Please wait a minute...
Frontiers in Energy

ISSN 2095-1701

ISSN 2095-1698(Online)

CN 11-6017/TK

邮发代号 80-972

2019 Impact Factor: 2.657

Frontiers in Energy  2017, Vol. 11 Issue (4): 535-567   https://doi.org/10.1007/s11708-017-0463-9
  本期目录
Surface tension of liquid metal: role, mechanism and application
Xi ZHAO1, Shuo XU1, Jing LIU2()
1. Beijing Key Lab of CryoBiomedical Engineering and Key Lab of Cryogenics, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences, Beijing 100190, China
2. Beijing Key Lab of CryoBiomedical Engineering and Key Lab of Cryogenics, Technical Institute of Physics and Chemistry, Chinese Academy of Sciences; Department of Biomedical Engineering, School of Medicine, Tsinghua University, Beijing 100084, China
 全文: PDF(1591 KB)   HTML
Abstract

Surface tension plays a core role in dominating various surface and interface phenomena. For liquid metals with high melting temperature, a profound understanding of the behaviors of surface tension is crucial in industrial processes such as casting, welding, and solidification, etc. Recently, the room temperature liquid metal (RTLM) mainly composed of gallium-based alloys has caused widespread concerns due to its increasingly realized unique virtues. The surface properties of such materials are rather vital in nearly all applications involved from chip cooling, thermal energy harvesting, hydrogen generation, shape changeable soft machines, printed electronics to 3D fabrication, etc. owing to its pretty large surface tension of approximately 700 mN/m. In order to promote the research of surface tension of RTLM, this paper is dedicated to present an overview on the roles and mechanisms of surface tension of liquid metal and summarize the latest progresses on the understanding of the basic knowledge, theories, influencing factors and experimental measurement methods clarified so far. As a practical technique to regulate the surface tension of RTLM, the fundamental principles and applications of electrowetting are also interpreted. Moreover, the unique phenomena of RTLM surface tension issues such as surface tension driven self-actuation, modified wettability on various substrates and the functions of oxides are discussed to give an insight into the acting mechanism of surface tension. Furthermore, future directions worthy of pursuing are pointed out.

Key wordssurface tension    liquid metal    soft machine    printed electronics    electrowetting    self-actuation
收稿日期: 2016-11-26      出版日期: 2017-12-14
Corresponding Author(s): Jing LIU   
 引用本文:   
. [J]. Frontiers in Energy, 2017, 11(4): 535-567.
Xi ZHAO, Shuo XU, Jing LIU. Surface tension of liquid metal: role, mechanism and application. Front. Energy, 2017, 11(4): 535-567.
 链接本文:  
https://academic.hep.com.cn/fie/CN/10.1007/s11708-017-0463-9
https://academic.hep.com.cn/fie/CN/Y2017/V11/I4/535
Fig.1  
Fig.2  
Fig.3  
Fig.4  
Fig.5  
Radius r/ nm Surface tension γ/(mJ·m–2)
Na Cs Ag Ni W
0.1 131.07 38.71 659.90 1329.31 1879.50
0.5 178.00 61.89 863.08 1674.78 2389.02
1 187.09 65.38 891.23 1721.94 2458.83
2 190.43 67.17 905.54 1745.86 2494.24
3 191.62 67.78 910.41 1753.89 2506.12
4 192.21 68.08 912.75 1757.90 2512.08
5 192.57 68.27 914.20 1760.32 2515.66
10 193.28 68.63 917.10 1765.15 2522.82
20 193.64 68.82 918.55 1767.58 2526.41
30 193.76 68.88 919.03 1768.38 2527.61
40 193.82 68.91 919.27 1768.79 2528.20
50 193.86 68.93 919.42 1769.03 2528.56
100 193.93 68.96 919.71 1769.52 2529.28
200 193.96 68.98 919.86 1769.76 2529.64
194.00 69.00 920.00 1770.00 2530.00
Tab.1  
Fig.6  
Elements T/K γ/(mN·m–1) Method Reference
Sn 560 598 Sessile drop [117]
Ni 1726 1687 Pendant drop [143]
Ti 1660 1475 Pendant drop [143]
Cu 1473 1318.1 Constrained drop [169]
Ag 1373 893.1 Constrained drop [169]
Sn90-Ag10 900 518.8 Sessile drop [110]
Sn90-Cu10 800 545.6 Sessile drop [111]
Bi46-Pb29-Sn25 368 423.5 Constrained drop [155]
Tab.2  
Fig.7  
Fig.8  
Fig.9  
Fig.10  
Fig.11  
Fig.12  
Fig.13  
Fig.14  
Fig.15  
Fig.16  
Fig.17  
Fig.18  
Fig.19  
Fig.20  
Fig.21  
1 J U Brackbill, D B Kothe, C Zemach. A continuum method for modeling surface tension. Journal of Computational Physics, 1992, 100(2): 335–354
https://doi.org/10.1016/0021-9991(92)90240-Y
2 E Y Ko, J Choi, J Y Park, I Sohn. Simulation of low carbon steel solidification and mold flux crystallization in continuous casting using a multi-mold simulator. Metals and Materials International, 2014, 20(1): 141–151
https://doi.org/10.1007/s12540-014-1017-x
3 M Shin, J S Oh, J Lee, S Jung, J Lee. Dissolution rate of solid iron into liquid Fe-C alloy. Metals and Materials International, 2014, 20(6): 1139–1143
https://doi.org/10.1007/s12540-014-6018-2
4 F Aqra, A Ayyad. Surface tension of liquid alkali, alkaline, and main group metals: theoretical treatment and relationship investigations. Metallurgical and Materials Transactions A, Physical Metallurgy and Materials Science, 2011, 42(9): 2680–2684
https://doi.org/10.1007/s11661-011-0686-z
5 M R Amin, R C Gosh, G M Bhuiyan. Surface tension of liquid transition and noble metals. Journal of Non-Crystalline Solids, 2013, 380: 42–47
https://doi.org/10.1016/j.jnoncrysol.2013.08.025
6 J Zhao, J R Li, S Liu, M Han. A method to measure surface tension of liquid superalloy at room temperature. Hot Working Technology, 2009, 38(23): 57–60
7 S M Seo, Y H Paik, D S Kim, W P Lee. Interfacial tension and contact angle variations of SUS304 melt in contact with solid oxides and CaO-SiO2-Al2O3 (CaF2) slags at 1470°C. Metals and Materials International, 1996, 2(2): 65–69
https://doi.org/10.1007/BF03025947
8 L Vitos, A V Ruban, H L Skriver, J Kollár. The surface energy of metals. Surface Science, 1998, 411(1-2): 186–202
https://doi.org/10.1016/S0039-6028(98)00363-X
9 S K Kim, W Wang, Y B Kang. Modeling surface tension of multicomponent liquid steel using modified quasichemical model and constrained Gibbs energy minimization. Metals and Materials International, 2015, 21(4): 765–774
https://doi.org/10.1007/s12540-015-4619-z
10 R C Gough, A M Morishita, J H Dang, M R Moorefield, W A Shiroma, A T Ohta. Rapid electrocapillary deformation of liquid metal with reversible shape retention. Micro & Nano Systems Letters, 2015, 3(1): 1–9
https://doi.org/10.1186/s40486-015-0017-z
11 C L Yaws. Handbook of Vapor Pressure: Volume 4: Inorganic Componds and Elements. Huston: Gulf Professional Publishing, 1995
12 F M Blair, J M Whitworth, J F Mccabe. The physical properties of a gallium alloy restorative material. Dental Materials Official Publication of the Academy of Dental Materials, 1995, 11(4): 277–280
https://doi.org/10.1016/0109-5641(95)80063-8
13 Q Zhang, Y Zheng, J Liu. Direct writing of electronics based on alloy and metal (DREAM) ink: a newly emerging area and its impact on energy, environment and health sciences. Frontiers in Energy, 2012, 6(4): 311–340
https://doi.org/10.1007/s11708-012-0214-x
14 X H Yang, S C Tan, J Liu. Thermal management of Li-ion battery with liquid metal. Energy Conversion and Management, 2016, 117: 577–585
https://doi.org/10.1016/j.enconman.2016.03.054
15 H S Ge, J Liu. Keeping smartphones cool with gallium phase change material. Journal of Heat Transfer, 2013, 135(5): 054503
https://doi.org/10.1115/1.4023392
16 H S Ge, H Y Li, S F Mei, J Liu. 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: 331–346
https://doi.org/10.1016/j.rser.2013.01.008
17 Y G Deng, J Liu. Design of practical liquid metal cooling device for heat dissipation of high performance CPUs. Journal of Electronic Packaging, 2010, 132(3): 031009
https://doi.org/10.1115/1.4002012
18 K Q Ma, J Liu. Nano liquid-metal fluid as ultimate coolant. Physics Letters A, 2007, 361(3): 252–256
https://doi.org/10.1016/j.physleta.2006.09.041
19 J Vetrovec, A S Litt, D A Copeland, J Junghans, R Durkee. Liquid metal heat sink for high-power laser diodes. In: International Society for Optics and Photonics, California, USA: SPIE LASE, 2013: 86050
20 J L Jackel, S Hackwood, J J Veselka, G Beni. Electrowetting switch for multimode optical fibers. Applied Optics, 1983, 22(11): 1765–1770
https://doi.org/10.1364/AO.22.001765
21 P Sen, C J Kim. Microscale liquid-metal switches—a review. IEEE Transactions on Industrial Electronics, 2009, 56(4): 1314–1330
https://doi.org/10.1109/TIE.2008.2006954
22 J T H Tsai, C M Ho, F C Wang, C T Liang. Ultrahigh contrast light valve driven by electrocapillarity of liquid gallium. Applied Physics Letters, 2009, 95(25): 251110
https://doi.org/10.1063/1.3278441
23 R D Ponce Wong, J D Posner, V J Santos. Flexible microfluidic normal force sensor skin for tactile feedback. Sensors and Actuators A, Physical, 2012, 179: 62–69
https://doi.org/10.1016/j.sna.2012.03.023
24 C Majidi, R Kramer, R J Wood. A non-differential elastomer curvature sensor for softer-than-skin electronics. Smart Materials and Structures, 2011, 20(10): 105017
https://doi.org/10.1088/0964-1726/20/10/105017
25 Y L Park, C Majidi, R Kramer, P Bérard, R J Wood. Hyperelastic pressure sensing with a liquid-embedded elastomer. Journal of Micromechanics and Microengineering, 2010, 20(12): 125029
https://doi.org/10.1088/0960-1317/20/12/125029
26 A Fassler, C Majidi. Soft-matter capacitors and inductors for hyperelastic strain sensing and stretchable electronics. Smart Materials and Structures, 2013, 22(5): 055023
https://doi.org/10.1088/0964-1726/22/5/055023
27 S Cheng, Z Wu. A microfluidic, reversibly stretchable, large-area wireless strain sensor. Advanced Functional Materials, 2011, 21(12): 2282–2290
https://doi.org/10.1002/adfm.201002508
28 J H So, J Thelen, A Qusba, G J Hayes, J Lazzi, M D Dickey. Reversibly deformable and mechanically tunable fluidic antennas. Advanced Functional Materials, 2009, 19(22): 3632–3637
https://doi.org/10.1002/adfm.200900604
29 S Cheng, A Rydberg, K Hjort, Z Wu. Liquid metal stretchable unbalanced loop antenna. Applied Physics Letters, 2009, 94(14): 144103
https://doi.org/10.1063/1.3114381
30 M Kubo, X Li, C Kim, M Hashimoto, B J Wiley, D Ham, G M Whitesides. Stretchable microfluidic radiofrequency antennas. Advanced Materials, 2010, 22(25): 2749–2752
https://doi.org/10.1002/adma.200904201
31 G J Hayes, J H So, A Qusba, M D Dickey, G Lazzi. Flexible liquid metal alloy (EGaIn) microstrip patch antenna. IEEE Transactions on Antennas and Propagation, 2012, 60(5): 2151–2156
https://doi.org/10.1109/TAP.2012.2189698
32 S Y Tang, K Khoshmanesh, V Sivan, P Petersen, A P O’mullane, D Abbott, A Mitchell, K Kalantarzadeh. Liquid metal enabled pump. Proceedings of the National Academy of Sciences of the United States of America, 2014, 111(9): 3304–3309
https://doi.org/10.1073/pnas.1319878111
33 S Y Tang, V Sivan, P Petersen, W Zhang, P D Morrison, K Kalantar-Zadeh, A Mitchell, K Khoshmanesh. Liquid metal actuator for inducing chaotic advection. Advanced Functional Materials, 2014, 24(37): 5851–5858
https://doi.org/10.1002/adfm.201400689
34 J Zhang, L Sheng, C Jin, J Liu. Liquid metal as connecting or functional recovery channel for the transected sciatic Nerve. Eprint arXiv:1404.5931, 2014
35 C Jin, J Zhang, X Li, X K Yang, X Y Yang, J J Li, J Liu. Injectable 3-D fabrication of medical electronics at the target biological tissues. Scientific Reports, 2013, 3: 3442
https://doi.org/10.1038/srep03442
36 Q Wang, Y Yu, K Q Pan, J Liu. Liquid metal angiography for mega contrast X-ray visualization of vascular network in reconstructing in-vitro organ anatomy. IEEE Transactions on Biomedical Engineering, 2014, 61(7): 2161–2166
https://doi.org/10.1109/TBME.2014.2317554
37 Y Lu, Q Y Hu, Y L Lin, D Pacardo, C Wang, W J Sun, F S Ligler, M D Dickey, Z Gu. Transformable liquid-metal nanomedicine. Nature Communications, 2015, 6: 10066
https://doi.org/10.1038/ncomms10066
38 J Zhang, R Guo, J Liu. Self-propelled liquid metal motors steered by a magnetic or electrical field for drug delivery. Journal of Materials Chemistry B, Materials for Biology and Medicine, 2016, 4(32): 5349–5357
https://doi.org/10.1039/C6TB00996D
39 S H Jeong, A Hagman, K Hjort, M Jobs, J Sundqvist, Z Wu. Liquid alloy printing of microfluidic stretchable electronics. Lab on a Chip, 2012, 12(22): 4657–4664
https://doi.org/10.1039/c2lc40628d
40 A Tabatabai, A Fassler, C Usiak, C Majidi. Liquid-phase gallium–indium alloy electronics with microcontact printing. Langmuir, 2013, 29(20): 6194–6200
https://doi.org/10.1021/la401245d
41 B A Gozen, A Tabatabai, O B Ozdoganlar, C Majidi. High-density soft-matter electronics with micron-scale line width. Advanced Materials, 2014, 26(30): 5211–5216
https://doi.org/10.1002/adma.201400502
42 L Wang, J Liu. Liquid phase 3D printing for quickly manufacturing conductive metal objects with low melting point alloy ink. Science China. Technological Sciences, 2014, 57(9): 1721–1728
https://doi.org/10.1007/s11431-014-5583-4
43 L Wang, J Liu. Compatible hybrid 3D printing of metal and nonmetal inks for direct manufacture of end functional devices. Science China, Technological Sciences, 2014, 57(11): 2089–2095
https://doi.org/10.1007/s11431-014-5657-3
44 J Zhang, Y Y Yao, L Sheng, J Liu. Self-fueled biomimetic liquid metal mollusk. Advanced Materials, 2015, 27(16): 2648–2655
https://doi.org/10.1002/adma.201405438
45 S C Tan, B Yuan, J Liu. Electrical method to control the running direction and speed of self-powered tiny liquid metal motors. Proceedings–Royal Society. Mathematical, Physical and Engineering Sciences, 2015, 471(2183): 20150297
https://doi.org/10.1098/rspa.2015.0297
46 S C Tan, H Gui, B Yuan, J Liu. Magnetic trap effect to restrict motion of self-powered tiny liquid metal motors. Applied Physics Letters, 2015, 107(7): 071904
https://doi.org/10.1063/1.4928713
47 X Tang, S Y Tang, V Sivan, W Zhang, A Mitchell, K Kalantarzadeh, K Khoshmanesh. Photochemically induced motion of liquid metal marbles. Applied Physics Letters, 2013, 103(17): 174104
https://doi.org/10.1063/1.4826923
48 A Zavabeti, T Daeneke, A F Chrimes, A P O’Mullane, J Z Ou, A Mitchell, K Khoshmanesh, K Kalantar-zadeh. Ionic imbalance induced self-propulsion of liquid metals. Nature Communications, 2016, 7: 12402
https://doi.org/10.1038/ncomms12402
49 S F Mei, Y X Gao, H Y Li, Z S Deng, J Liu. Thermally induced porous structures in printed gallium coating to make transparent conductive film. Applied Physics Letters, 2013, 102(4): 041905
https://doi.org/10.1063/1.4789978
50 K Doudrick, S Liu, E M Mutunga, K L Klein, V Damle, K K Varanasi, K Rykaczewski. Different shades of oxide: from nanoscale wetting mechanisms to contact printing of gallium-based liquid metals. Langmuir, 2014, 30(23): 6867–6877
https://doi.org/10.1021/la5012023
51 M J Regan, H Tostmann, P S Pershan, O M Magnussen, E Dimasi, B M Ocko, M Deutsch. X-ray study of the oxidation of liquid-gallium surfaces. Physical Review B: Condensed Matter and Materials Physics, 1997, 55(16): 10786–10790
https://doi.org/10.1103/PhysRevB.55.10786
52 M J Regan, P S Pershan, O M Magnussen, B M Ocko, M Deutsch, L E Berman. X-ray reflectivity studies of liquid metal and alloy surfaces. Physical Review B: Condensed Matter, 1997, 55(23): 15874–15884
https://doi.org/10.1103/PhysRevB.55.15874
53 L Cademartiri, M M Thuo, C A Nijhuis, W F Reus, S Tricard, J R Barber, R N S Sodhi, P Brodersen, C Kim, R C Chiechi, G M Whitesides. Electrical resistance of AgTS–S(CH2)n–1CH3//Ga2O3/EGaIn tunneling junctions. Journal of Physical Chemistry C, 2012, 116(20): 10848–10860
https://doi.org/10.1021/jp212501s
54 N Ilyas, D P Butcher, M F Durstock, C E Tabor. Ion exchange membranes as an interfacial medium to facilitate gallium liquid metal alloy mobility. Advanced Materials Interfaces, 2016, 3(9): 1500665
https://doi.org/10.1002/admi.201500665
55 J Tang, Y Zhou, J Liu, J Wang, W Zhu. Liquid metal actuated ejector vacuum system. Applied Physics Letters, 2015, 106(3): 031901
https://doi.org/10.1063/1.4906098
56 M J Baldwin, T Lynch, L Chousal, R P Seraydarian, R P Doerner, S C Luckhardt. An injector device for producing clean-surface liquid metal samples of Li, Ga and Sn–Li in vacuum. Fusion Engineering and Design, 2004, 70(2): 107–113
https://doi.org/10.1016/S0920-3796(03)00415-0
57 T Liu, P Sen, C J Kim. Characterization of nontoxic liquid-metal alloy Galinstan for applications in microdevices. Journal of Microelectromechanical Systems, 2012, 21(2): 443–450
https://doi.org/10.1109/JMEMS.2011.2174421
58 Q Zhang, Y X Gao, J Liu. Atomized spraying of liquid metal droplets on desired substrate surfaces as a generalized way for ubiquitous printed electronics. Applied Physics A, 2014, 116: 1091–1097
59 Y X Gao, J Liu. Gallium-based thermal interface material with high complianceand wettability. Applied Physics A, Materials Science & Processing, 2012, 107(3): 701–708
https://doi.org/10.1007/s00339-012-6887-5
60 D Esinenco, I Codreanu, R Rebigan. Design of inkjet printing head, based on electrowetting effect, for printable electronics applications. In: International Semiconductor Conference, Sinaia, Romania: IEEE, 2006, 2: 443–446
61 V K Semenchenko. Surface Phenomena in Metals and Alloys.Oxford: Pergamon Press, 1962
62 E Chacon, F Flores, G Navascues. A theory for liquid metal surface tension. Journal of Physics F: Metal Physics, 1984, 14(7): 1587–1601
https://doi.org/10.1088/0305-4608/14/7/009
63 S A Safran. Statistical Thermodynamics of Surfaces, Interfaces, and Membranes. Vol. 90. New York: Perseus Books, 1994
64 A Mersmann. Calculation of interfacial tensions. Journal of Crystal Growth, 1990, 102(4): 841–847
https://doi.org/10.1016/0022-0248(90)90850-K
65 T S Jain, J J De Pablo. Calculation of interfacial tension from density of states. Journal of Chemical Physics, 2003, 118(9): 4226–4229
https://doi.org/10.1063/1.1540613
66 R M Digilov. Semi-empirical model for prediction of crystal–melt interfacial tension. Surface Science, 2004, 555(1–3): 68–74
https://doi.org/10.1016/j.susc.2004.02.024
67 O G Nino-Amezquita, S Enders, P T Jaeger, R Eggers. Measurement and prediction of interfacial tension of binary mixtures. Industrial & Engineering Chemistry Research, 2010, 49(2): 592–601
https://doi.org/10.1021/ie901209z
68 G J Gloor, G Jackson, F Blas, E M Del Rio, E De Miguel. Prediction of the vapor-liquid interfacial tension of nonassociating and associating fluids with the SAFT-VR density functional theory. Journal of Physical Chemistry C, 2007, 111(43): 15513–15522
https://doi.org/10.1021/jp072344i
69 J C Barrett. Some estimates of the surface tension of curved surfaces using density functional theory. Journal of Chemical Physics, 2006, 124(14): 144705
https://doi.org/10.1063/1.2179425
70 D Fu, J F Lu, J C Liu, Y G Li. Prediction of interfacial tension for binary liquid-liquid systems based on density functional theory. Journal of Chemical Industry and Engineering, 2002, 53(9): 892–898
71 M Telo Da Gama, R Evans, T Sluckin. The structure and surface tension of the liquid-vapour interface of a model of a molten salt. Molecular Physics, 1980, 41(6): 1355–1372
https://doi.org/10.1080/00268978000103591
72 J D Weeks. Structure and thermodynamics of the liquid–vapor interface. Journal of Chemical Physics, 1977, 67(7): 3106–3121
https://doi.org/10.1063/1.435276
73 M Johnson, S Nordholm. Generalized van der Waals theory. VI. Application to adsorption. Journal of Chemical Physics, 1981, 75(4): 1953–1957
https://doi.org/10.1063/1.442220
74 P S Ho, T Kwok. Electromigration in metals. Reports on Progress in Physics, 1989, 52(3): 301–348
https://doi.org/10.1088/0034-4885/52/3/002
75 S T Pai, J P Marton. Electromigration in metals. Canadian Journal of Physics, 1977, 55(2): 103–115
https://doi.org/10.1139/p77-013
76 G Beni, S Hackwood, J L Jackel. Continuous electrowetting effect. Applied Physics Letters, 1982, 40(10): 912–914
https://doi.org/10.1063/1.92952
77 E Gongadze, R U Van, A Iglič. Generalized stern models of the electric double layer considering the spatial variation of permittvity and finite size of ions in saturation regime. Cellular & Molecular Biology Letters, 2011, 16(4): 576–594
https://doi.org/10.2478/s11658-011-0024-x
78 D C Grahame. Electrode processes and the electrical double layer. Annual Review of Physical Chemistry, 1955, 6(1): 337–358
https://doi.org/10.1146/annurev.pc.06.100155.002005
79 W C Daywitt. The electron-vacuum coupling force in the Dirac electron theory and its relation to the zitterbewegung. Progress in Physics, 2013, 3: 25–28
80 J Enderby, N March. Electron theory of metals and liquid state theory. Advances in Physics, 1967, 16(64): 691–702
https://doi.org/10.1080/00018736700101815
81 G. ScatchardThe Gibbs adsorption isotherm 1. Journal of physical chemistry, 1962, 66(4): 618–620
82 G Lippmann. Relationship between the electric and capillary phenomena. Gauthier-Villars, 1875 (in French)
83 A Quinn, R Sedev, J Ralston. Contact angle saturation in electrowetting. Journal of Physical Chemistry B, 2005, 109(13): 6268–6275
https://doi.org/10.1021/jp040478f
84 K Nogi, K Ogino, A McLean, W A Miller. The temperature coefficient of the surface tension of pure liquid metals. Metallurgical Transactions B, Process Metallurgy, 1986, 17(1): 163–170
https://doi.org/10.1007/BF02670829
85 B J Keene. Review of data for the surface tension of pure metals. International Materials Reviews, 1993, 38(4): 157–192
https://doi.org/10.1179/imr.1993.38.4.157
86 Wikipedia. Surface tension. 2016-11-13
87 H M Lu, Q Jiang. Surface tension and its temperature coefficient for liquid metals. Journal of Physical Chemistry B, 2005, 109(32): 15463–15468
https://doi.org/10.1021/jp0516341
88 B Dayal. Surface tension and melting point. Nature, 1952, 169(4311): 1010
https://doi.org/10.1038/1691010a0
89 G Xiao. An empirical formula between the surface tensions and the melting points for metals. Jiangxi Science, 1987, 5(4): 31–35 (in Chinese)
90 D Ceotto. Empirical equation for predicting the surface tension of some liquid metals at their melting point. Russian Journal of Physical Chemistry, 2014, 88(7): 1269–1272
https://doi.org/10.1134/S0036024414070073
91 F Aqra, A Ayyad. Surface energies of metals in both liquid and solid states. Applied Surface Science, 2011, 257(15): 6372–6379
https://doi.org/10.1016/j.apsusc.2011.01.123
92 K Arafune, M Sugiura, A Hirata. Investigation of thermal Marangoni convection in low- and high-Prandtl-number fluids. Journal of Chemical Engineering of Japan, 1999, 32(1): 104–109
https://doi.org/10.1252/jcej.32.104
93 N Eustathopoulos, B Drevet, E Ricci. Temperature coefficient of surface tension for pure liquid metals. Journal of Crystal Growth, 1998, 191(1–2): 268–274
https://doi.org/10.1016/S0022-0248(98)00012-8
94 H Kobatake, J Brillo, J Schmitz, P Y Pichon. Surface tension of binary Al–Si liquid alloys. Journal of Materials Science, 2015, 50(9): 3351–3360
https://doi.org/10.1007/s10853-015-8883-6
95 P R Scheller. Surface effects and flow conditions in small volume melts with varying sulphur content. Steel Research, 2001, 72(3): 76–80
https://doi.org/10.1002/srin.200100087
96 J J Yu, D F Ruan, Y R Li, J C Chen. Experimental study on thermocapillary convection of binary mixture in a shallow annular pool with radial temperature gradient. Experimental Thermal and Fluid Science, 2015, 61: 79–86
https://doi.org/10.1016/j.expthermflusci.2014.10.015
97 Q Z Zhang, L Peng, F Wang, J Liu. Thermocapillary convection with bidirectional temperature gradients in a shallow annular pool of silicon melt: effects of ambient temperature and pool rotation. International Journal of Heat and Mass Transfer, 2016, 101: 354–364
https://doi.org/10.1016/j.ijheatmasstransfer.2016.05.015
98 Wikipedia. Marangoni effect. https://en.wikipedia.org/wiki/Marangoni_effect. 2016-10-16
99 B B Alchagirov, A G Mozgovoi. The surface tension of molten gallium at high temperatures. High Temperature, 2005, 43(5): 791–792
https://doi.org/10.1007/s10740-005-0124-2
100 B B Alchagirov, R K Dadashev, F F Dyshekova, D Z Elimkhanov. Temperature dependence of the surface tension of indium. Russian Journal of Physical Chemistry A, 2013, 87(6): 890–894
https://doi.org/10.1134/S0036024413050026
101 A B Alchagirov, B B Alchagirov, K B Khokonov. A device for the study of the surface tension of liquid metal solutions with an increased elasticity of intrinsic vapors. Instruments and Experimental Techniques, 2003, 46(3): 413–415
https://doi.org/10.1023/A:1024495212143
102 S Ozawa, S Takahashi, S Suzuki, H Sugawara, H Fukuyama. Relationship of surface tension, oxygen partial pressure, and temperature for molten iron. Japanese Journal of Applied Physics, 2011, 50(11S): 11R05
103 S Ozawa, S Takahashi, N Watanabe, H Fukuyama. Influence of oxygen adsorption on surface tension of molten nickel measured under reducing gas atmosphere. International Journal of Thermophysics, 2014, 35(9–10): 1705–1711
https://doi.org/10.1007/s10765-014-1674-5
104 F Aqra, A Ayyad. Surface tension of pure liquid bismuth and its temperature dependence: theoretical calculations. Materials Letters, 2011, 65(4): 760–762
https://doi.org/10.1016/j.matlet.2010.11.038
105 F Aqra, A Ayyad. Theoretical temperature-dependence surface tension of pure liquid gold. Materials Letters, 2011, 65(14): 2124–2126
https://doi.org/10.1016/j.matlet.2011.04.063
106 T Dubberstein, H P Heller. Surface tension and density of liquid gold, silver, and tin. High Temperatures–High Pressures, 2015, 44(5): 393–406
107 K A Yakimovich, A G Mozgovoi. Experimental investigation of the density and surface tension of molten lithium at temperatures up to 1300 K. High Temperature, 2000, 38(4): 657–659
https://doi.org/10.1007/BF02755816
108 P Fima, R Nowak, N Sobczak. Effect of metal purity and testing procedure on surface tension measurements of liquid tin. Journal of Materials Science, 2010, 45(8): 2009–2014
https://doi.org/10.1007/s10853-009-3973-y
109 E Ricci, E Arato, A Passerone, P Costa. Oxygen tensioactivity on liquid-metal drops. Advances in Colloid and Interface Science, 2005, 117(1–3): 15–32
https://doi.org/10.1016/j.cis.2005.05.007
110 P Fima. Surface tension and density of liquid Sn–Ag alloys. Applied Surface Science, 2011, 257(8): 3265–3268
https://doi.org/10.1016/j.apsusc.2010.11.002
111 P Fima. Surface tension and density of liquid Sn–Cu alloys. Applied Surface Science, 2010, 257(2): 468–471
https://doi.org/10.1016/j.apsusc.2010.07.013
112 F Aqra, A Ayyad, F Takrori. Model calculation of the surface tension of liquid Ga–Bi alloy. Applied Surface Science, 2011, 257(8): 3577–3580
https://doi.org/10.1016/j.apsusc.2010.11.079
113 E Ricci, L Nanni, M Vizza, A Passerone. Dynamic surface tension measurements of liquid metals in the presence of oxygen. In: International conference on high temperature capillarity HTC, Krakow, Poland: Foundry Research Institute,1997: 188–193
114 S Ozawa, K Morohoshi, T Hibiya, H Fukuyama. Influence of oxygen partial pressure on surface tension of molten silver. Journal of Applied Physics, 2010, 107(1): 014910
https://doi.org/10.1063/1.3275047
115 C R Heiple. Mechanism for minor element effect on GTA fusion zone geometry. Welding Journal, 1982, 61(4): 97–102
116 B B Alchagirov, R K Dadashev, F F Dyshekova, D Z Elimkhanov. The surface tension of indium: methods and results of investigations. High Temperature, 2014, 52(6): 920–938
https://doi.org/10.1134/S0018151X14060017
117 Z F Yuan, K Mukai, K Takagi, M Ohtaka, W L Huang, Q S Liu. Surface tension and its temperature coefficient of molten tin determined with the sessile drop method at different oxygen partial pressures. Journal of Colloid and Interface Science, 2002, 254(2): 338–345
https://doi.org/10.1006/jcis.2002.8589
118 L Fiori, E Ricci, E Arato. Dynamic surface tension measurements on molten metal-oxygen systems: model validation on molten tin. Acta Materialia, 2003, 51(10): 2873–2890
https://doi.org/10.1016/S1359-6454(03)00092-2
119 D Giuranno, E Ricci, E Arato, P Costa. Dynamic surface tension measurements of an aluminium–oxygen system. Acta Materialia, 2006, 54(10): 2625–2630
https://doi.org/10.1016/j.actamat.2006.02.005
120 E Ricci, T Lanata, D Giuranno, E Arato. The effective oxidation pressure of indium-oxygen system. Journal of Materials Science, 2008, 43(9): 2971–2977
https://doi.org/10.1007/s10853-007-2429-5
121 E Ricci, M Ratto, E Arato, P Costa, A Passerone. A theoretical approach for the interpretation of liquid metal surface tension measurements in the presence of oxygen. Transactions of the Iron & Steel Institute of Japan, 2000, 40 (Suppl): S139–S143
https://doi.org/10.2355/isijinternational.40.Suppl_S139
122 V Ghetta, J Fouletier, D Chatain. Oxygen adsorption isotherms at the surfaces of liquid Cu and Au-Cu alloys and their interfaces with Al2O3 detected by wetting experiments. Acta Materialia, 1996, 44(5): 1927–1936
https://doi.org/10.1016/1359-6454(95)00312-6
123 Z Yuan, J Fan, J Li, J Ke, K Mukai. Surface tension of molten bismuth at different oxygen partial pressure with the sessile drop method. Scandinavian Journal of Metallurgy, 2004, 33(6): 338–346
https://doi.org/10.1111/j.1600-0692.2004.00704.x
124 M Abbasi, J Lee, M Shin, Y Kim, Y Kang. Effect of oxygen adsorption on surface tension of liquid copper: experiments and thermodynamic models. Applied Surface Science, 2014, 313: 116–122
https://doi.org/10.1016/j.apsusc.2014.05.153
125 A Kasama, A Mclean, W A Miller, Z Morita, M J Ward. Surface tension of liquid iron and iron-oxygen alloys. Canadian Metallurgical Quarterly, 1983, 22(1): 9–17
https://doi.org/10.1179/cmq.1983.22.1.9
126 K Morohoshi, M Uchikoshi, M Isshiki, H Fukuyama. Surface tension of liquid iron as functions of oxygen activity and temperature. ISIJ International, 2011, 51(10): 1580–1586
https://doi.org/10.2355/isijinternational.51.1580
127 M P SanSoucie, J R Rogers, V Kumar, J Rodriguez, X Xiao, D M Matson. Effects of environmental oxygen content and dissolved oxygen on the surface tension and viscosity of liquid nickel. International Journal of Thermophysics, 2016, 37: 76
https://doi.org/10.1007/s10765-016-2085-6
128 L Fiori, E Ricci, E Arato, P Costa. Dynamic surface tension measurements on a molten metal-oxygen system: the behaviour of the temperature coefficient of the surface tension of molten tin. Journal of Materials Science, 2005, 40(9): 2155–2159
https://doi.org/10.1007/s10853-005-1907-x
129 E Ricci, A Passerone, J C Joud. Thermodynamic study of adsorption in liquid metal-oxygen systems. Surface Science, 1988, 206(3): 533–553
https://doi.org/10.1016/0039-6028(88)90152-5
130 M A Shebzukhova, Z A Shebzukhov, A A Shebzukhov. The Tolman parameter, self-absorption, and surface tension on flat and curved surfaces of liquid metals. Bulletin of the Russian Academy of Sciences. Physics, 2010, 74(5): 697–704
https://doi.org/10.3103/S1062873810050333
131 R C Tolman. The effect of droplet size on surface tension. Journal of Chemical Physics, 1949, 17(3): 333–337
https://doi.org/10.1063/1.1747247
132 H M Lu, Q Jiang. Size dependent surface energy and surface tension. In: IEEE Conference on Emerging Technologies-Nanoelectronics, Singapore: IEEE, 2006: 21–24
133 M A Shebzukhova, A A Shebzukhov. Surface energy and surface tension of liquid metal nanodrops. EPJ Web of Conferences. EDP Sciences, 2011, 15: 01027
134 V Vinš, M Fransen, J Hykl, J Hrubý. Surface tension of supercooled water determined by using a counterpressure capillary rise method. Journal of Physical Chemistry B, 2015, 119(17): 5567–5575
https://doi.org/10.1021/acs.jpcb.5b00545
135 M H Ghatee, H Ghazipour. Highly accurate liquid–liquid interfacial tension measurement by a convenient capillary apparatus. Fluid Phase Equilibria, 2014, 377: 76–81
https://doi.org/10.1016/j.fluid.2014.06.018
136 R Luo, D Zhang, Z Zeng, R L Lytton. Effect of surface tension on the measurement of surface energy components of asphalt binders using the Wilhelmy plate method. Construction & Building Materials, 2015, 98: 900–909
https://doi.org/10.1016/j.conbuildmat.2015.08.125
137 M Součková, J Klomfar, J Pátek. Surface tension of 1-alkyl-3-methylimidazolium based ionic liquids with trifluoromethanesulfonate and tetrafluoroborate anion. Fluid Phase Equilibria, 2011, 303(2): 184–190
https://doi.org/10.1016/j.fluid.2011.01.027
138 J Klomfar, M Součková, J Pátek. Surface tension measurements with validated accuracy for four 1-alkyl-3-methylimidazolium based ionic liquids. Journal of Chemical Thermodynamics, 2010, 42(3): 323–329
https://doi.org/10.1016/j.jct.2009.09.007
139 A S Alkindi, Y M Alwahaibi, A H Muggeridge. Physical properties (density, excess molar volume, viscosity, surface tension, and refractive index) of ethanol+ glycerol. Journal of Chemical & Engineering Data, 2008, 53(12): 2793–2796
https://doi.org/10.1021/je8004479
140 V B Fainerman, R Miller, P Joos. The measurement of dynamic surface tension by the maximum bubble pressure method. Colloid & Polymer Science, 1994, 272(6): 731–739
https://doi.org/10.1007/BF00659287
141 V B Fainerman, V N Kazakov, S V Lylyk, A V Makievski, R Miller. Dynamic surface tension measurements of surfactant solutions using the maximum bubble pressure method — limits of applicability. Colloids and Surfaces A, Physicochemical and Engineering Aspects, 2004, 250(1–3): 97–102
https://doi.org/10.1016/j.colsurfa.2004.01.041
142 R Sangiorgi, M L Muolo, D Chatain, N Eustathopoulos. Wettability and work of adhesion of nonreactive liquid metals on silica. Journal of the American Ceramic Society, 1988, 71(9): 742–748
https://doi.org/10.1111/j.1151-2916.1988.tb06407.x
143 K F Man. Surface tension measurements of liquid metals by the quasi-containerless pendant drop method. International Journal of Thermophysics, 2000, 21(3): 793–804
https://doi.org/10.1023/A:1006601821432
144 B Vinet, J P Garandet, L Cortella. Surface tension measurements of refractory liquid metals by the pendant drop method under ultrahigh vacuum conditions: extension and comments on Tate’s law. Journal of Applied Physics, 1993, 73(8): 3830–3834
https://doi.org/10.1063/1.352891
145 B J Keene, K C Mills, R F Brooks. Surface properties of liquid metals and their effects on weldability. Materials Science and Technology, 1985, 1(7): 559–567
https://doi.org/10.1179/mst.1985.1.7.559
146 H Takiguchi, Y Nagasaka. Development of near-infrared laser-induced capillary wave method to measure viscosity and surface tension. Transactions of the Japan Society of Mechanical Engineers, 2013, 79(800): 690–700
https://doi.org/10.1299/kikaib.79.690
147 R Osada, T Hoshino, K Okada, Y Ohmasa, M Yao. Surface tension of room temperature ionic liquids measured by dynamic light scattering. Journal of Chemical Physics, 2009, 130(18): 184705
https://doi.org/10.1063/1.3125182
148 S D Korkmaz, Ş Korkmaz. Investigation of surface properties of liquid transition metals: surface tension and surface entropy. Applied Surface Science, 2010, 257(1): 261–265
https://doi.org/10.1016/j.apsusc.2010.06.082
149 F Bashforth, J C Adams. An Attempt to Test the Theories of Capillary Action: by Comparing the Theoretical and Measured Forms of Drops of Fluid with an Explanation of the Method of Integration Employed in Constucting the Tables Which Give the Theoretical Forms of Such Drops. Cambridge: Cambridge University Press, 1883
150 J Andreas, E Hauser, W Tucker. Boundary tension by pendant drops 1. Journal of Physical Chemistry, 1938, 42(8): 1001–1019
https://doi.org/10.1021/j100903a002
151 K Schaefers, G Kuppermann, U Thiedemann, J Qin, M Frohberg. A new variant for measuring the surface tension of liquid metals and alloys by the oscillating drop method. International Journal of Thermophysics, 1996, 17(5): 1173–1179
https://doi.org/10.1007/BF01442004
152 E Pichon, D Nain. A Laplace equation approach for shape comparison. Proceedings of SPIE–The International Society for Optics and Photonics, 2006, 6141: 614119
153 J V Naidich. The wettability of solids by liquid metals. Progress in Surface & Membrane Science, 1981, 14: 353–484
https://doi.org/10.1016/B978-0-12-571814-1.50011-7
154 J Lee, A Kiyose, S Nakatsuka, M Nakamoto, T Tanaka. Improvements in surface tension measurements of liquid metals having low capillary constants by the constrained drop method. ISIJ International, 2004, 44(11): 1793–1799
https://doi.org/10.2355/isijinternational.44.1793
155 Y Plevachuk, V Sklyarchuk, G Gerbeth, S Eckert, R Novakovic. Surface tension and density of liquid Bi–Pb, Bi–Sn and Bi–Pb–Sn eutectic alloys. Surface Science, 2011, 605(11–12): 1034–1042
https://doi.org/10.1016/j.susc.2011.02.026
156 N Sobczak, R Nowak, W Radziwill, J Budzioch, A Glenz. Experimental complex for investigations of high temperature capillarity phenomena. Materials Science and Engineering A, 2008, 495(12): 43–49
https://doi.org/10.1016/j.msea.2007.11.094
157 L Liggieri, A Passerone. An automatic technique for measuring the surface tension of liquid metals. High Temperature Technology, 1989, 7(2): 82–86
https://doi.org/10.1080/02619180.1989.11753417
158 C Maze, G Burnet. A non-linear regression method for calculating surface tension and contact angle from the shape of a sessile drop. Surface Science, 1969, 13(2): 451–470
https://doi.org/10.1016/0039-6028(69)90204-0
159 R Aune, S Seetharaman, L Battezzati, I Egry, F Schmidt-Hohagen, J Etay, H J Fecht, R Wunderlich, A Passerone, E Ricci, R Novakovic, D Giuranno. Surface tension measurements of Al-Ni based alloys from ground-based and parabolic flight experiments: results from the ThermoLab project. Microgravity Science and Technology, 2006, 18: 73
https://doi.org/10.1007/BF02870383
160 I Egry, R Brooks, D Hollandmoritz, R Novakovic, T Matsushita, E Ricci, S Seetharaman, R Wunderlich, D Jarvis. Thermophysical properties of γ-titanium aluminide: the European IMPRESS Project. International Journal of Thermophysics, 2007, 28(3): 1026–1036
https://doi.org/10.1007/s10765-007-0219-6
161 M Kucharski, P Fima, P Skrzyniarz, W Przebinda-Stefanowa. Surface tension and density of Cu-Ag, Cu-In and Ag-In alloys. Archives of Metallurgy and Materials, 2006, 51(3): 389–397
162 Y Plevachuk, W Hoyer, I Kaban, M Köhler, R Novakovic. Experimental study of density, surface tension, and contact angle of Sn-Sb-based alloys for high temperature soldering. Journal of Materials Science, 2010, 45(8): 2051–2056
https://doi.org/10.1007/s10853-009-4120-5
163 J Lee, T H Le, M Shin. Density and surface tension of liquid Fe-Mn alloys. Metallurgical and Materials Transactions B, Process Metallurgy and Materials Processing Science, 2011, 42(3): 546–549
https://doi.org/10.1007/s11663-011-9490-9
164 J Brillo, Y Plevachuk, I Egry. Surface tension of liquid Al–Cu–Ag ternary alloys. Journal of Materials Science, 2010, 45(19): 5150–5157
https://doi.org/10.1007/s10853-010-4512-6
165 J Willner, G Siwiec, J Botor. The surface tension of liquid Cu–Fe–Sb alloys. Applied Surface Science, 2010, 256(9): 2939–2943
https://doi.org/10.1016/j.apsusc.2009.11.054
166 Z Guo, M Hindler, W Yuan, A Mikula. The density and surface tension of In–Sn and Cu–In–Sn alloys. Monatshefte für Chemie-Chemical Monthly, 2011, 142(6): 579–584
https://doi.org/10.1007/s00706-011-0501-y
167 Z N Guo, S Li, A Mikula, W X Yuan. Surface tension of liquid Au-Bi-Sn alloys. Rare Metals, 2012, 31(3): 250–254
https://doi.org/10.1007/s12598-012-0500-0
168 V P Chentsov, V G Shevchenko, A G Mozgovoi, M A Pokrasin. Density and surface tension of heavy liquid-metal coolants: Gallium and indium. Inorganic Materials: Applied Research, 2011, 2(5): 468–473
https://doi.org/10.1134/S2075113311050108
169 R Novakovic, E Ricci, D Giuranno, A Passerone. Surface and transport properties of Ag–Cu liquid alloys. Surface Science, 2005, 576(1–3): 175–187
https://doi.org/10.1016/j.susc.2004.12.009
170 I Egry, D Hollandmoritz, R Novakovic, E Ricci, R Wunderlich, N Sobczak. Thermophysical properties of liquid AlTi-based alloys. International Journal of Thermophysics, 2010, 31(4): 949–965
https://doi.org/10.1007/s10765-010-0704-1
171 R Nowak, T Lanata, N Sobczak, E Ricci, D Giuranno, R Novakovic, D Hollandmoritz, I Egry. Surface tension of γ-TiAl-based alloys. Journal of Materials Science, 2010, 45(8): 1993–2001
https://doi.org/10.1007/s10853-009-4061-z
172 E Ricci, D Giuranno, N Sobczak. Further development of testing procedures for high temperature surface tension measurements. Journal of Materials Engineering and Performance, 2013, 22(11): 3381–3388
https://doi.org/10.1007/s11665-013-0624-x
173 S Amore, D Giuranno, R Novakovic, E Ricci, R Nowak, N Sobczak. Thermodynamic and surface properties of liquid Ge-Si alloys. Calphad-computer Coupling of Phase Diagrams & Thermochemistry, 2014, 44(1): 95–101
https://doi.org/10.1016/j.calphad.2013.07.014
174 E C Okress, D M Wroughton, G Comenetz, P H Brace, J C R Kelly. Electromagnetic levitation of solid and molten metals. Journal of Applied Physics, 1952, 23(5): 545–552
https://doi.org/10.1063/1.1702249
175 M E Fraser, W K Lu, A E Hamielec, R Murarka. Surface tension measurements on pure liquid iron and nickel by an oscillating drop technique. Metallurgical and Materials Transactions B, Process Metallurgy and Materials Processing Science, 1971, 2(3): 817–823
176 R Murarka, W K Lu, A E Hamielec. Surface tension of pure liquid and supercooled iron. Metallurgical and Materials Transactions B, Process Metallurgy and Materials Processing Science, 1971, 2(10): 2949–2950
177 R N Murarka, W K Lu, A E Hamielec. Effect of dissolved oxygen on the surface tension of liquid iron. Canadian Metallurgical Quarterly, 1975, 14(2): 111–115
https://doi.org/10.1179/000844375795050337
178 I Egry, E Ricci, R Novakovic, S Ozawa. Surface tension of liquid metals and alloys–recent developments. Advances in Colloid and Interface Science, 2010, 159(2): 198–212
https://doi.org/10.1016/j.cis.2010.06.009
179 J Brillo, G Lohöfer, F Schmidt-Hohagen, S Schneider, I Egry. Thermophysical property measurements of liquid metals by electromagnetic levitation. International Journal of Materials & Product Technology, 2006, 26(3/4): 247–273
https://doi.org/10.1504/IJMPT.2006.009469
180 I Egry, G Lohoefer, G Jacobs. Surface tension of liquid metals: results from measurements on ground and in space. Physical Review Letters, 1995, 75(22): 4043–4046
https://doi.org/10.1103/PhysRevLett.75.4043
181 D L Cummings, D A Blackburn. Oscillations of magnetically levitated aspherical droplets. Journal of Fluid Mechanics, 1991, 224: 395–416
https://doi.org/10.1017/S0022112091001817
182 J Brillo, I Egry, T Matsushita. Density and surface tension of liquid ternary Ni-Cu-Fe alloys. International Journal of Thermophysics, 2006, 97(1): 28–34
183 J Brillo, I Egry. Surface tension of nickel, copper, iron and their binary alloys. Journal of Materials Science, 2005, 40(9): 2213–2216
https://doi.org/10.1007/s10853-005-1935-6
184 I Egry, J Brillo. Surface tension and density of liquid metallic alloys measured by electromagnetic levitation. Journal of Chemical & Engineering Data, 2009, 54(9): 2347–2352
https://doi.org/10.1021/je900119n
185 J Schmitz, J Brillo, I Egry. Surface tension of liquid Cu and anisotropy of its wetting of sapphire. Journal of Materials Science, 2010, 45(8): 2144–2149
https://doi.org/10.1007/s10853-010-4212-2
186 J Brillo, G Kolland. Surface tension of liquid Al-Au binary alloys. Journal of Materials Science, 2016, 51(10): 4888–4901
https://doi.org/10.1007/s10853-016-9794-x
187 J Brillo, I Egry, J Westphal. Density and thermal expansion of liquid binary Al-Ag and Al-Cu alloys. International Journal of Materials Research, 2008, 99(2): 162–167
https://doi.org/10.3139/146.101623
188 J Brillo, G Lauletta, L Vaianella, E Arato, D Giuranno, R Novakovic, E Ricci. Surface tension of liquid Ag–Cu binary alloys. Transactions of the Iron & Steel Institute of Japan, 2014, 54(9): 2115–2119
https://doi.org/10.2355/isijinternational.54.2115
189 R K Wunderlich, H J Fecht. Surface tension and viscosity of NiAl catalytic precursor alloys from microgravity experiments. International Journal of Materials Research, 2011, 102(9): 1164–1173
https://doi.org/10.3139/146.110572
190 S Amore, J Brillo, I Egry, R Novakovic. Surface tension of liquid Cu-Ti binary alloys measured by electromagnetic levitation and thermodynamic modelling. Applied Surface Science, 2011, 257(17): 7739–7745
https://doi.org/10.1016/j.apsusc.2011.04.019
191 K Zhou, H P Wang, J Chang, B Wei. Surface tension measurement of metastable liquid Ti–Al–Nb alloys. Applied Physics A, Materials Science & Processing, 2011, 105(1): 211–214
https://doi.org/10.1007/s00339-011-6491-0
192 J Chang, H P Wang, K Zhou, B Wei. Surface tension measurement of undercooled liquid Ni-based multicomponent alloys. Philosophical Magazine Letters, 2012, 92(9): 428–435
https://doi.org/10.1080/09500839.2012.685768
193 I Egry, G Lohöfer, P Neuhaus, S Sauerland. Surface tension measurements of liquid metals using levitation, microgravity, and image processing. International Journal of Thermophysics, 1992, 13(1): 65–74
https://doi.org/10.1007/BF00503356
194 I Egry. Surface tension measurements of liquid metals by the oscillating drop technique. Journal of Materials Science, 1991, 26(11): 2997–3003
https://doi.org/10.1007/BF01124834
195 I Egry, G Lohoefer, E Schwartz, J Szekely, P Neuhaus. Surface tension measurements on liquid metals in microgravity. Metallurgical and Materials Transactions B, Process Metallurgy and Materials Processing Science, 1998, 29(5): 1031–1035
https://doi.org/10.1007/s11663-998-0071-5
196 M Ohnishi, Y Nagasaka. Measurement of surface tension and viscosity of molten lithium niobate by the surface laser-light scattering method. High Temperatures—High Pressures, 2000, 32(1): 103–108
https://doi.org/10.1068/htwu131
197 V G Levich. Physicochemical Hydrodynamics. New Jersey: Prentice Hall, 1962
198 Y Nagasaka, Y Kobayashi. Effect of atmosphere on the surface tension and viscosity of molten LiNbO3 measured using the surface laser-light scattering method. Journal of Crystal Growth, 2007, 307(1): 51–58
https://doi.org/10.1016/j.jcrysgro.2007.01.050
199 F K Wang, H Y Yue, X W Fan, Z G Liu. Surface tension and viscosity measurement with surface laser light scattering method. Thermal Science, 2013, 17(5): 1467–1471
https://doi.org/10.2298/TSCI1305467W
200 A Ayyad, F Aqra. Theoretical consideration of the anomalous temperature dependence of the surface tension of pure liquid gallium. Theoretical Chemistry Accounts, 2010, 127(5): 443–448
https://doi.org/10.1007/s00214-010-0731-9
201 A Ayyad, I Mechdiev, W Freyland. Light scattering study of surface freezing and surface viscoelasticity in a eutectic liquid Ga–Bi alloy. Chemical Physics Letters, 2002, 359(3–4): 326–330
https://doi.org/10.1016/S0009-2614(02)00712-1
202 Y Minami. Surface tension measurement of liquid metal with inelastic light-scattering spectroscopy of a thermally excited capillary wave. Applied Physics B, Lasers and Optics, 2014, 117(3): 969–972
https://doi.org/10.1007/s00340-014-5915-x
203 R Osada, T Hoshino, K Okada, Y Ohmasa, M Yao. Surface tension of room temperature ionic liquids measured by dynamic light scattering. Journal of Chemical Physics, 2009, 130(18): 184705
https://doi.org/10.1063/1.3125182
204 B J Kirby. Micro- and Nanoscale Fluid Mechanics: Transport in Microfluidic Devices. Cambridge: Cambridge University Press, 2010
205 H C Chang, L Y Yeo. Electrokinetically Driven Microfluidics and Nanofluidics. Cambridge: Cambridge University Press, 2010
206 J S Hong, S H Ko, K H Kang, I S Kang. A numerical investigation on AC electrowetting of a droplet. Microfluidics and Nanofluidics, 2008, 5(2): 263–271
https://doi.org/10.1007/s10404-007-0246-4
207 S Berry, J Kedzierski, B Abedian. Low voltage electrowetting using thin fluoroploymer films. Journal of Colloid and Interface Science, 2006, 303(2): 517–524
https://doi.org/10.1016/j.jcis.2006.08.004
208 R Shamai, D Andelman, B Berge, R Hayes. Water, electricity, and between … on electrowetting and its applications. Soft Matter, 2008, 4(1): 38–45
https://doi.org/10.1039/B714994H
209 D Thomas, M C Audry, R M Thibaut, P Kleimann, F Chassagneux, M Maillard, A Brioude. Charge injection in dielectric films during electrowetting actuation under direct current voltage. Thin Solid Films, 2015, 590: 224–229
https://doi.org/10.1016/j.tsf.2015.08.001
210 D Klarman, D Andelman, M Urbakh. A model of electrowetting, reversed electrowetting, and contact angle saturation. Langmuir, 2011, 27(10): 6031–6041
https://doi.org/10.1021/la2004326
211 C W Monroe, L Daikhin, M Urbakh, A Kornyshev. Electrowetting with an interface between two immiscible electrolytic solutions. In: 210th ECS Meeting. Cancun, Mexico: ECS, 2006: 43
212 C W Monroe, L I Daikhin, M Urbakh, A A Kornyshev. Electrowetting with electrolytes. Physical Review Letters, 2006, 97(13): 136102
https://doi.org/10.1103/PhysRevLett.97.136102
213 T B Jones, J D Fowler, Y S Chang, C J Kim. Frequency-based relationship of electrowetting and dielectrophoretic liquid microactuation. Langmuir, 2003, 19(18): 7646–7651
https://doi.org/10.1021/la0347511
214 K H Kang. How electrostatic fields change contact angle in electrowetting. Langmuir, 2002, 18(26): 10318–10322
https://doi.org/10.1021/la0263615
215 F Mugele, J C Baret. Electrowetting: from basics to applications. Journal of Physics Condensed Matter, 2005, 17(28): R705–R774
https://doi.org/10.1088/0953-8984/17/28/R01
216 R Sedev. Electrowetting: electrocapillarity, saturation, and dynamics. European Physical Journal. Special Topics, 2011, 197(1): 307–319
https://doi.org/10.1140/epjst/e2011-01473-4
217 K L Wang, T B Jones. Saturation effects in dynamic electrowetting. Applied Physics Letters, 2005, 86(5): 054104
https://doi.org/10.1063/1.1861501
218 B Shapiro, H Moon, R L Garrell, C J Kim. Equilibrium behavior of sessile drops under surface tension, applied external fields, and material variations. Journal of Applied Physics, 2003, 93(9): 5794–5811
https://doi.org/10.1063/1.1563828
219 X H Yang, S C Tan, B Yuan, J Liu. Alternating electric field actuated oscillating behavior of liquid metal and its application. Science China Technological Sciences, 2016, 59(4): 597–603
https://doi.org/10.1007/s11431-016-6026-1
220 S C Tan, Y X Zhou, L Wang, J Liu. Electrically driven chip cooling device using hybrid coolants of liquid metal and aqueous solution. Science China Technological Sciences, 2016, 59(2): 301–308
https://doi.org/10.1007/s11431-015-5943-8
221 J Lee, H Moon, J Fowler, T Schoellhammer, C J Kim. Electrowetting and electrowetting-on-dielectric for microscale liquid handling. Sensors and Actuators A: Physical, 2002, 95(2–3): 259–268
https://doi.org/10.1016/S0924-4247(01)00734-8
222 K S Yun, I J Cho, J U Bu, C J Kim. A surface-tension driven micropump for low-voltage and low-power operations. Journal of Microelectromechanical Systems, 2002, 11(5): 454–461
https://doi.org/10.1109/JMEMS.2002.803286
223 J Lee, C J C Kim. Liquid micromotor driven by continuous electrowetting. In: Proceedings of 11th Annual International Workshop on Micro Electro Mechanical Systems. Heidelberg, Germany: IEEE, 1998: 538–543
224 H J Lee, C J Kim. Surface-tension-driven microactuation based on continuous electrowetting. Journal of Microelectromechanical Systems, 2000, 9(2): 171–180
https://doi.org/10.1109/84.846697
225 J Ni, C J Zhong, S J Coldiron, M D Porter. Electrochemically actuated mercury pump for fluid flow and delivery. Analytical Chemistry, 2001, 73(1): 103–110
https://doi.org/10.1021/ac0007478
226 M G Pollack, R B Fair, A D Shenderov. Electrowetting-based actuation of liquid droplets for microfluidic applications. Applied Physics Letters, 2000, 77(11): 1725–1726
https://doi.org/10.1063/1.1308534
227 U C Yi, C J Kim. Characterization of electrowetting actuation on addressable single-side coplanar electrodes. Journal of Micromechanics and Microengineering, 2006, 16(10): 2053–2059
https://doi.org/10.1088/0960-1317/16/10/018
228 A Accardo, F Mecarini, M Leoncini, F Brandi, E Di Cola, M Burghammer, C Riekel, E Di Fabrizio. Fast, active droplet interaction: coalescence and reactive mixing controlled by electrowetting on a superhydrophobic surface. Lab on a Chip, 2013, 13(3): 332–335
https://doi.org/10.1039/C2LC41193H
229 T Krupenkin, J A Taylor. Reverse electrowetting as a new approach to high-power energy harvesting. Nature Communications, 2011, 2: 448
https://doi.org/10.1038/ncomms1454
230 J K Moon, J Jeong, D Lee, H K Pak. Electrical power generation by mechanically modulating electrical double layers. Nature Communications, 2013, 4: 1487
https://doi.org/10.1038/ncomms2485
231 J Thramann. Generation of electrical energy in a ski or snowboard. US Patent No. 9024462, 2015
232 B Berge, J Peseux. Variable focal lens controlled by an external voltage: an application of electrowetting. European Physical Journal E, 2000, 3(2): 159–163
https://doi.org/10.1007/s101890070029
233 S Kuiper, B H W Hendriks. Variable-focus liquid lens for miniature cameras. Applied Physics Letters, 2004, 85(7): 1128–1130
https://doi.org/10.1063/1.1779954
234 R A Hayes, B J Feenstra. Video-speed electronic paper based on electrowetting. Nature, 2003, 425(6956): 383–385
https://doi.org/10.1038/nature01988
235 H You, A J Steckl. Three-color electrowetting display device for electronic paper. Applied Physics Letters, 2010, 97(2): 023514
https://doi.org/10.1063/1.3464963
236 B J Feenstra, R A Hayes, R Van Dijk, R G H Boom. Electrowetting-based displays: bringing microfluidics alive on-screen. In:19th IEEE International Conference on Micro Electro Mechanical Systems. Istanbul, Turkey: IEEE, 2006: 48–53
237 R B Fair, A Khlystov, T D Tailor, V Ivanov, R D Evans, V Srinivasan, V K Pamula, M G Pollack, P B Griffin, J Zhou. Chemical and biological applications of digital-microfluidic devices. IEEE Design & Test of Computers, 2007, 24(1): 10–24
https://doi.org/10.1109/MDT.2007.8
238 S K Cho, H Moon, C J Kim. Creating, transporting, cutting, and merging liquid droplets by electrowetting-based actuation for digital microfluidic circuits. Journal of Microelectromechanical Systems, 2003, 12(1): 70–80
https://doi.org/10.1109/JMEMS.2002.807467
239 Y Yu, Q Wang, L Yi, J Liu. Channelless fabrication for large-scale preparation of room temperature liquid metal droplets. Advanced Engineering Materials, 2014, 16(2): 255–262
https://doi.org/10.1002/adem.201300420
240 L Sheng, Z Z He, Y Y Yao, J Liu. Transient state machine enabled from the colliding and coalescence of a swarm of autonomously running liquid metal motors. Small, 2015, 11(39): 5253–5261
https://doi.org/10.1002/smll.201501364
241 W Gao, A Pei, J Wang. Water-driven micromotors. ACS Nano, 2012, 6(9): 8432–8438
https://doi.org/10.1021/nn303309z
242 B Yuan, L Wang, X H Yang, Y J Ding, S C Tan, L T Yi, Z Z He, J Liu. Liquid metal machine triggered violin-like wire oscillator. 2016, 3(10): 1600212
243 C W Monroe, L I Daikhin, M Urbakh, A A Kornyshev. Principles of electrowetting with two immiscible electrolytic solutions. Journal of Physics Condensed Matter, 2006, 18(10): 2837–2869
https://doi.org/10.1088/0953-8984/18/10/009
244 D C Grahame. The electrical double layer and the theory of electrocapillarity. Chemical Reviews, 1947, 41(3): 441–501
https://doi.org/10.1021/cr60130a002
245 A A Kornyshev, A R Kucernak, M Marinescu, C W Monroe, A E S Sleightholme, M Urbakh. Ultra-low-voltage electrowetting. Journal of Physical Chemistry C, 2010, 114(35): 14885–14890
https://doi.org/10.1021/jp101051e
246 Y Y Yao, J Liu. Liquid metal wheeled small vehicle for cargo delivery. Royal Scoiety of Chemistry Advances, 2016, 6: 56482–56488
247 B Yuan, S C Tan, Y X Zhou, J Liu. Self-powered macroscopic Brownian motion of spontaneously running liquid metal motors. Chinese Science Bulletin, 2015, 60(13): 1203–1210
248 W Q Fang, Z Z He, J Liu. Electro-hydrodynamic shooting phenomenon of liquid metal stream. Applied Physics Letters, 2014, 105(13): 134104
https://doi.org/10.1063/1.4897309
249 S Y Tang, Y Lin, I D Joshipura, K Khoshmanesh, M D Dickey. Steering liquid metal flow in microchannels using low voltages. Lab on a Chip, 2015, 15(19): 3905–3911
https://doi.org/10.1039/C5LC00742A
250 S Y Tang, V Sivan, K Khoshmanesh, A P O’mullane, X Tang, B Gol, N Eshtiaghi, F Lieder, P Petersen, A Mitchell, K Kalantar-zadeh. Electrochemically induced actuation of liquid metal marbles. Nanoscale, 2013, 5(13): 5949–5957
https://doi.org/10.1039/c3nr00185g
251 A F Chrimes, K J Berean, A Mitchell, G Rosengarten, K Kalantar-Zadeh. Controlled electrochemical deformation of liquid-phase gallium. ACS Applied Materials & Interfaces, 2016, 8(6): 3833–3839
https://doi.org/10.1021/acsami.5b10625
252 L Sheng, J Zhang, J Liu. Diverse transformations of liquid metals between different morphologies. Advanced Materials, 2014, 26(34): 6036–6042
https://doi.org/10.1002/adma.201400843
253 L Wang, J Liu. Liquid metal folding patterns induced by electric capillary force. Applied Physics Letters, 2016, 108(16): 161602
https://doi.org/10.1063/1.4947440
254 M Mohammed, R Sundaresan, M D Dickey. Self-running liquid metal drops that delaminate metal films at record velocities. ACS Applied Materials & Interfaces, 2015, 7(41): 23163–23171
https://doi.org/10.1021/acsami.5b06978
255 A Hirsch, H O Michaud, A P Gerratt, S V De Mulatier, S P Lacour. Intrinsically stretchable biphasic (solid–liquid) thin metal films. Advanced Materials, 2016, 28(22): 4507–4512
https://doi.org/10.1002/adma.201506234
256 Y Zheng, Z Z He, J Yang, J Liu. Personal electronics printing via tapping mode composite liquid metal ink delivery and adhesion mechanism. Scientific Reports, 2014, 4: 4588
https://doi.org/10.1038/srep04588
257 Y Zheng, Z Z He, Y X Gao, J Liu. Direct desktop printed-circuits-on-paper flexible electronics. Scientific Reports, 2013, 3: 1786
https://doi.org/10.1038/srep01786
258 Q Wang, Y Yu, J Yang, J Liu. Fast fabrication of flexible functional circuits based on liquid metal dual-trans printing. Advanced Materials, 2015, 27(44): 7109–7116
https://doi.org/10.1002/adma.201502200
259 Y Zheng, Q Zhang, J Liu. Pervasive liquid metal based direct writing electronics with roller-ball pen. AIP Advances, 2013, 3(11): 112117
https://doi.org/10.1063/1.4832220
260 Y X Gao, H Y Li, J Liu. Direct writing of flexible electronics through room temperature liquid metal ink. PLoS One, 2012, 7(9): e45485
https://doi.org/10.1371/journal.pone.0045485
261 Y Yu, J Zhang, J Liu. Biomedical implementation of liquid metal ink as drawable ECG electrode and skin circuit. PLoS One, 2013, 8(3): e58771
https://doi.org/10.1371/journal.pone.0058771
262 C R Guo, Y Yu, J Liu. Rapidly patterning conductive components on skin substrates as physiological testing devices via liquid metal spraying and pre-designed mask. Journal of Materials Chemistry B, Materials for Biology and Medicine, 2014, 2(35): 5739–5745
https://doi.org/10.1039/C4TB00660G
263 D Zrnic, D Swatik. On the resistivity and surface tension of the eutectic alloy of gallium and indium. Journal of the Less Common Metals, 1969, 18(1): 67–68
https://doi.org/10.1016/0022-5088(69)90121-0
264 M D Dickey, R C Chiechi, R J Larsen, E A Weiss, D A Weitz, G M Whitesides. Eutectic gallium-indium (EGaIn): a liquid metal alloy for the formation of stable structures in microchannels at room temperature. Advanced Functional Materials, 2008, 18(7): 1097–1104
https://doi.org/10.1002/adfm.200701216
265 J W Boley, E L White, G T C Chiu, R K Kramer. Direct writing of gallium-indium alloy for stretchable electronics. Advanced Functional Materials, 2014, 24(23): 3501–3507
https://doi.org/10.1002/adfm.201303220
266 Q Xu, N Oudalov, Q Guo, H M Jaeger, E Brown. Effect of oxidation on the mechanical properties of liquid gallium and eutectic gallium-indium. Physics of Fluids, 2012, 24(6): 063101
https://doi.org/10.1063/1.4724313
267 R J Larsen, M D Dickey, G M Whitesides, D A Weitz. Viscoelastic properties of oxide-coated liquid metals. Journal of Rheology (New York, N.Y.), 2009, 53(6): 1305–1326
https://doi.org/10.1122/1.3236517
268 C Jin, J Zhang, X K Li, X Y Yang, J J Li, J Liu. Injectable 3-D fabrication of medical electronics at the target biological tissues. Scientific Reports, 2013, 3: 3442
https://doi.org/10.1038/srep03442
269 J Zhang, L Sheng, J Liu. Synthetically chemical-electrical mechanism for controlling large scale reversible deformation of liquid metal objects. Scientific Reports, 2014, 4: 7116
https://doi.org/10.1038/srep07116
270 R C Gough, J H Dang, M R Moorefield, G B Zhang, L H Hihara, W A Shiroma, A T Ohta. Self-actuation of liquid metal via redox reaction. ACS Applied Materials & Interfaces, 2016, 8(1): 6–10
https://doi.org/10.1021/acsami.5b09466
271 W Shen, R T Edwards, C J Kim. Electrostatically actuated metal-droplet microswitches integrated on CMOS chip. Journal of Microelectromechanical Systems, 2006, 15(4): 879–889
https://doi.org/10.1109/JMEMS.2006.878877
272 M L Hammock, A Chortos, B C K Tee, J B H Tok, Z Bao. 25th anniversary article: the evolution of electronic skin (E-Skin): a brief history, design considerations, and recent progress. Advanced Materials, 2013, 25(42): 5997–6038
https://doi.org/10.1002/adma.201302240
273 Y L Park, B R Chen, R J Wood. Design and fabrication of soft artificial skin using embedded microchannels and liquid conductors. IEEE Sensors Journal, 2012, 12(8): 2711–2718
https://doi.org/10.1109/JSEN.2012.2200790
274 R K Kramer, C Majidi, R J Wood. Wearable tactile keypad with stretchable artificial skin. In: IEEE International Conference on Robotics & Automation, IEEE, 2011: 1103–1107
275 S Bauer, S Bauer-Gogonea, I Graz, M Kaltenbrunner, C Keplinger, R Schwödiauer. 25th anniversary article: a soft future: from robots and sensor skin to energy harvesters. Advanced Materials, 2014, 26(1): 149–162
https://doi.org/10.1002/adma.201303349
276 L Hu, L Wang, Y J Ding, S H Zhan, J Liu. Manipulation of liquid metals on a graphite surface. Advanced Materials, 2016, 28(41): 9210–9217
https://doi.org/10.1002/adma.201601639
Viewed
Full text


Abstract

Cited

  Shared   
  Discussed