Unconventional hydrodynamics of hybrid fluid made of liquid metals and aqueous solution under applied fields

Review Article


The hydrodynamic characteristics of hybrid fluid made of liquid metal/aqueous solution are elementary in the design and operation of conductive flow in a variety of newly emerging areas such as chip cooling, soft robot, and biomedical practices. In terms of physical and chemical properties, such as density, thermal conductivity and electrical conductivity, their huge differences between the two fluidic phases remain a big challenge for analyzing the hybrid flow behaviors. Besides, the liquid metal immersed in the solution can move and deform when administrated with non-contact electromagnetic force, or even induced by redox reaction, which is entirely different from the cases of conventional contact force. Owing to its remarkable capability in flow and deformation, liquid metal immersed in the solution is apt to deform on an extremely large scale, resulting in marked changes on its boundary and interface. However, the working mechanisms of the movement and deformation of liquid metal lack appropriate models to describe such scientific issues via a set of well-established unified equations. To promote investigations in this important area, the present paper is dedicated to summarizing this unconventional hydrodynamics from experiment, theory, and simulation. Typical experimental phenomena and basic working mechanisms are illustrated, followed by the movement and deformation theories to explain these phenomena. Several representative simulation methods are then proposed to tackle the governing functions of the electrohydrodynamics. Finally, prospects and challenges are raised, offering an insight into the new physics of the hybrid fluid under applied fields.


liquid metal hybrid fluid hydrodynamics surface tension applied fields self-actuation 


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This work was partially supported by the National Natural Science Foundation of China Key Project (Grant No. 91748206), the Dean’s Research Funding and the Frontier Project of the Chinese Academy of Sciences, as well as Beijing Municipal Science (Grant No. z1511000037 15002).


  1. 1.
    Eow J S, Ghadiri M. Motion, deformation and break-up of aqueous drops in oils under high electric field strengths. Chemical Engineering & Processing Process Intensification, 2003, 42(4): 259–272CrossRefGoogle Scholar
  2. 2.
    Eow J S, Ghadiri M, Sharif A. Deformation and break-up of aqueous drops in dielectric liquids in high electric fields. Journal of Electrostatics, 2001, 51–52(1): 463–469CrossRefGoogle Scholar
  3. 3.
    Eow J S, Ghadiri M, Sharif A. Experimental studies of deformation and break-up of aqueous drops in high electric fields. Colloids and Surfaces. A, Physicochemical and Engineering Aspects, 2003, 225 (1–3): 193–210CrossRefGoogle Scholar
  4. 4.
    Tsouris C, Depaoli D W, Feng J Q, Basaran O A, Scott T C. Electrostatic spraying of nonconductive fluids into conductive fluids. AIChE Journal, 1994, 40(11): 1920–1923CrossRefGoogle Scholar
  5. 5.
    Choi J, Kim Y J, Lee S, Son S U, Ko H S, Nguyen V D, Byun D. Drop-on-demand printing of conductive ink by electrostatic field induced inkjet head. Applied Physics Letters, 2008, 93(19): 193508CrossRefGoogle Scholar
  6. 6.
    Choo R T C, Toguri J M. The electrodynamic behavior of metal and metal sulphide droplets in slags. Canadian Metallurgical Quarterly, 1992, 31(2): 113–126CrossRefGoogle Scholar
  7. 7.
    Mangelsdorf C S, White L R. Electrophoretic mobility of a spherical colloidal particle in an oscillating electric field. Journal of the Chemical Society, Faraday Transactions 2, 1992, 88(24): 3567–3581CrossRefGoogle Scholar
  8. 8.
    O’Brien R W, White L R. Electrophoretic mobility of a spherical colloidal particle. Journal of the Chemical Society, Faraday Transactions 2, 1978, 74(1): 1607–1626CrossRefGoogle Scholar
  9. 9.
    Schnitzer O, Itzchak F, Ehud Y. Electrokinetic flows about conducting drops. Journal of Fluid Mechanics, 2013, 722: 394–423MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Stone H A. Dynamics of drop deformation and breakup in viscous fluids. Annual Review of Fluid Mechanics, 2003, 26(26): 65–102MATHGoogle Scholar
  11. 11.
    Moffatt H K. Rotation of a liquid metal under the action of a rotating magnetic field. In: MHD-Flows and Turbulence. II. Jerusalem: Israel Universities Press, 1980, 45–62Google Scholar
  12. 12.
    Karyappa D, Deshmukh S D, Thaokar R M. Breakup of a conducting drop in a uniform electric field. Journal of Fluid Mechanics, 2014, 754(754): 550–589CrossRefGoogle Scholar
  13. 13.
    Yang X H, Tan S C, Yuan B, Liu J. Alternating electric field actuated oscillating behavior of liquid metal and its application. Science China. Technological Sciences, 2016, 59(4): 597–603CrossRefGoogle Scholar
  14. 14.
    Plumlee H R. Effects of electrostatic forces on drop collision and coalescence in air. Dissertation for the Doctoral Degree. Urbana-Champaign: University of Illinois at Urbana-Champaign, 1965Google Scholar
  15. 15.
    Tryggvason G, Juric D, Nobari M H R, Selman N. Computations of drop collision and coalescence. In: NASA. Lewis Research Center, 2nd Microgravity Fluid Physics Conference, 1994Google Scholar
  16. 16.
    Gough R C, Morishita AM, Dang J H, MoorefieldMR, ShiromaW A, Ohta A T. Rapid electrocapillary deformation of liquid metal with reversible shape retention. Micro & Nano Systems Letters, 2015, 3(1): 1–9CrossRefGoogle Scholar
  17. 17.
    Zhao X, Xu S, Liu J. Surface tension of liquid metal: role, mechanism and application. Frontiers in Energy, 2017, 11(4): 535–567CrossRefGoogle Scholar
  18. 18.
    Sheng L, Zhang J, Liu J. Diverse transformations of liquid metals between different morphologies. Advanced Materials, 2014, 26(34): 6036–6042CrossRefGoogle Scholar
  19. 19.
    Zhang J, Yao Y, Sheng L, Liu J. Self-fueled biomimetic liquid metal mollusk. Advanced Materials, 2015, 27(16): 2648–2655CrossRefGoogle Scholar
  20. 20.
    Yuan B, Wang L, Yang X, Ding Y, Tan S, Yi L, He Z, Liu J. Liquid metal machine triggered violin-like wire oscillator. Advancement of Science, 2016, 3(10): 1600212Google Scholar
  21. 21.
    Hu L, Wang L, Ding Y, Zhan S, Liu J. Manipulation of liquid metals on a graphite surface. Advanced Materials, 2016, 28(41): 9210–9217CrossRefGoogle Scholar
  22. 22.
    Yi L, Ding Y, Yuan B, Wang L, Tian L, Chen C, Liu F, Lu J, Song S, Liu J. Breathing to harvest energy as a mechanism towards making a liquid metal beating heart. RSC Advances, 2016, 6: 94692–94698CrossRefGoogle Scholar
  23. 23.
    Zhao X, Tang J, Liu J. Surfing liquid metal droplet on the same metal bath via electrolyte interface. Applied Physics Letters, 2017, 111(10), 101603CrossRefGoogle Scholar
  24. 24.
    Ma K Q, Liu J. Heat-driven liquid metal cooling device for the thermal management of a computer chip. Journal of Physics. D, Applied Physics, 2007, 40(15): 4722–4729CrossRefGoogle Scholar
  25. 25.
    Ma K, Liu J. Liquid metal cooling in thermal management of computer chips. Frontiers of Energy and Power Engineering in China, 2007, 1(4): 384–402CrossRefGoogle Scholar
  26. 26.
    Ma K Q, Liu J, Xiang S H, Xie K W, Zhou Y X. Study of thawing behavior of liquid metal used as computer chip coolant. International Journal of Thermal Sciences, 2009, 48(5): 964–974CrossRefGoogle Scholar
  27. 27.
    Deng Y, Liu J. Hybrid liquid metal–water cooling system for heat dissipation of high power density microdevices. Heat and Mass Transfer, 2010, 46(11–12): 1327–1334CrossRefGoogle Scholar
  28. 28.
    Tan S C, Zhou Y X, Wang L, Liu J. Electrically driven chip cooling device using hybrid coolants of liquid metal and aqueous solution. Science China. Technological Sciences, 2016, 59(2): 301–308CrossRefGoogle Scholar
  29. 29.
    Tang J, Wang J, Liu J, Zhou Y. A volatile fluid assisted thermopneumatic liquid metal energy harvester. Applied Physics Letters, 2016, 108(2): 023903CrossRefGoogle Scholar
  30. 30.
    Tang W, Jiang T, Fan F R, Yu A F, Zhang C, Cao X, Wang Z L. Liquid-metal electrode for high-performance triboelectric nanogenerator at an instantaneous energy conversion efficiency of 70.6%. Advanced Functional Materials, 2015, 25(24): 3718–3725CrossRefGoogle Scholar
  31. 31.
    Sánchez S, Soler L, Katuri J. Chemically powered micro- and nanomotors. Angewandte Chemie International Edition, 2015, 54 (5): 1414–1444CrossRefGoogle Scholar
  32. 32.
    Gao M, Gui L. Possibility and mechanism study of liquid-metal based micro electroosmotic flow pumps for long-time running purpose. In: ASME 2015 13th International Conference on Nanochannels, Microchannels, and Minichannels collocated with the ASME 2015 International Technical Conference and Exhibition on Packaging and Integration of Electronic and Photonic Microsystems, San Francisco, California, USA, 2015Google Scholar
  33. 33.
    Tang S Y, Khoshmanesh K, Sivan V, Petersen P, O’ Mullane A P, Abbott D, Mitchell A, Kalantar-Zadeh K. Liquid metal enabled pump. Proceedings of the National Academy of Sciences of the United States of America, 2014, 111(9): 3304–3309CrossRefGoogle Scholar
  34. 34.
    Liu J. Liquid metal machine is evolving to soft robotics. Science China. Technological Sciences, 2016, 59(11): 1793–1794CrossRefGoogle Scholar
  35. 35.
    Yu Y Z, Lu J R, Liu J. 3D printing for functional electronics by injection and package of liquid metals into channels of mechanical structures. Materials & Design, 2017, 122: 80–89CrossRefGoogle Scholar
  36. 36.
    Gui H, Tan S C, Wang Q, Yu Y, Liu F J, Lin J, Liu J. Spraying printing of liquid metal electronics on various clothes to compose wearable functional device. Science China. Technological Sciences, 2017, 60(2): 306–316CrossRefGoogle Scholar
  37. 37.
    Ge H, Li H, Mei S, Liu J. Low melting point liquid metal as a new class of phase change material: an emerging frontier in energy area. Renewable & Sustainable Energy Reviews, 2013, 21(5): 331–346CrossRefGoogle Scholar
  38. 38.
    Mei S, Gao Y, Li H, Deng Z, Liu J. Thermally induced porous structures in printed gallium coating to make transparent conductive film. Applied Physics Letters, 2013, 102(4): 041905CrossRefGoogle Scholar
  39. 39.
    Vazquez G, Alvarez E, Navaza J M. Surface tension of alcohol + water from 20°C to 50°C. Journal of Chemical & Engineering Data, 1995, 40(3): 611–614CrossRefGoogle Scholar
  40. 40.
    Tan S C, Yuan B, Liu J. Electrical method to control the running direction and speed of self-powered tiny liquid metal motors. Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, 2015, 471(2183): 32–38Google Scholar
  41. 41.
    Zhang J, Yao Y, Liu J. Autonomous convergence and divergence of the self-powered soft liquid metal vehicles. Science Bulletin, 2015, 60(10): 943–951CrossRefGoogle Scholar
  42. 42.
    Bojarevičs A, Beinerts T, Sarma M, Gelfgat Y. Experiments on liquid metal flow induced by rotating magnetic dipole moment. Journal for Manufacturing Science & Production, 2015, 46(1): 6–4Google Scholar
  43. 43.
    Tan S C, Gui H, Yuan B, Liu L. Magnetic trap effect to restrict motion of self-powered tiny liquid metal motors. Applied Physics Letters, 2015, 18(7): 13424Google Scholar
  44. 44.
    Yuan B, He Z, Fang W, Bao X, Liu J. Liquid metal spring: oscillating coalescence and ejection of contacting liquid metal droplets. Science Bulletin, 2015, 60(6): 648–653CrossRefGoogle Scholar
  45. 45.
    Yuan B, Tan S, Zhou Y, Liu J. Self-powered macroscopic Brownian motion of spontaneously running liquid metal motors. Science Bulletin, 2015, 60(13): 1203–1210CrossRefGoogle Scholar
  46. 46.
    Sheng L, He Z, Yao Y, Liu J. Transient state machine enabled from the colliding and coalescence of a swarm of autonomously running liquid metal motors. Small, 2015, 11(39): 5253–5261CrossRefGoogle Scholar
  47. 47.
    Fang W Q, He Z Z, Liu J. Electro-hydrodynamic shooting phenomenon of liquid metal stream. Applied Physics Letters, 2014, 105(13): 134104CrossRefGoogle Scholar
  48. 48.
    Zhang J, Sheng L, Liu J. Synthetically chemical-electrical mechanism for controlling large scale reversible deformation of liquid metal objects. Scientific Reports, 2014, 4(1): 7116CrossRefGoogle Scholar
  49. 49.
    Hu L, Yuan B, Liu J. Liquid metal amoeba with spontaneous pseudopodia formation and motion capability. Scientific Reports, 2017, 7(1): 7256CrossRefGoogle Scholar
  50. 50.
    Wang L, Liu J. Electromagnetic rotation of a liquid metal sphere or pool within a solution. Proceedings of the Royal Society. Mathematical, Physical and Engineering Sciences, 2015, 471 (2178): 20150177CrossRefGoogle Scholar
  51. 51.
    Ma K. Study on liquid metal cooling method for thermal management of computer chip. Dissertation for the Doctoral Degree. Beijing: Technical Institute of Physics and Chemistry, Chinese Academy of Science, 2008Google Scholar
  52. 52.
    Xie K. Study on the liquid metal cooling method for thermal management of computer. Dissertation for the Master Degree. Beijing: Technical Institute of Physics and Chemistry, Chinese Academy of Science, 2009Google Scholar
  53. 53.
    Morley N B, Burris J, Cadwallader L C, Nornberg M D. GaInSn usage in the research laboratory. Review of Scientific Instruments, 2008, 79(5): 056107CrossRefGoogle Scholar
  54. 54.
    Pacio J, Wetzel T. Assessment of liquid metal technology status and research paths for their use as efficient heat transfer fluids in solar central receiver systems. Solar Energy, 2013, 93(7): 11–22CrossRefGoogle Scholar
  55. 55.
    Scharmann F, Cherkashinin G, Breternitz V, Knedlik C, Hartung G, Weber T, Schaefer J A. Viscosity effect on GaInSn studied by XPS. Surface and Interface Analysis, 2004, 36(8): 981–985CrossRefGoogle Scholar
  56. 56.
    Gao Y, Liu J. Gallium-based thermal interface material with high compliance and wettability. Applied Physics. A, Materials Science & Processing, 2012, 107(3): 701–708CrossRefGoogle Scholar
  57. 57.
    Gongadze E, Rienen U, Iglič A. Generalized stern models of the electric double layer considering the spatial variation of permittivity and finite size of ions in saturation regime. Cellular & Molecular Biology Letters, 2011, 16(4): 576–594CrossRefGoogle Scholar
  58. 58.
    Grahame D C. Electrode processes and the electrical double layer. Annual Review of Physical Chemistry, 1995, 6(1): 337–358CrossRefGoogle Scholar
  59. 59.
    Saville D A. ELECTROHYDRODYNAMICS: the Taylor-Melcher leaky dielectric model. Annual Review of Fluid Mechanics, 2003, 29(29): 27–64MathSciNetGoogle Scholar
  60. 60.
    Haase R, Harff K. On electroosmosis and related phenomena. Journal of Membrane Science. 1983, 12(3): 279–288CrossRefGoogle Scholar
  61. 61.
    Frumkin A. New electrocapillary phenomena. Journal of Colloid Science, 1946, 1(3): 277–291CrossRefGoogle Scholar
  62. 62.
    Booth F. The cataphoresis of spherical fluid droplets in electrolytes. Journal of Chemical Physics, 1951, 19(11): 1331–1336MathSciNetCrossRefGoogle Scholar
  63. 63.
    Levich V G, Rice S A. Physicochemical hydrodynamics. Physics Today, 1963, 16(5): 75–75CrossRefGoogle Scholar
  64. 64.
    Ohshima H, Healy T W, White L R. Electrokinetic phenomena in a dilute suspension of charged mercury drops. Journal of the Chemical Society, Faraday Transactions, 1984, 80(12): 1643–1667CrossRefGoogle Scholar
  65. 65.
    Schnitzer O, Yariv E. Nonlinear electrokinetic flow about a polarized conducting drop. Physical Review E, 2013, 87(4): 041002CrossRefGoogle Scholar
  66. 66.
    Hua J, Lim L K, Wang C H. Numerical simulation of deformation/ motion of a drop suspended in viscous liquids under influence of steady electric fields. Physics of Fluids, 2008, 20(11): 113302CrossRefMATHGoogle Scholar
  67. 67.
    Teigen K E, Munkejord S T. Influence of surfactant on drop deformation in an electric field. Physics of Fluids, 2010, 22(11): 112104CrossRefGoogle Scholar
  68. 68.
    Feng J Q, Scott T C. A computational analysis of electrohydrodynamics of a leaky dielectric drop in an electric field. Journal of Fluid Mechanics, 1996, 311: 289–326CrossRefMATHGoogle Scholar
  69. 69.
    Lü Y, Tian C, He L, Zhang Q, Wang Z. Numerical simulations on the double-droplets coalescence under the coupling effects of electric field and shearing field. Acta Petrolei Sinica, 2015, 36: 238–245Google Scholar
  70. 70.
    Melheim J A. Computer simulation of turbulent electrocoalescence. Dissertation for the Master’s Degree. Norway: Fakultet for Ingeniørvitenskap Og Teknologi, 2007Google Scholar
  71. 71.
    Wang F C, Feng J T, Zhao Y P. The head-on colliding process of binary liquid droplets at low velocity: high-speed photography experiments and modeling. Journal of Colloid and Interface Science, 2008, 326(1): 196–200CrossRefGoogle Scholar
  72. 72.
    Thompson R L, Dewitt K J, Labus T L. Marangoni bubble notion phenomenon in zero gravity. Chemical Engineering Communications, 2007, 5(5–6): 299–314Google Scholar
  73. 73.
    Wang F C, Yang F, Zhao Y P. Size effect on the coalescenceinduced self-propelled droplet. Applied Physics Letters, 2011, 98 (5): 053112CrossRefGoogle Scholar
  74. 74.
    Taylor G. Studies in electrohydrodynamics. I. the circulation produced in a drop by electrical field. Proceedings of the Royal Society A, 1966, 291(1425): 159–166Google Scholar
  75. 75.
    Ajayi O O. A note on Taylor’s electrohydrodynamic theory. Proceedings of the Royal Society A, 1719, 1978(364): 499–507MATHGoogle Scholar
  76. 76.
    Gough R C, Dang J H, Moorefield M R, Zhang G B, Hihara L H, Shiroma W A, Ohta A T. Self-actuation of liquid metal via redox reaction. ACS Applied Materials & Interfaces, 2016, 8(1): 6–10CrossRefGoogle Scholar
  77. 77.
    Torza S, Cox R G, Mason S G. Electrohydrodynamic deformation and burst of liquid drops. Philosophical Transactions of the Royal Society of London A, 1971, 269(1198): 295–319CrossRefGoogle Scholar
  78. 78.
    Nichols B D, Hirt C W, Hotchkiss R S. A fractional volume of fluid method for free boundary dynamics. Lecture Notes in Physics, 1980, 141: 304–309CrossRefGoogle Scholar
  79. 79.
    Tomar G, Gerlach D, Biswas G, Alleborn N, Sharma A, Durst F, Welch S W J, Delgado A. Two-phase electrohydrodynamic simulations using a volume-of-fluid approach. Journal of Computational Physics, 2007, 227(2): 1267–1285MathSciNetCrossRefMATHGoogle Scholar
  80. 80.
    Shan X, Chen H. Lattice Boltzmann model for simulating flows with multiple phases and components. Physical Review E, 1993, 47(3): 1815–1819CrossRefGoogle Scholar
  81. 81.
    Zhang J, Kwok D Y. A 2D lattice Boltzmann study on electrohydrodynamic drop deformation with the leaky dielectric theory. Journal of Computational Physics, 2005, 206(1): 150–161CrossRefMATHGoogle Scholar
  82. 82.
    Miksis M J. Shape of a drop in an electric field. Physics of Fluids, 1981, 24(11): 1967–1972MathSciNetCrossRefMATHGoogle Scholar
  83. 83.
    Sherwood J D. Breakup of fluid droplets in electric and magnetic fields. Journal of Fluid Mechanics, 2006, 188(188): 133–146MATHGoogle Scholar
  84. 84.
    Baygents J C, Rivette N J, Stone H A. Electrohydrodynamic deformation and interaction of drop pairs. Journal of Fluid Mechanics, 1998, 368(368): 359–375CrossRefMATHGoogle Scholar
  85. 85.
    Lac E, Homsy G M. Axisymmetric deformation and stability of a viscous drop in a steady electric field. Journal of Fluid Mechanics, 2007, 590(590): 239–264MathSciNetMATHGoogle Scholar
  86. 86.
    Stone H A, Lister J R, Brenner M P. Drops with conical ends in electric and magnetic fields. Proceedings of the Royal Society A, 1999, 455(1981): 329CrossRefMATHGoogle Scholar
  87. 87.
    Tsukada T, Katayama T, Ito Y, Hozawa M. Theoretical and experimental studies of circulations inside and outside a deformed drop under a uniform electric field. Journal of Chemical Engineering of Japan, 1993, 26(6): 698–703CrossRefGoogle Scholar
  88. 88.
    Strang G, Fix G J. An Analysis of the Finite Element method. Englewood Cliffs: Prentice-Hall, 1973Google Scholar
  89. 89.
    Feng J Q, Scott T C. A computational analysis of electrohydrodynamics of a leaky dielectric drop in an electric field. Journal of Fluid Mechanics, 1996, 311: 289–326CrossRefMATHGoogle Scholar
  90. 90.
    Fernández A, Tryggvason G, Che J, Ceccio S L. The effects of electrostatic forces on the distribution of drops in a channel flow: two-dimensional oblate drops. Physics of Fluids, 2005, 17(9): 093302CrossRefMATHGoogle Scholar
  91. 91.
    Tryggvason G, Bunner B, Esmaeeli A, Juric D, Al-Rawahi N, Tauber W, Han J, Nas S, Jan Y J. A front-tracking method for the computations of multiphase flow. Journal of Computational Physics, 2001, 169(2): 708–759MathSciNetCrossRefMATHGoogle Scholar
  92. 92.
    Unverdi S O, Tryggvason G. A front-tracking method for viscous, incompressible, multi-fluid flows. Journal of Computational Physics, 1992, 100(1): 25–37CrossRefMATHGoogle Scholar
  93. 93.
    Hua J, Lim L K, Wang C H. Numerical simulation of deformation/ motion of a drop suspended in viscous liquids under influence of steady electric fields. Physics of Fluids, 2008, 20(11): 113302CrossRefMATHGoogle Scholar

Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • Xu-Dong Zhang
    • 1
    • 2
  • Yue Sun
    • 1
    • 2
  • Sen Chen
    • 1
    • 2
  • Jing Liu
    • 1
    • 2
    • 3
  1. 1.Beijing Key Lab of Cryo-Biomedical Engineering and Key Lab of Cryogenics, Technical Institute of Physics and ChemistryChinese Academy of SciencesBeijingChina
  2. 2.School of Future TechnologyUniversity of Chinese Academy of SciencesBeijingChina
  3. 3.Department of Biomedical Engineering, School of MedicineTsinghua UniversityBeijingChina

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