Hostname: page-component-cd9895bd7-jkksz Total loading time: 0 Render date: 2024-12-26T08:51:10.692Z Has data issue: false hasContentIssue false
  • English
  • Français

Towards a phenomenological model on the deformation and orientation dynamics of finite-sized bubbles in both quiescent and turbulent media

Published online by Cambridge University Press:  04 June 2021

Ashik Ullah Mohammad Masuk ,
Yinghe Qi ,
Ashwanth K.R. Salibindla  and
Rui Ni Open the ORCID record for Rui Ni [Opens in a new window]
Ashik Ullah Mohammad Masuk
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD21218, USA
Yinghe Qi
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD21218, USA
Ashwanth K.R. Salibindla
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD21218, USA
Rui Ni*
Affiliation:
Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD21218, USA
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A phenomenological model is proposed to describe the deformation and orientation dynamics of finite-sized bubbles in both quiescent and turbulent aqueous media. This model extends and generalizes a previous work that is limited to only the viscous deformation of neutrally buoyant droplets, conducted by Maffettone & Minale (J. Non-Newtonian Fluid Mech., vol. 78, 1998, pp. 227–241), into a high Reynolds number regime where the bubble deformation is dominated by flow inertia. By deliberately dividing flow inertia into contributions from the slip velocity and velocity gradients, a new formulation for bubble deformation is constructed and validated against two experiments designed to capture the deformation and orientation dynamics of bubbles simultaneously with two types of surrounding flows. The relative importance of each deformation mechanism is measured by its respective dimensionless coefficient, which can be isolated and evaluated independently through several experimental constraints without multi-variable fitting, and the results agree with the model predictions well. The acquired coefficients imply that bubbles reorient through body rotation as they rise in water at rest but through deformation along a different direction in turbulence. Finally, we provide suggestions on how to implement the proposed framework for characterizing the dynamics of deformable bubbles/drops in simulations.

JFM classification

Drops and Bubbles: Bubble dynamics Multiphase and Particle-laden Flows: Gas/liquid flow Turbulent Flows: Isotropic turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 920 , 10 August 2021 , A4
Check for updates
Copyright
© The Author(s), 2021. 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.)

Footnotes

‡

This author contributed equally to this work with the first author.

References

REFERENCES

Allende, S., Henry, C. & Bec, J. 2018 Stretching and buckling of small elastic fibers in turbulence. Phys. Rev. Lett. 121 (15), 154501.CrossRefGoogle ScholarPubMed
Aoyama, S., Hayashi, K., Hosokawa, S. & Tomiyama, A. 2018 Shapes of single bubbles in infinite stagnant liquids contaminated with surfactant. Exp. Therm. Fluid Sci. 96, 460–469.CrossRefGoogle Scholar
Bellani, G. & Variano, E.A. 2012 Slip velocity of large neutrally buoyant particles in turbulent flows. New J. Phys. 14 (12), 125009.CrossRefGoogle Scholar
Bentley, B.J. & Leal, L.G. 1986 An experimental investigation of drop deformation and breakup in steady, two-dimensional linear flows. J. Fluid Mech. 167, 241–283.CrossRefGoogle 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.CrossRefGoogle Scholar
Cano-Lozano, J.C., Martinez-Bazan, C., Magnaudet, J. & Tchoufag, J. 2016 Paths and wakes of deformable nearly spheroidal rising bubbles close to the transition to path instability. Phys. Rev. Fluids 1 (5), 053604.CrossRefGoogle Scholar
Challabotla, N.R., Zhao, L. & Andersson, H.I. 2015 Orientation and rotation of inertial disk particles in wall turbulence. J. Fluid Mech. 766, R2.CrossRefGoogle Scholar
Cisse, M., Homann, H. & Bec, J. 2013 Slipping motion of large neutrally buoyant particles in turbulence. J. Fluid Mech. 735, R1.CrossRefGoogle Scholar
Delvigne, G.A.L. & Sweeney, C.E. 1988 Natural dispersion of oil. Oil Chem. Pollut. 4 (4), 281–310.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
Elghobashi, S. 2019 Direct numerical simulation of turbulent flows laden with droplets or bubbles. Annu. Rev. Fluid Mech. 51, 217–244.CrossRefGoogle Scholar
Ern, P., Risso, F., Fabre, D. & Magnaudet, J., 2012 Wake-induced oscillatory paths of bodies freely rising or falling in fluids. Annu. Rev. Fluid Mech. 44, 97–121.CrossRefGoogle Scholar
Fernandes, P.C., Ern, P., Risso, F. & Magnaudet, J. 2008 Dynamics of axisymmetric bodies rising along a zigzag path. J. Fluid Mech. 606, 209–223.CrossRefGoogle Scholar
Guido, S., Minale, M. & Maffettone, P.L. 2000 Drop shape dynamics under shear-flow reversal. J. Rheol. 44 (6), 1385–1399.CrossRefGoogle Scholar
Guido, S. & Villone, M. 1998 Three-dimensional shape of a drop under simple shear flow. J. Rheol. 42 (2), 395–415.CrossRefGoogle Scholar
Homann, H. & Bec, J. 2010 Finite-size effects in the dynamics of neutrally buoyant particles in turbulent flow. J. Fluid Mech. 651, 81–91.CrossRefGoogle Scholar
Jeffery, G.B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102 (715), 161–179.Google Scholar
Kang, I.S. & Leal, L.G. 1987 Numerical solution of axisymmetric, unsteady free-boundary problems at finite Reynolds number. I. Finite-difference scheme and its application to the deformation of a bubble in a uniaxial straining flow. Phys. Fluids 30 (7), 1929–1940.CrossRefGoogle Scholar
Kennedy, M.R., Pozrikidis, C. & Skalak, R. 1994 Motion and deformation of liquid drops, and the rheology of dilute emulsions in simple shear flow. Comput. Fluids 23 (2), 251–278.CrossRefGoogle Scholar
Kirchhoff, G. 1870 Ueber die bewegung eines rotationskörpers in einer flüssigkeit. J. Reine Angew. Math. 1870 (71), 237–262.Google Scholar
Laın, S., Bröder, D., Sommerfeld, M. & Göz, M.F. 2002 Modelling hydrodynamics and turbulence in a bubble column using the Euler–Lagrange procedure. Intl J. Multiphase Flow 28 (8), 1381–1407.CrossRefGoogle Scholar
Lohse, D. 2018 Bubble puzzles: from fundamentals to applications. Phys. Rev. Fluids 3 (11), 110504.CrossRefGoogle Scholar
Maffettone, P.L. & Minale, M. 1998 Equation of change for ellipsoidal drops in viscous flow. J. Non-Newtonian Fluid Mech. 78 (2–3), 227–241.CrossRefGoogle Scholar
Magnaudet, J. & Eames, I. 2000 The motion of high-Reynolds-number bubbles in inhomogeneous flows. Annu. Rev. Fluid Mech. 32 (1), 659–708.CrossRefGoogle Scholar
Marchioli, C., Fantoni, M. & Soldati, A. 2010 Orientation, distribution, and deposition of elongated, inertial fibers in turbulent channel flow. Phys. Fluids 22 (3), 033301.CrossRefGoogle Scholar
Marchioli, C. & Soldati, A. 2015 Turbulent breakage of ductile aggregates. Phys. Rev. E 91 (5), 053003.CrossRefGoogle ScholarPubMed
Masuk, A.U.M, Salibindla, A.K.R & Ni, R. 2021 a Simultaneous measurements of deforming Hinze-scale bubbles with surrounding turbulence. J. Fluid Mech. 910, A21.CrossRefGoogle Scholar
Masuk, A.U.M, Salibindla, A.K.R & Ni, R. 2021 b The orientational dynamics of deformable finite-sized bubbles in turbulence. J. Fluid Mech. 915, A79.CrossRefGoogle Scholar
Masuk, A.U.M., Salibindla, A. & Ni, R. 2019 a A robust virtual-camera 3D shape reconstruction of deforming bubbles/droplets with additional physical constraints. Intl J. Multiphase Flow 120, 103088.CrossRefGoogle Scholar
Masuk, A.U.M., Salibindla, A., Tan, S. & Ni, R. 2019 b V-ONSET (Vertical Octagonal Noncorrosive Stirred Energetic Turbulence): a vertical water tunnel with a large energy dissipation rate to study bubble/droplet deformation and breakup in strong turbulence. Rev. Sci. Instrum. 90 (8), 085105.CrossRefGoogle ScholarPubMed
Mathai, V., Lohse, D. & Sun, C. 2020 Bubbly and buoyant particle–laden turbulent flows. Annu. Rev. Condens. Matter Phys. 11, 529–559.CrossRefGoogle Scholar
Maxey, M.R. & Riley, J.J. 1983 Equation of motion for a small rigid sphere in a nonuniform flow. Phys. Fluids 26 (4), 883–889.CrossRefGoogle Scholar
Moore, D.W. 1959 The rise of a gas bubble in a viscous liquid. J. Fluid Mech. 6 (1), 113–130.CrossRefGoogle Scholar
Moore, D.W. 1965 The velocity of rise of distorted gas bubbles in a liquid of small viscosity. J. Fluid Mech. 23 (4), 749–766.CrossRefGoogle Scholar
Mordant, N., Crawford, A.M. & Bodenschatz, E. 2004 Experimental Lagrangian acceleration probability density function measurement. Physica D 193 (1–4), 245–251.CrossRefGoogle Scholar
Mougin, G. & Magnaudet, J. 2001 Path instability of a rising bubble. Phys. Rev. Lett. 88 (1), 014502.CrossRefGoogle ScholarPubMed
Mougin, G. & Magnaudet, J. 2002 The generalized Kirchhoff equations and their application to the interaction between a rigid body and an arbitrary time-dependent viscous flow. Intl J. Multiphase Flow 28 (11), 1837–1851.CrossRefGoogle Scholar
Mougin, G. & Magnaudet, J. 2006 Wake-induced forces and torques on a zigzagging/spiralling bubble. J. Fluid Mech. 567, 185–194.CrossRefGoogle Scholar
Ni, R., Kramel, S., Ouellette, N.T. & Voth, G.A. 2015 Measurements of the coupling between the tumbling of rods and the velocity gradient tensor in turbulence. J. Fluid Mech. 766, 202–225.CrossRefGoogle Scholar
Osher, S. & Fedkiw, R.P. 2001 Level set methods: an overview and some recent results. J. Comput. Phys. 169 (2), 463–502.CrossRefGoogle Scholar
Risso, F. 2018 Agitation, mixing, and transfers induced by bubbles. Annu. Rev. Fluid Mech. 50, 25–48.CrossRefGoogle Scholar
Salibindla, A.K.R., Masuk, A.U.M., Tan, S. & Ni, R. 2020 Lift and drag coefficients of deformable bubbles in intense turbulence determined from bubble rise velocity. J. Fluid Mech. 894, A20.CrossRefGoogle Scholar
Scardovelli, R. & Zaleski, S. 1999 Direct numerical simulation of free-surface and interfacial flow. Annu. Rev. Fluid Mech. 31 (1), 567–603.CrossRefGoogle Scholar
Schanz, D., Gesemann, S. & Schröder, A. 2016 Shake-the-box: Lagrangian particle tracking at high particle image densities. Exp. Fluids 57 (5), 70.CrossRefGoogle Scholar
Shan, X. & Chen, H. 1993 Lattice Boltzmann model for simulating flows with multiple phases and components. Phys. Rev. E 47 (3), 1815.CrossRefGoogle ScholarPubMed
Shew, W.L. & Pinton, J.-F. 2006 Dynamical model of bubble path instability. Phys. Rev. Lett. 97 (14), 144508.CrossRefGoogle ScholarPubMed
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.CrossRefGoogle Scholar
Stone, H.A. 1994 Dynamics of drop deformation and breakup in viscous fluids. Annu. Rev. Fluid Mech. 26 (1), 65–102.CrossRefGoogle Scholar
Sussman, M., Smereka, P. & Osher, S. 1994 A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114 (1), 146–159.CrossRefGoogle Scholar
Tan, S., Salibindla, A., Masuk, A.U.M. & Ni, R. 2020 Introducing openLPT: new method of removing ghost particles and high-concentration particle shadow tracking. Exp. Fluids 61 (2), 47.CrossRefGoogle Scholar
Tayler, A.B., Holland, D.J., Sederman, A.J. & Gladden, L.F. 2012 Exploring the origins of turbulence in multiphase flow using compressed sensing MRI. Phys. Rev. Lett. 108 (26), 264505.CrossRefGoogle ScholarPubMed
Taylor, G.I. 1932 The viscosity of a fluid containing small drops of another fluid. Proc. R. Soc. Lond. A 138 (834), 41–48.Google Scholar
Taylor, G.I. 1934 The formation of emulsions in definable fields of flow. Proc. R. Soc. Lond. A 146 (858), 501–523.Google Scholar
Torza, S., Cox, R.G. & Mason, S.G. 1972 Particle motions in sheared suspensions XXVII. Transient and steady deformation and burst of liquid drops. J. Colloid Interface Sci. 38 (2), 395–411.CrossRefGoogle Scholar
Tripathi, M.K., Sahu, K.C. & Govindarajan, R. 2015 Dynamics of an initially spherical bubble rising in quiescent liquid. Nat. Commun. 6 (1), 1–9.CrossRefGoogle ScholarPubMed
Tryggvason, G., Bunner, B., Esmaeeli, A., Juric, D., Al-Rawahi, N., Tauber, W., Han, J., Nas, S. & Jan, Y.-J. 2001 A front-tracking method for the computations of multiphase flow. J. Comput. Phys. 169 (2), 708–759.CrossRefGoogle Scholar
Ugural, A.C. & Fenster, S.K. 2003 Advanced Strength and Applied Elasticity. Pearson Education.Google Scholar
Unverdi, S.O. & Tryggvason, G. 1992 A front-tracking method for viscous, incompressible, multi-fluid flows. J. Comput. Phys. 100, 25–37.CrossRefGoogle Scholar
Variano, E.A., Bodenschatz, E. & Cowen, E.A. 2004 A random synthetic jet array driven turbulence tank. Exp. Fluids 37 (4), 613–615.CrossRefGoogle Scholar
Voth, G.A. & Soldati, A. 2017 Anisotropic particles in turbulence. Annu. Rev. Fluid Mech. 49, 249–276.CrossRefGoogle Scholar
Wanninkhof, R. & McGillis, W.R. 1999 A cubic relationship between air-sea $\textrm {CO}_2$ exchange and wind speed. Geophys. Res. Lett. 26 (13), 1889–1892.CrossRefGoogle Scholar
Yang, D., Chen, B., Chamecki, M. & Meneveau, C. 2015 Oil plumes and dispersion in Langmuir, upper-ocean turbulence: large-eddy simulations and K-profile parameterization. J. Geophys. Res.: Oceans 120 (7), 4729–4759.CrossRefGoogle Scholar