
Center for Combustion Energy, Key Laboratory for Thermal Science and Power Engineering of Ministry of Education, Department of Energy and Power Engineering, Tsinghua University, Beijing100084, PR China Department of Engineering Mechanics, School of Aerospace Engineering, Tsinghua University, Beijing100084, PR China Physics of Fluids Group, Max Planck-University of Twente Centre for Complex Fluid Dynamics, University of Twente, 7500 AEEnschede, The Netherlands
*
†Email address for correspondence: chaosun@tsinghua.edu.cn
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Abstract

Turbulent emulsions are complex physical systems characterized by a strong and dynamical coupling between small-scale droplets and large-scale rheology. By using a specifically designed Taylor–Couette shear flow system, we are able to characterize the statistical properties of a turbulent emulsion made of oil droplets dispersed in an ethanol–water continuous solution, at an oil volume fraction up to 40 %. We find that the dependence of the droplet size on the Reynolds number of the flow at a volume fraction of 1 % can be well described by the Hinze criterion. The distribution of droplet sizes is found to follow a log-normal distribution, hinting at a fragmentation process as the possible mechanism dominating droplet formation. Additionally, the effective viscosity of the turbulent emulsion increases with the volume fraction of the dispersed oil phase, and decreases when the shear strength is increased. We find that the dependence of the effective viscosity on the shear rate can be described by the Herschel–Bulkley model, with a flow index monotonically decreasing with increasing oil volume fraction. This finding indicates that the degree of shear thinning systematically increases with the volume fraction of the dispersed phase. The current findings have important implications for bridging the knowledge on turbulence and low-Reynolds-number emulsion flows to turbulent emulsion flows.

JFM classification

Complex Fluids: Emulsions Multiphase and Particle-laden Flows: Multiphase flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 912 , 10 April 2021 , A13
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Adams, S., Frith, W.J. & Stokes, J.R. 2004 Influence of particle modulus on the rheological properties of agar microgel suspensions. J. Rheol. 48, 1195–1213.CrossRefGoogle Scholar
Bakhuis, D., Ezeta, R., Bullen, P.A., Marin, A., Lohse, D., Sun, C. & Huisman, S.G. 2020 Catastrophic phase inversion in turbulent Taylor–Couette flow. Phys. Rev. Lett. arXiv:2010.03200.Google Scholar
Bosbach, J., Weiss, S. & Ahlers, G. 2012 Plume fragmentation by bulk interactions in turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 108, 054501.CrossRefGoogle ScholarPubMed
Boxall, J.A., Koh, C.A., Sloan, E.D., Sum, A.K. & Wu, D.T. 2012 Droplet size scaling of water-in-oil emulsions under turbulent flow. Langmuir 28 (1), 104–110.CrossRefGoogle ScholarPubMed
Bremond, N. & Villermaux, E. 2006 Atomization by jet impact. J. Fluid Mech. 549, 273–306.CrossRefGoogle Scholar
De Vita, F., Rosti, M.E., Caserta, S. & Brandt, L. 2019 On the effect of coalescence on the rheology of emulsions. J. Fluid Mech. 880, 969–991.CrossRefGoogle Scholar
Derkach, S.R. 2009 Rheology of emulsions. Adv. Colloid Interface Sci. 151 (1–2), 1–23.CrossRefGoogle ScholarPubMed
Ezeta, R., Huisman, S.G., Sun, C. & Lohse, D. 2018 Turbulence strength in ultimate Taylor–Couette turbulence. J. Fluid Mech. 836, 397–412.CrossRefGoogle Scholar
Faroughi, S.A. & Huber, C. 2015 A generalized equation for rheology of emulsions and suspensions of deformable particles subjected to simple shear at low Reynolds number. Rheol. Acta 54 (2), 85–108.CrossRefGoogle Scholar
Farzad, R., Puttinger, S., Pirker, S. & Schneiderbauer, S. 2018 Investigation of droplet size distribution for liquid-liquid emulsions in taylor-couette flows. J. Disper. Sci. Technol. 39 (2), 250–258.CrossRefGoogle Scholar
van Gils, D.P.M., Bruggert, G.-W., Lathrop, D.P., Sun, C. & Lohse, D. 2011 a The Twente turbulent Taylor–Couette (T3C) facility: strongly turbulent (multiphase) flow between two independently rotating cylinders. Rev. Sci. Instrum. 82 (2), 025105.CrossRefGoogle ScholarPubMed
Van Gils, D.P.M., Huisman, S.G., Bruggert, G.-W., Sun, C. & Lohse, D. 2011 b Torque scaling in turbulent Taylor–Couette flow with co-and counterrotating cylinders. Phys. Rev. Lett. 106 (2), 024502.CrossRefGoogle ScholarPubMed
van Gils, D.P.M., Huisman, S.G., Grossmann, S., Sun, C. & Lohse, D. 2012 Optimal Taylor–Couette turbulence. J. Fluid Mech. 706, 118–149.CrossRefGoogle Scholar
Grossmann, S., Lohse, D. & Sun, C. 2016 High–Reynolds number Taylor–Couette turbulence. Annu. Rev. Fluid Mech. 48, 53–80.CrossRefGoogle Scholar
Guazzelli, E. & Pouliquen, O. 2018 Rheology of dense granular suspensions. J. Fluid Mech. 852, P1.CrossRefGoogle Scholar
Herschel, W.H. & Bulkley, R. 1926 Konsistenzmessungen von gummi-benzöllosungen. Kolloidn. Z. 39, 291–300.CrossRefGoogle Scholar
Hinze, J.O. 1955 Fundamentals of the hydrodynamic mechanism of splitting in dispersion processes. AIChE J. 1 (3), 289–295.CrossRefGoogle Scholar
Huisman, S.G., Van Der Veen, R.C.A., Sun, C. & Lohse, D. 2014 Multiple states in highly turbulent Taylor–Couette flow. Nat. Commun. 5 (1), 1–5.CrossRefGoogle ScholarPubMed
Kilpatrick, P.K. 2012 Water-in-crude oil emulsion stabilization: review and unanswered questions. Energy Fuels 26 (7), 4017–4026.CrossRefGoogle Scholar
Krieger, I.M. 1972 Rheology of monodisperse latices. Adv. Colloid Interface Sci. 3 (2), 111–136.CrossRefGoogle Scholar
Krieger, I.M. & Dougherty, T.J. 1959 A mechanism for non-newtonian flow in suspensions of rigid spheres. J. Rheol. 3 (1), 137–152.Google Scholar
Lemenand, T., Della Valle, D., Dupont, P. & Peerhossaini, H. 2017 Turbulent spectrum model for drop-breakup mechanisms in an inhomogeneous turbulent flow. Chem. Engng Sci. 158, 41–49.CrossRefGoogle Scholar
Lemenand, T., Della Valle, D., Zellouf, Y. & Peerhossaini, H. 2003 Droplets formation in turbulent mixing of two immiscible fluids in a new type of static mixer. Intl J. Multiphase Flow 29 (5), 813–840.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. 2007 Critical review of techniques and methodologies for characterization of emulsion stability. Crit. Rev. Food Sci. 47 (7), 611–649.CrossRefGoogle ScholarPubMed
Ostilla-Mónico, R., Van Der Poel, E.P., Verzicco, R., Grossmann, S. & Lohse, D. 2014 Boundary layer dynamics at the transition between the classical and the ultimate regime of Taylor–Couette flow. Phys. Fluids 26 (1), 015114.CrossRefGoogle Scholar
Pacek, A.W., Man, C.C. & Nienow, A.W. 1998 On the sauter mean diameter and size distributions in turbulent liquid/liquid dispersions in a stirred vessel. Chem. Engng Sci. 53 (11), 2005–2011.CrossRefGoogle Scholar
Pacek, A.W., Nienow, A.W. & Moore, I.P.T. 1994 On the structure of turbulent liquid—liquid dispersed flows in an agitated vessel. Chem. Engng Sci. 49 (20), 3485–3498.CrossRefGoogle Scholar
Pal, R., Yan, Y. & Masliyah, J. 1992 Rheology of emulsions. Adv. Chem. 231, 131–170.CrossRefGoogle Scholar
Perlekar, P., Biferale, L., Sbragaglia, M., Srivastava, S. & Toschi, F. 2012 Droplet size distribution in homogeneous isotropic turbulence. Phys. Fluids 24 (6), 065101.CrossRefGoogle Scholar
Rosti, M.E., Brandt, L. & Mitra, D. 2018 Rheology of suspensions of viscoelastic spheres: deformability as an effective volume fraction. Phys. Rev. Fluids 3 (1), 012301.CrossRefGoogle Scholar
Saiki, Y., Prestidge, C.A. & Horn, R.G. 2007 Effects of droplet deformability on emulsion rheology. Colloids Surf. A 299 (1–3), 65–72.CrossRefGoogle Scholar
Singh, A. & Nott, P.R. 2003 Experimental measurements of the normal stresses in sheared Stokesian suspensions. J. Fluid Mech. 490, 293–320.CrossRefGoogle Scholar
Spernath, A. & Aserin, A. 2006 Microemulsions as carriers for drugs and nutraceuticals. Adv. Colloid Interface Sci. 128, 47–64.CrossRefGoogle ScholarPubMed
Stickel, J.J. & Powell, R.L. 2005 Fluid mechanics and rheology of dense suspensions. Annu. Rev. Fluid Mech. 37, 129–149.CrossRefGoogle Scholar
Tadros, Th.F. 1994 Fundamental principles of emulsion rheology and their applications. Colloids Surf. A 91, 39–55.CrossRefGoogle Scholar
Urdahl, O., Fredheim, A.O. & Løken, K.-P. 1997 Viscosity measurements of water-in-crude-oil emulsions under flowing conditions: a theoretical and practical approach. Colloids Surf. A 123, 623–634.CrossRefGoogle Scholar
Villermaux, E. 2007 Fragmentation. Annu. Rev. Fluid Mech. 39, 419–446.CrossRefGoogle Scholar
Villone, M.M. & Maffettone, P.L. 2019 Dynamics, rheology, and applications of elastic deformable particle suspensions: a review. Rheol. Acta 58 (3–4), 109–130.CrossRefGoogle Scholar
Wang, L., Li, X., Zhang, G., Dong, J. & Eastoe, J. 2007 Oil-in-water nanoemulsions for pesticide formulations. J. Colloid Interface Sci. 314 (1), 230–235.CrossRefGoogle ScholarPubMed
Zarraga, I.E., Hill, D.A. & Leighton, D.T.Jr. 2000 The characterization of the total stress of concentrated suspensions of noncolloidal spheres in newtonian fluids. J. Rheol. 44 (2), 185–220.CrossRefGoogle Scholar
Zhou, Q., Sun, C. & Xia, K.-Q. 2007 Morphological evolution of thermal plumes in turbulent Rayleigh–Bénard convection. Phys. Rev. Lett. 98, 074501.CrossRefGoogle ScholarPubMed