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

Abstract

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 mecha- nisms 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.

Key words： liquid metal; hybrid fluid; hydrodynamics; surface tension; applied fields; self-actuation

Acknowledgments

This work is partially supported by the NSFC 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. z151100003715002).

References

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): 259–272

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): 463–469

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): 193–210

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): 1920–1923

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): 193508

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): 113–126

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): 3567–3581

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): 1607–1626

9 Schnitzer O, Itzchak F, Ehud Y. Electrokinetic flows about conducting drops. Journal of Fluid Mechanics, 2013, 722: 394–423

10 Stone H A. Dynamics of drop deformation and breakup in viscous fluids. Annual Review of Fluid Mechanics, 2003, 26(26): 65–102

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, 45–62

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): 550–589

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): 597–603

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, 1965

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, 1994

16 Gough R C, Morishita A M, Dang J H, Moorefield M R, Shiroma W A, Ohta A T. Rapid electrocapillary deformation of liquid metal with reversible shape retention. Micro & Nano Systems Letters, 2015, 3(1): 1–9

17 Zhao X, Xu S, Liu J. Surface tension of liquid metal: role, mechanism and application. Frontiers in Energy, 2017, 11(4): 535–567

18 Sheng L, Zhang J, Liu J. Diverse transformations of liquid metals between different morphologies. Advanced Materials, 2014, 26(34): 6036–6042

PMID

19 Zhang J, Yao Y, Sheng L, Liu J. Self-fueled biomimetic liquid metal mollusk. Advanced Materials, 2015, 27(16): 2648–2655

PMID

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): 1600212

PMID

21 Hu L, Wang L, Ding Y, Zhan S, Liu J. Manipulation of liquid metals on a graphite surface. Advanced Materials, 2016, 28(41): 9210–9217

PMID

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: 94692–94698

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), 101603

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): 4722–4729

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): 384–402

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): 964–974

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): 1327–1334

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): 301–308

29 Tang J, Wang J, Liu J, Zhou Y. A volatile fluid assisted thermo-pneumatic liquid metal energy harvester. Applied Physics Letters, 2016, 108(2): 023903

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): 3718–3725

31 Sánchez S, Soler L, Katuri J. Chemically powered micro- and nanomotors. Angewandte Chemie International Edition, 2015, 54(5): 1414–1444

PMID

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, 2015

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): 3304–3309

PMID

34 Liu J. Liquid metal machine is evolving to soft robotics. Science China. Technological Sciences, 2016, 59(11): 1793–1794

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: 80–89

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): 306–316

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): 331–346

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): 041905

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): 611–614

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): 32–38

41 Zhang J, Yao Y, Liu J. Autonomous convergence and divergence of the self-powered soft liquid metal vehicles. Science Bulletin, 2015, 60(10): 943–951

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): 6–4

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): 13424

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): 648–653

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): 1203–1210

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): 5253–5261

PMID

47 Fang W Q, He Z Z, Liu J. Electro-hydrodynamic shooting phenomenon of liquid metal stream. Applied Physics Letters, 2014, 105(13): 134104

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): 7116

PMID

49 Hu L, Yuan B, Liu J. Liquid metal amoeba with spontaneous pseudopodia formation and motion capability. Scientific Reports, 2017, 7(1): 7256

PMID

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): 20150177

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, 2008

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, 2009

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): 056107

PMID

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): 11–22

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): 981–985

56 Gao Y, Liu J. Gallium-based thermal interface material with high compliance and wettability. Applied Physics. A, Materials Science & Processing, 2012, 107(3): 701–708

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): 576–594

PMID

58 Grahame D C. Electrode processes and the electrical double layer. Annual Review of Physical Chemistry, 1995, 6(1): 337–358

59 Saville D A. ELECTROHYDRODYNAMICS: the Taylor-Melcher leaky dielectric model. Annual Review of Fluid Mechanics, 2003, 29(29): 27–64

60 HaaseR, Harff K. On electroosmosiis and related phenomena. Journal of Membrane Science. 1983, 12(3): 279–288

61 Frumkin A. New electrocapillary phenomena. Journal of Colloid Science, 1946, 1(3): 277–291

62 Booth F. The cataphoresis of spherical fluid droplets in electrolytes. Journal of Chemical Physics, 1951, 19(11): 1331–1336

63 Levich V G, Rice S A. Physicochemical hydrodynamics. Physics Today, 1963, 16(5): 75–75

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): 1643–1667

65 Schnitzer O, Yariv E. Nonlinear electrokinetic flow about a polarized conducting drop. Physical Review E, 2013, 87(4): 041002

PMID

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): 113302

67 Teigen K E, Munkejord S T. Influence of surfactant on drop deformation in an electric field. Physics of Fluids, 2010, 22(11): 112104

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: 289–326

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: 238–245

70 Melheim J A. Computer simulation of turbulent electrocoalescence. Dissertation for the Master’s Degree. Norway: Fakultet for Ingeniørvitenskap Og Teknologi, 2007

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): 196–200

PMID

72 Thompson R L, Dewitt K J, Labus T L. Marangoni bubble notion phenomenon in zero gravity. Chemical Engineering Communications, 2007, 5(5-6): 299–314

73 Wang F C, Yang F, Zhao Y P. Size effect on the coalescence-induced self-propelled droplet. Applied Physics Letters, 2011, 98(5): 053112

74 Taylor G. Studies in electrohydrodynamics. I. the circulation produced in a drop by electrical field. Proceedings of the Royal Society of A, 1966, 291(1425): 159–166

75 Ajayi O O. A note on Taylor’s electrohydrodynamic theory. Proceedings of the Royal Society A, 1719, 1978(364): 499–507

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): 6–10

PMID

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): 295–319

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, 141:304–309

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): 1267–1285

80 Shan X, Chen H. Lattice Boltzmann model for simulating flows with multiple phases and components. Physical Review E, 1993, 47(3): 1815–1819

PMID

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): 150–161

82 Miksis M J. Shape of a drop in an electric field. Physics of Fluids, 1981, 24(11): 1967–1972

83 Sherwood J D. Breakup of fluid droplets in electric and magnetic fields. Journal of Fluid Mechanics, 2006, 188(188): 133–146

84 Baygents J C, Rivette N J, Stone H A. Electrohydrodynamic deformation and interaction of drop pairs. Journal of Fluid Mechanics, 1998, 368(368): 359–375

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): 239–264

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): 329

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): 698–703

88 Strang G, Fix G J. An Analysis of the Finite Element method. Englewood Cliffs: Prentice-Hall, 1973

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: 289–326

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): 093302

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): 708–759

92 Unverdi S O, Tryggvason G. A front-tracking method for viscous, incompressible, multi-fluid flows. Journal of Computational Physics, 1992, 100(1): 25–37

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): 113302