0
Review Article

Fluid Mechanics of Liquid Metal Batteries

[+] Author and Article Information
Douglas H. Kelley

Department of Mechanical Engineering,
University of Rochester,
Rochester, NY 14627
e-mail: d.h.kelley@rochester.edu

Tom Weier

Institute of Fluid Dynamics,
Helmholtz-Zentrum Dresden-Rossendorf,
Bautzner Landstr. 400,
Dresden 01328, Germany
e-mail: t.weier@hzdr.de

Manuscript received September 14, 2017; final manuscript received November 27, 2017; published online January 31, 2018. Assoc. Editor: Jörg Schumacher.

Appl. Mech. Rev 70(2), 020801 (Jan 31, 2018) (23 pages) Paper No: AMR-17-1064; doi: 10.1115/1.4038699 History: Received September 14, 2017; Revised November 27, 2017

The design and performance of liquid metal batteries (LMBs), a new technology for grid-scale energy storage, depend on fluid mechanics because the battery electrodes and electrolytes are entirely liquid. Here, we review prior and current research on the fluid mechanics of LMBs, pointing out opportunities for future studies. Because the technology in its present form is just a few years old, only a small number of publications have so far considered LMBs specifically. We hope to encourage collaboration and conversation by referencing as many of those publications as possible here. Much can also be learned by linking to extensive prior literature considering phenomena observed or expected in LMBs, including thermal convection, magnetoconvection, Marangoni flow, interface instabilities, the Tayler instability, and electro-vortex flow. We focus on phenomena, materials, length scales, and current densities relevant to the LMB designs currently being commercialized. We try to point out breakthroughs that could lead to design improvements or make new mechanisms important.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.

References

Kassakian, J. G. , and Schmalensee, R. , 2011, The Future of the Electric Grid: An Interdisciplinary MIT Study, Massachusetts Institute of Technology, Cambridge, MA.
Whittingham, M. S. , 2012, “History, Evolution, and Future Status of Energy Storage,” Proc. IEEE, 100, pp. 1518–1534. [CrossRef]
Backhaus, S. , and Chertkov, M. , 2013, “Getting a Grip on the Electrical Grid,” Phys. Today, 66(5), pp. 42–48. [CrossRef]
Nardelli, P. H. J. , Rubido, N. , Wang, C. , Baptista, M. S. , Pomalaza-Raez, C. , Cardieri, P. , and Latva-aho, M. , 2014, “Models for the Modern Power Grid,” Eur. Phys. J. Spec. Top, 223(12), pp. 2423–2437. [CrossRef]
Bones, R. J. , Teagle, D. A. , Brooker, S. D. , and Cullen, F. L. , 1989, “Development of a Ni, NiCl2 Positive Electrode for a Liquid Sodium (ZEBRA) Battery Cell,” J. Electrochem. Soc., 136(5), pp. 1274–1277. [CrossRef]
Sudworth, J. L. , 2001, “The Sodium/Nickel Chloride (ZEBRA) Battery,” J. Power Sources, 100(1–2), pp. 149–163. [CrossRef]
Lu, X. , Li, G. , Kim, J. Y. , Mei, D. , Lemmon, J. P. , Sprenkle, V. L. , and Liu, J. , 2014, “Liquid-Metal Electrode to Enable Ultra-Low Temperature Sodium-Beta Alumina Batteries for Renewable Energy Storage,” Nat. Commun., 5, p. 4578. [PubMed]
Fukunaga, A. , Nohira, T. , Kozawa, Y. , Hagiwara, R. , Sakai, S. , Nitta, K. , and Inazawa, S. , 2012, “Intermediate-Temperature Ionic Liquid NaFSA-KFSA and Its Application to Sodium Secondary Batteries,” J. Power Sources, 209, pp. 52–56. [CrossRef]
Nitta, K. , Inazawa, S. , Sakai, S. , Fukunaga, A. , Itani, E. , Numata, K. , Hagiwara, R. , and Nohira, T. , 2013, “Development of Molten Salt Electrolyte Battery,” SEI Tech. Rev., 76, pp. 33–39. http://global-sei.com/technology/tr/bn76/pdf/76-06.pdf
Cairns, E. J. , Crouthamel, C. E. , Fischer, A. K. , Foster, M. S. , Hesson, J. C. , Johnson, C. E. , Shimotake, H. , and Tevebaugh, A. D. , 1967, “Galvanic Cells With Fused-Salt Electrolytes,” Argonne National Laboratory, Lemont, IL, Report No. ANL-7316. https://www.osti.gov/scitech/biblio/4543889
Kim, H. , Boysen, D. A. , Newhouse, J. M. , Spatcco, B. L. , Chung, B. , Burke, P. J. , Bradwell, D. J. , Jiang, K. , Tomaszowska, A. A. , Wang, K. , Wei, W. , Ortiz, L. A. , Barriga, S. A. , Poizeau, S. M. , and Sadoway, D. R. , 2013, “Liquid Metal Batteries: Past, Present, and Future,” Chem. Rev., 113(3), pp. 2075–2099. [CrossRef] [PubMed]
Weier, T. , Bund, A. , El-Mofid, W. , Horstmann, G. M. , Lalau, C.-C. , Landgraf, S. , Nimtz, M. , Starace, M. , Stefani, F. , and Weber, N. , 2017, “Liquid Metal Batteries - Materials Selection and Fluid Dynamics,” IOP Conf. Ser.: Mater. Sci. Eng., 228(1), p. 012013. [CrossRef]
Ning, X. , Phadke, S. , Chung, B. , Yin, H. , Burke, P. J. , and Sadoway, D. R. , 2015, “Self-Healing Li–Bi Liquid Metal Battery for Grid-Scale Energy Storage,” J. Power Sources, 275, pp. 370–376. [CrossRef]
Bradwell, D. J. , Kim, H. , Sirk, A. H. C. , and Sadoway, D. R. , 2012, “Magnesium-Antimony Liquid Metal Battery for Stationary Energy Storage,” J. Am. Chem. Soc., 134(4), pp. 1895–1897. [CrossRef] [PubMed]
Wang, K. , Jiang, K. , Chung, B. , Ouchi, T. , Burke, P. J. , Boysen, D. A. , Bradwell, D. J. , Kim, H. , Muecke, U. , and Sadoway, D. R. , 2014, “Lithium-Antimony-Lead Liquid Metal Battery for Grid-Level Storage,” Nature, 514(7522), pp. 348–350. [CrossRef] [PubMed]
Xu, J. , Kjos, O. S. , Osen, K. S. , Martinez, A. M. , Kongstein, O. E. , and Haarberg, G. M. , 2016, “Na-Zn Liquid Metal Battery,” J. Power Sources, 332, pp. 274–280. [CrossRef]
Xu, J. , Martinez, A. M. , Osen, K. S. , Kjos, O. S. , Kongstein, O. E. , and Haarberg, G. M. , 2017, “Electrode Behaviors of Na-Zn Liquid Metal Battery,” J. Electrochem. Soc., 164(12), pp. A2335–A2340. [CrossRef]
Kim, H. , Boysen, D. A. , Ouchi, T. , and Sadoway, D. R. , 2013, “Calcium-Bismuth Electrodes for Large-Scale Energy Storage (Liquid Metal Batteries),” J. Power Sources, 241, pp. 239–248. [CrossRef]
Ouchi , T. , Kim , H. , Spatocco , B. L. , and Sadoway, D. R. , 2016, “Calcium-Based Multi-Element Chemistry for Grid-Scale Electrochemical Energy Storage,” Nat. Commun., 7, p. 10999.
Li, H. , Yin, H. , Wang, K. , Cheng, S. , Jiang, K. , and Sadoway, D. R. , 2016, “Liquid Metal Electrodes for Energy Storage Batteries,” Adv. Energy Mater, 6(14), p. 1600483. [CrossRef]
Johnson, C. E. , and Hathaway, E. J. , 1971, “Solid-Liquid Phase Equilibria for the Ternary Systems Li(F,Cl,I) and Na(F,Cl,I),” J. Electrochem. Soc., 118(4), pp. 631–634. [CrossRef]
Swinkels, D. A. J. , 1971, “Molten Salt Batteries and Fuel Cells,” Advances in Molten Salt Chemistry, Vol. 1, J. Braunstein , G. Mamantov , and G. Smith , eds., Plenum Press, New York, pp. 165–223. [CrossRef]
Spatocco, B. L. , and Sadoway, D. R. , 2015, “Cost-Based Discovery for Engineering Solutions,” Advances in Electrochemical Science and Engineering: Electrochemical Engineering Across Scales: From Molecules to Processes, Vol. 15, R. Alikre , P. Bartlett , and J. Lipkowsi , eds., Wiley-VCH, Weinheim, Germany, Chap. 7. [CrossRef]
Drossbach, P. , 1952, Grundriß der allgemeinen technischen Elektrochemie, Gebrüder Borntraeger, Berlin-Nikolassee, Germany.
Betts, A. G. , 1905, “Making Aluminium,” U.S. Patent No. 795,886. https://encrypted.google.com/patents/US795886
Hoopes, W. , 1901, “Process of the Purification of Aluminium,” Alcoa, Pittsburgh, PA, U.S. Patent No. 673,364. http://www.google.com.pg/patents/US673364
Hoopes, W. , 1925, “Electrolytically Refined Aluminum and Articles Made Therefrom,” Alcoa, Pittsburgh, PA, U.S. Patent No. 1,534,315. https://www.google.com/patents/US1534315
Frary, F. C. , 1925, “The Electrolytic Refining of Aluminum,” Trans. Am. Electrochem. Soc., 47, pp. 275–286.
Müller, R. , 1932, Allgemeine und technische Elektrochemie, Springer, Vienna, Austria. [CrossRef]
Hoopes, W. , Edwards, J. D. , and Horsfield, B. T. , 1925, “Electrolytic Cell and Method of Lining the Same,” Alcoa, Pittsburgh, PA, U.S. Patent No. 1,534,322. http://www.google.com.pg/patents/US1534322
Shimotake, H. , and Hesson, J. C. , 1968, “New Bimetallic EMF Cell Shows Promise in Direct Energy Conversion,” Atomic Energy Commission/NASA, Washington, DC, Report No. ARG-10183. https://ntrs.nasa.gov/search.jsp?R=19680000415
von Zeerleder, A. , 1955, “Aluminium,” Die technische Elektrolyse im Schmelzfluss (Handbuch der technischen Elektrochemie, Vol. 3), G. Eger, ed., Akademische Verlagsgesellschaft Geest & Portig K.-G, Leipzig, Germany, pp. 56–364.
Eger, G. , ed., 1955, Die technische Elektrolyse im Schmelzfluss, (Handbuch der technischen Elektrochemie, Vol. 3), Akademische Verlagsgesellschaft Geest & Portig K.-G, Leipzig, Germany.
Beljajew, A. I. , Rapoport, M. B. , and Firsanowa, L. A. , 1957, Metallurgie des Aluminiums, Vol. 2, VEB Verlag Technik, Berlin.
Gadeau, R. A. , 1939, “L'aluminium Raffiné,” Reine Metalle: Herstellung, Eigenschaften, Verwendung, A. E. van Arkel , ed., Springer, Berlin, pp. 145–167.
Gadeau, R. A. , 1936, “Refining of Aluminum,” U.S. Patent No. 2,034,339. http://google.com/patents/US2034339
Hurter, H. , 1937, “Improvements in or Relating to the Electrolytic Refining of Aluminium,” GB Patent No. 469,361.
Pearson, T. G. , and Phillips, H. W. L. , 1957, “The Production and Properties of Super-Purity Aluminium,” Metall. Rev., 2(1), pp. 305–360.
Dube, M. C. , 1954, “Extraction and Refining of Aluminium,” Symposium Non-Ferrous Metal Industry, Jamshedpur, India, Feb. 1–3, pp. 127–138.
Wolstenholme, G. A. , 1982, “Aluminum Extraction,” Molten Salt Technology, D. G. Lovering , ed., Springer, New York, pp. 13–55. [CrossRef]
Yan, X. Y. , and Fray, D. J. , 2010, “Molten Salt Electrolysis for Sustainable Metals Extraction and Materials Processing—A Review,” Electrolysis: Theory, Types and Applications, S. Kuai and J. Meng , eds., Nova Science, New York.
Edwards, J. D. , Frary, F. C. , and Jeffries, Z. , 1930, Aluminum and Its Production, McGraw-Hill, New York.
Singleton, E. L. , and Sullivan, T. A. , 1973, “Electronic Scrap Reclamation,” J. Metals, 25(6), pp. 31–34.
Tiwari, B. L. , and Sharma, R. A. , 1984, “Electrolytic Removal of Magnesium From Scrap Aluminum,” J. Metals, 36(7), pp. 41–43.
Gesing, A. J. , Das, S. K. , and Loutfy, R. O. , 2016, “Production of Magnesium and Aluminum-Magnesium Alloys From Recycled Secondary Aluminum Scrap Melts,” J. Metals, 68(2), pp. 585–592.
Gesing, A. J. , and Das, S. K. , 2017, “Use of Thermodynamic Modeling for Selection of Electrolyte for Electrorefining of Magnesium From Aluminum Alloy Melts,” Metall. Mater. Trans. B, 48(1), pp. 132–145. [CrossRef]
Olsen, E. , and Rolseth, S. , 2010, “Three-Layer Electrorefining of Silicon,” Metall. Mater. Trans. B, 41(2), pp. 295–302. [CrossRef]
Olsen, E. , Rolseth, S. , and Thonstad, J. , 2014, “Electrorefining of Silicon by the Three-Layer Principle in a CaF2-Based Electrolyte,” Molten Salts in Chemistry and Technology, M. Gaune-Escard and G. M. Haarberg , eds., Wiley, Hoboken, NJ, pp. 569–576. [CrossRef]
Oishi, T. , Koyama, K. , and Tanaka, M. , 2016, “Electrorefining of Silicon Using Molten Salt and Liquid Ally Electrodes,” J. Electrochem. Soc., 163(14), pp. E385–E389. [CrossRef]
Roberts, R. , 1958, “The Fuel Cell round Table,” J. Electrochem. Soc., 105(7), pp. 428–432. [CrossRef]
Liebhafsky, H. A. , 1967, “Regenerative Electrochemical Systems: An Introduction,” Regenerative EMF Cells (Advances in Chemistry), Vol. 64, C. E. Crouthamel and H. L. Recht , eds., American Chemical Society, Washington, DC, pp. 1–10. [CrossRef]
McCully, R. C. , Rymarz, T. M. , and Nicholson, S. B. , 1967, “Regenerative Chloride Systems for Conversion of Heat to Electrical Energy,” Regenerative EMF Cells (Advances in Chemistry), Vol. 64, C. E. Crouthamel and H. L. Recht , eds., American Chemical Society, Washington, DC, pp. 198–212. [CrossRef]
Chum, H. L. , and Osteryoung, R. A. , 1980, “Review of Thermally Regenerative Electrochemical Systems Volume 1: Synopsis and Executive Summary,” Solar Energy Research Institute, Golden, CO, Report No. SERI/TR-332-416. https://www.nrel.gov/docs/legosti/old/416_v1.pdf
Chum, H. L. , and Osteryoung, R. A. , 1981, “Review of Thermally Regenerative Electrochemical Systems Volume 2,” Solar Energy Research Institute, Golden, CO, Report No. SERI/TR-332-416. https://www.nrel.gov/docs/legosti/old/416_v2.pdf
Yeager, E. , 1958, “Fuel Cells: Basic Considerations,” 12th Annual Battery Research and Development Conference, Fort Monmouth, NJ, pp. 2–4.
Liebhafsky, H. A. , 1959, “The Fuel Cell and the Carnot Cycle,” J. Electrochem. Soc., 106(12), pp. 1068–1071. [CrossRef]
Shearer, R. E. , and Werner, R. C. , 1958, “Thermally Regenerative Ionic Hydride Galvanic Cell,” J. Electrochem. Soc., 105(11), p. 693. [CrossRef]
Ciarlariello, T. A. , McDonough, J. B. , and Shearer, R. E. , 1961, “Study of Energy Conversion Devices—Report No. 7,” MSA Research Corporation, Callery, PA, Report No. MSAR 61-99. https://www.osti.gov/scitech/biblio/4827416-study-energy-conversion-devices-report-final-report-july-may
Lawroski, S. , Vogel, R. C. , and Munnecke, V. H. , 1961, “Chemical Engineering Division Summary Report,” Argonne National Laboratory, Lemont, IL, Report No. ANL-6379. https://babel.hathitrust.org/cgi/pt?id=mdp.39015077571142;view=1up;seq=3
Roy, P. , Salamah, A. , Maldonado, J. , and Narkiewicz, R. S. , 1993, “HYTEC—A Thermally Regenerative Fuel Cell,” AIP Conf. Proc., 271(2), pp. 913–921.
Wietelmann, U. , 2014, “Applications of Lithium-Containing Hydrides for Energy Storage and Conversion,” Chem. Ing. Tech., 86(12), pp. 2190–2194. [CrossRef]
Agruss, B. , 1966, “Regenerative Battery,” General Motors, Detroit, MI, U.S. Patent No. 3,245,836. http://www.google.co.in/patents/US3245836
Henderson, R. E. , Agruss, B. , and Caple, W. G. , 1961, “Resume of Thermally Regenerative Fuel Cell Systems,” Energy Conversion for Space Power (Progress in Astronautics and Aeronautics), Vol. 3, N. W. Snyder , ed., Academic Press, Cambridge, MA, pp. 411–423. [CrossRef]
Agruss, B. , and Karas, H. R. , 1962, “First Quarterly Technical Progress Report on Design and Development of a Liquid Metal Cell for the Period 1 January 1962–31 March 1962,” Allison Division of General Motors Corporation, Detroit, MI, Report No. EDR 2678.
Lawroski, S. , Vogel, R. C. , and Munnecke, V. H. , 1962, “Chemical Engineering Division Summary Report,” Argonne National Laboratory, Lemont, IL, Report No. ANL-6477. https://babel.hathitrust.org/cgi/pt?id=mdp.39015077571126;view=1up;seq=3
Austin, L. G. , 1967, “Fuel Cells—A Review of Government-Sponsored Research, 1950–1964,” National Aeronautics and Space Administration, Washington, DC, Report No. NASA-SP-120. https://naca.larc.nasa.gov/search.jsp?R=19670030808&qs=N%3D4294060006%2B4294954200%2B4294958566
Agruss, B. , Karas, H. R. , and Decker, V. L. , 1962, “Design and Development of a Liquid Metal Fuel Cell,” Aeronautical Systems Division, Dir/Aeromechanics, Flight Accessoire Lab, Wright-Patterson AFB, Dayton, OH, Report No. ASD-TDR-62-1045. http://www.google.co.in/url?sa=t&rct=j&q=&esrc=s&source=web&cd=6&cad=rja&uact=8&ved=0ahUKEwiT-IzF1JXYAhUHSiYKHZ6dBToQFgg1MAU&url=http%3A%2F%2Fwww.dtic.mil%2Fget-tr-doc%2Fpdf%3FAD%3DAD0296861&usg=AOvVaw1eNQnZeuNuAUI_js1LwtXK
Agruss, B. , 1963, “Nuclear Liquid Metal Cell for Space Power,” 17th Annual Power Sources Conference, May 21–23, pp. 100–103.
Agruss, B. , and Karas, H. R. , 1967, “The Thermally Regenerative Liquid Metal Concentration Cell,” Regenerative EMF Cells (Advances in Chemistry), Vol. 64, R. Gold , ed., American Chemical Society, Washington, DC, pp. 62–81. [CrossRef]
Kerr, R. L. , 1967, “Regenerative Fuel Cells,” Performance Forecast of Selected Static Energy Conversion Devices, 29th Meeting of AGARD Propulsion and Energetics Panel, G. W. Sherman and L. Devol, eds., AGARD, Air Force Aero Propulsion Laboratory and Aerospace Research Laboratories Department of the Air Force, pp. 658–715.
Groce, I. J. , and Oldenkamp, R. D. , 1967, “Development of a Thermally Regenerative Sodium-Mercury Galvanic System—Part II: Design, Construction, and Testing of a Thermally Regenerative Sodium-Mercury Galvanic System,” Regenerative EMF Cells (Advances in Chemistry), Vol. 64, C. E. Crouthamel, and H. L. Recht, eds., American Chemical Society, Washington, DC, pp. 43–52. [CrossRef]
Crouthamel, C. E. , and Recht, H. L. , eds., 1967, Regenerative EMF Cells, (Advances in Chemistry), Vol. 64, American Chemical Society, Washington, DC. [CrossRef]
Weaver, R. D. , Smith, S. W. , and Willmann, N. L. , 1962, “The Sodium|Tin Liquid-Metal Cell,” J. Electrochem. Soc., 109(8), pp. 653–657. [CrossRef]
Shimotake, H. , Rogers, G. L. , and Cairns, E. J. , 1969, “Secondary Cells With Lithium Anodes and Immobilized Fused-Salt Electrolytes,” Ind. Eng. Chem. Process Des. Dev., 8(1), pp. 51–56. [CrossRef]
Cairns, E. J. , and Shimotake, H. , 1969, “High-Temperature Batteries,” Science, 164(3886), pp. 1347–1355. [CrossRef] [PubMed]
Vogel, R. C. , Proud, E. R. , and Royal, J. , 1968, “Chemical Engineering Division Semiannual Report,” Argonne National Laboratory, Lemont, IL, Report No. ANL-7525. https://www.osti.gov/scitech/servlets/purl/4731424/
Lawroski, S. , Vogel, R. C. , Levenson, M. , and Munnecke, V. H. , 1963, “Chemical Engineering Division Research Highlights,” Argonne National Laboratory, Lemont, IL, Report No. ANL-6766. https://catalog.hathitrust.org/Record/006865162
Vogel, R. C. , Burris, L. , Tevebaugh, A. D. , Webster, D. S. , Proud, E. R. , and Royal, J. , 1971, “Chemical Engineering Division Research Highlights,” Argonne National Laboratory, Lemont, IL, Report No. ANL-7850. https://www.osti.gov/scitech/biblio/1050822-chemical-engineering-division-research-highlights-january-december
Spatocco, B. L. , Ouchi, T. , Lambotte, G. , Burke, P. J. , and Sadoway, D. R. , 2015, “Low-Temperature Molten Salt Electrolytes for Membrane-Free Sodium Metal Batteries,” J. Electrochem. Soc., 162(14), pp. A2729–A2736. [CrossRef]
Grube, G. , 1930, Grundzüge der theoretischen und angewandten Elektrochemie, 2nd ed., Theodor Steinkopff, Dresden, Leipzig, Germany.
Gossrau, G. , 1955, “Calcium, Strontium, Barium,” Die technische Elektrolyse im Schmelzfluss, (Handbuch der technischen Elektrochemie, Vol. 3), G. Eger, ed., Akademische Verlagsgesellschaft Geest & Portig K.-G, Leipzig, Germany, pp. 424–464.
Wenger, E. , Epstein, M. , and Kribus, A. , 2017, “Thermo-Electro-Chemical Storage (TECS) of Solar Energy,” Appl. Energy, 190, pp. 788–799. [CrossRef]
Steunenberg, R. K. , and Burris, L. , 2000, “From Test Tube to Pilot Plant: A 50 Year History of the Chemical Technology Division at Argonne National Laboratory,” Argonne National Laboratory, Lemont, IL, Report No. ANL-00/16.
Bockris, J. O. , ed., 1972, Electrochemistry of Cleaner Environments, Plenum Press, New York. [CrossRef]
Hietbrink, E. H. , McBree, J. , Selis, S. M. , Tricklebank, S. B. , and Witherspoon, R. R. , 1972, “Electrochemical Power Sources for Vehicle Propulsion,” Electrochemistry of Cleaner Environments, J. O. Bockris, ed., Plenum Press, New York, pp. 47–97. [CrossRef]
Vogel, R. C. , Levenson, M. , Proud, E. R. , and Royal, J. , 1968, “Chemical Engineering Division Research Highlights,” Argonne National Laboratory, Lemont, IL, Report No. ANL-7550.
Kyle, M. L. , Cairns, E. J. , and Webster, D. S. , 1973, “Lithium/Sulfur Batteries for Off-Peak Energy Storage: A Preliminary Comparison of Energy Storage and Peak Power Generation Systems,” Argonne National Laboratory, Lemont, IL, Report No. ANL-7958. https://catalog.hathitrust.org/Record/012212518
Bradwell, D. , 2006, “Technical and Economic Feasibility of a High-Temperature Self-Assembling Battery,” Master's thesis, Massachusetts Institute of Technology, Cambridge, MA. https://dspace.mit.edu/handle/1721.1/37683
Bradwell, D. , 2011, “LIQUID Metal Batteries: Ambipolar Electrolysis and Alkaline Earth Electroalloying Cells,” Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA. https://dspace.mit.edu/handle/1721.1/62741
Ray, H. S. , 2006, Introduction to Melts—Molten Salts, Slags and Glasses, Allied Publishers, New Delhi, India.
Rao, Y. K. , and Patil, B. V. , 1971, “Thermodynamic Study of the Mg-Sb System,” Metall. Trans., 2(7), pp. 1829–1835.
Leung, P. , Heck, S. C. , Amietszajew, T. , Mohamed, M. R. , Conde, M. B. , Dashwood, R. J. , and Bhagat, R. , 2015, “Performance and Polarization Studies of the Magnesium-Antimony Liquid Metal Battery With the Use of In-Situ Reference Electrode,” RSC Adv., 5(101), pp. 83096–83105. [CrossRef]
Sadoway, D. , Ceder, G. , and Bradwell, D. , 2012, “High-Amperage Energy Storage Device With Liquid Metal Negative Electrode and Methods,” Massachusetts Institute of Technology, Cambridge, MA, U.S. Patent No. 8,268,471 B2. http://www.google.com/patents/US8268471
Ouchi, T. , and Sadoway, D. R. , 2017, “Positive Current Collector for LiǁSb-Pb Liquid Metal Battery,” J. Power Sources, 357, pp. 158–163. [CrossRef]
Sadoway, D. R. , 2016, “Innovation in Stationary Electricity Storage: The Liquid Metal Battery,” Stanford Energy Seminar, Stanford, CA, Oct. 31. https://engineering.stanford.edu/events/energy-seminar-don-sadoway-innovation-stationary-electricity-storage-liquid-metal-battery
Bojarevics, V. , Tucs, A. , and Pericleous, K. , 2016, “MHD Model for Liquid Metal Batteries,” Tenth PAMIR International Conference—Fundamental and Applied MHD, DIEE, Cagliari, Italy, June 20–24, pp. 638–642.
Bojarevics, V. , and Tucs, A. , 2017, “MHD of Large Scale Liquid Metal Batteries,” Light Metals 2017 (The Minerals, Metals & Materials Series) Springer, New York, pp. 687–692. [CrossRef]
Chillà, F. , and Schumacher, J. , 2012, “New Perspectives in Turbulent Rayleigh-Bénard Convection,” Eur. Phys. J. E, 35(7), p. 58. [CrossRef]
Lohse, D. , and Xia, K.-Q. , 2010, “Small-Scale Properties of Turbulent Rayleigh-Bénard Convection,” Annu. Rev. Fluid Mech., 42(1), pp. 335–364. [CrossRef]
Ahlers, G. , 2009, “Turbulent Convection,” Physics, 2, p. 74. [CrossRef]
Bodenschatz, E. , Pesch, W. , and Ahlers, G. , 2000, “Recent Developments in Rayleigh-Bénard Convection,” Annu. Rev. Fluid Mech., 32(1), pp. 709–778. [CrossRef]
Nuclear Energy Agency, 2015, Handbook on Lead-Bismuth Eutectic Alloy and Lead Properties, Materials Compatibility, Thermal-Hydraulics and Technologies, Nuclear Energy Agency, Paris, France, pp. 1–950.
Iida, T. , and Guthrie, R. I. L. , 2015, The Thermophysical Properties of Metallic Liquids, Vol. 1, Oxford University Press, Oxford, UK.
Iida, T. , and Guthrie, R. I. L. , 2015, The Thermophysical Properties of Metallic Liquids, Vol. 2, Oxford University Press, Oxford, UK.
Davidson, H. W. , 1968, “Compilation of Thermophysical Properties of Liquid Lithium,” National Aeronautics and Space Administration, Washington, DC, Report No. NASA TN D-4650. https://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/19680018893.pdf
Sobolev, V. , 2011, “Database of Thermophysical Properties of Liquid Metal Coolants for GEN-IV,” SCK·CEN, Mol, Belgium, Report No. SCK·CEN-BLG-1069. https://inis.iaea.org/search/search.aspx?orig_q=RN:43095088
Grossmann, S. , and Lohse, D. , 2000, “Scaling in Thermal Convection: A Unifying Theory,” J. Fluid Mech., 407, pp. 27–56. [CrossRef]
Horanyi, S. , Krebs, L. , and Müller, U. , 1999, “Turbulent Rayleigh–Bénard Convection in Low Prandtl–Number Fluids,” Int. J. Heat Mass Transfer, 42(21), pp. 3983–4003. [CrossRef]
Jones, C. A. , Moore, D. R. , and Weiss, N. O. , 1976, “Axisymmetric Convection in a Cylinder,” J. Fluid Mech., 73(2), pp. 353–388. [CrossRef]
Weiss, N. O. , and Proctor, M. R. E. , 2014, Magnetoconvection, Cambridge University Press, Cambridge, UK. [CrossRef]
Davidson, P. A. , 2001, An Introduction to Magnetohydrodynamics, Cambridge University Press, Cambridge, UK. [CrossRef]
Chandrasekhar, S. , 1954, “On the Inhibition of Convection by a Magnetic Field—II,” Phil. Mag., 45(370), pp. 1177–1191. [CrossRef]
Busse, F. H. , and Clever, R. M. , 1982, “Stability of Convection Rolls in the Presence of a Vertical Magnetic Field,” Phys. Fluids, 25(6), pp. 931–935. [CrossRef]
Burr, U. , and Müller, U. , 2001, “Rayleigh-Bénard Convection in Liquid Metal Layers Under the Influence of a Vertical Magnetic Field,” Phys. Fluids, 13(11), pp. 3247–3257. [CrossRef]
Aurnou, J. M. , and Olson, P. L. , 2001, “Experiments on Rayleigh-Bénard Convection, Magnetoconvection and Rotating Magnetoconvection in Liquid Gallium,” J. Fluid Mech., 430, pp. 283–307. [CrossRef]
Zürner, T. , Liu, W. , Krasnov, D. , and Schumacher, J. , 2016, “Heat and Momentum Transfer for Magnetoconvection in a Vertical External Magnetic Field,” Phys. Rev. E, 94(4), p. 043108. [CrossRef] [PubMed]
Burr, U. , and Müller, U. , 2002, “Rayleigh-Bénard Convection in Liquid Metal Layers Under the Influence of a Horizontal Magnetic Field,” J. Fluid Mech., 453, pp. 345–369. [CrossRef]
Moffatt, H. K. , 1967, “On the Suppression of Turbulence by a Uniform Magnetic Field,” J. Fluid Mech., 28(3), pp. 571–592. [CrossRef]
Yanagisawa, T. , Hamano, Y. , Miyagoshi, T. , Yamagishi, Y. , Tasaka, Y. , and Takeda, Y. , 2013, “Convection Patterns in a Liquid Metal Under an Imposed Horizontal Magnetic Field,” Phys. Rev. E, 88(6), p. 063020.
Kelley, D. H. , and Sadoway, D. R. , 2014, “Mixing in a Liquid Metal Electrode,” Phys. Fluids, 26(5), p. 057102. [CrossRef]
Perez, A. , and Kelley, D. H. , 2015, “Ultrasound Velocity Measurement in a Liquid Metal Electrode,” J. Vis. Exp., 102, p. e52622.
Béltran, A. , 2017, “MHD Natural Convection Flow in a Liquid Metal Electrode,” Appl. Therm. Eng., 114, pp. 1203–1212. [CrossRef]
Shen, Y. , and Zikanov, O. , 2016, “Thermal Convection in a Liquid Metal Battery,” Theor. Comput. Fluid Dyn., 30(4), pp. 275–294. [CrossRef]
Zikanov, O. , and Shen, Y. , 2016, “Mechanisms of Instability in Liquid Metal Batteries,” Tenth PAMIR International Conference—Fundamental and Applied MHD, DIEE, Cagliari, Italy, June 20–24, pp. 522–526.
Barriga, S. A. , 2013, “An Electrochemical Investigation of the Chemical Diffusivity in Liquid Metal Alloys,” Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA. https://dspace.mit.edu/handle/1721.1/81058
Janz, G. J. , Dampier, F. W. , Lakshminarayanan, G. R. , Lorenz, P. K. , and Tomkins, R. P. T. , 1968, Molten Salts: Volume 1, Electrical Conductance, Density, and Viscosity Data, National Bureau of Standards, Washington, DC.
Janz, G. J. , Allen, C. B. , Bansal, N. P. , Murphy, R. M. , and Tomkins, R. P. T. , 1979, Physical Properties Data Compilations Relevant to Energy Storage—II: Molten Salts: Data on Single and Multi-Component Salt Systems, National Bureau of Standards, Washington, DC, pp. 1–450.
Todreas, N. E. , Hejzlar, P. , Fong, C. J. , Nikiforova, A. , Petroski, R. , Shwageraus, E. , and Whitman, J. , 2008, “Flexible Conversion Ratio Fast Reactor Systems Evaluation,” Massachusetts Institute of Technology, Cambridge, MA, Report No. MIT-NFC-PR-101. https://dspace.mit.edu/handle/1721.1/75737
Masset, P. , Henry, A. , Poinso, J.-Y. , and Poignet, J.-C. , 2006, “Ionic Conductivity Measurements of Molten Iodide-Based Electrolytes,” J. Power Sources, 160(1), pp. 752–757. [CrossRef]
Masset, P. , Schoeffert, S. , Poinso, J.-Y. , and Poignet, J.-C. , 2005, “Retained Molten Salt Electrolytes in Thermal Batteries,” J. Power Sources, 139(1–2), pp. 356–365. [CrossRef]
Köllner, T. , Boeck, T. , and Schumacher, J. , 2017, “Thermal Rayleigh-Marangoni Convection in a Three-Layer Liquid-Metal-Battery Model,” Phys. Rev. E, 95(5), p. 053114. [CrossRef] [PubMed]
Xiang, L. , and Zikanov, O. , 2017, “Subcritical Convection in an Internally Heated Layer,” Phys. Rev. Fluids, 2(6), p. 063501. [CrossRef]
Foster, M. S. , 1967, “Laboratory Studies of Intermetallic Cells,” Regenerative EMF Cells (Advances in Chemistry), Vol. 64, C. E. Crouthamel and H. L. Recht, eds., American Chemical Society, Washington, DC, pp. 136–148. [CrossRef]
Goluskin, D. , 2015, Internally Heated Convection and Rayleigh-Bénard Convection, Springer, New York.
Shattuck, M. D. , Behringer, R. P. , Johnson, G. A. , and Georgiadis, J. G. , 1997, “Convection and Flow in Porous Media—Part 1: Visualization by Magnetic Resonance Imaging,” J. Fluid Mech., 332, pp. 215–245. [CrossRef]
Howle, L. E. , Behringer, R. P. , and Georgiadis, J. G. , 1997, “Convection and Flow in Porous Media—Part 2: Visualization by Shadowgraph,” J. Fluid Mech., 332, pp. 247–262. [CrossRef]
Weber, N. , Galindo, V. , Priede, J. , Stefani, F. , and Weier, T. , 2015, “The Influence of Current Collectors on Tayler Instability and Electro-Vortex Flows in Liquid Metal Batteries,” Phys. Fluids, 27(1), p. 014103. [CrossRef]
Davis, S. H. , 1987, “Thermocapillary Instabilities,” Annu. Rev. Fluid Mech., 19(1), pp. 403–435. [CrossRef]
Schatz, M. F. , and Neitzel, G. P. , 2001, “Experiments on Thermocapillary Instabilities,” Annu. Rev. Fluid Mech., 33(1), pp. 93–127. [CrossRef]
Colinet, P. , Legros, J. C. , and Velarde, M. G. , 2001, Nonlinear Dynamics of Surface-Tension-Driven Instabilities, Wiley-VCH, Weinheim, Germany. [CrossRef]
Prange, M. , Wanschura, M. , Kuhlmann, H. C. , and Rath, H. J. , 1999, “Linear Stability of Thermocapillary Convection in Cylindrical Liquid Bridges Under Axial Magnetic Fields,” J. Fluid Mech., 394, pp. 281–302. [CrossRef]
Morthland, T. E. , and Walker, J. S. , 1996, “Thermocapillary Convection During Floating-Zone Silicon Growth With a Uniform or Non-Uniform Magnetic Field,” J. Cryst. Growth, 158(4), pp. 471–479. [CrossRef]
Bratsun, D. A. , and De Wit, A. , 2004, “On Marangoni Convective Patterns Driven by an Exothermic Chemical Reaction in Two-Layer Systems,” Phys. Fluids, 16(4), pp. 1082–1096. [CrossRef]
Köllner, T. , Schwarzenberger, K. , Eckert, K. , and Boeck, T. , 2013, “Multiscale Structures in Solutal Marangoni Convection: Three-Dimensional Simulations and Supporting Experiments,” Phys. Fluids, 25(9), p. 092109. [CrossRef]
Köllner, T. , Schwarzenberger, K. , Eckert, K. , and Boeck, T. , 2015, “Solutal Marangoni Convection in a Hele–Shaw Geometry: Impact of Orientation and Gap Width,” Eur. Phys. J.-Spec. Top, 224(2), pp. 261–276. [CrossRef]
Jensen, K. F. , Einset, E. O. , and Fotiadis, D. I. , 1991, “Flow Phenomena in Chemical Vapor Deposition of Thin Films,” Annu. Rev. Fluid Mech, 23(1), pp. 197–232. [CrossRef]
Craster , R. V. , and Matar, O. K. , 2009, “Dynamics and Stability of Thin Liquid Films,” Rev. Mod. Phys., 81(3), pp. 1131–1198. [CrossRef]
VanHook, S. J. , Schatz, M. F. , McCormick, W. D. , Swift, J. B. , and Swinney, H. L. , 1995, “Long-Wavelength Instability in Surface-Tension-Driven Bénard Convection,” Phys. Rev. Lett., 75(24), pp. 4397–4400. [CrossRef] [PubMed]
Pearson, J. R. A. , 1958, “On Convection Cells Induced by Surface Tension,” J. Fluid Mech., 4(5), pp. 489–500. [CrossRef]
Smith, K. A. , 1966, “On Convective Instability Induced by Surface-Tension Gradients,” J. Fluid Mech., 24(2), pp. 401–414. [CrossRef]
Koschmieder, E. L. , and Switzer, D. W. , 1992, “The Wavenumbers of Supercritical Surface-Tension-Driven Bénard Convection,” J. Fluid Mech., 240(1), pp. 533–548. [CrossRef]
VanHook, S. J. , Schatz, M. F. , Swift, J. B. , McCormick, W. D. , and Swinney, H. L. , 1997, “Long-Wavelength Surface-Tension-Driven Bénard Convection: Experiment and Theory,” J. Fluid Mech., 345, pp. 45–78. [CrossRef]
Welander, P. , 1964, “Convective Instability in a Two-Layer Fluid Heated Uniformly From Above,” Tellus, 16(3), pp. 349–358.
Walsh, W. J. , Gay, E. C. , Arntzen, J. D. , Kincinas, J. E. , Cairns, E. J. , and Webster, D. S. , 1971, “Lithium/Chalcogen Secondary Cells for Components in Electric Vehicular-Propulsion Generating Systems,” Argonne National Laboratory, Lemont, IL, Report No. ANL-7999. https://babel.hathitrust.org/cgi/pt?id=mdp.39015086453050
Newhouse, J. M. , 2014, “Modeling the Operating Voltage of Liquid Metal Battery Cells,” Ph.D. thesis, Massachusetts Institute of Technology, Cambridge, MA. https://dspace.mit.edu/handle/1721.1/89840
Scriven, L. E. , and Sternling, C. V. , 1964, “On Cellular Convection Driven by Surface-Tension Gradients: Effects of Mean Surface Tension and Surface Viscosity,” J. Fluid Mech., 19(3), pp. 321–340. [CrossRef]
Janz, G. J. , Tomkins, R. P. T. , Allen , C. B., Downey , J. R., Jr. , Garner, G. L. , Krebs, U. , and Singer, S. K. , 1975, “Molten Salts: Volume 4—Part 2: Chlorides and Mixtures—Electrical Conductance, Density, Viscosity, and Surface Tension Data,” J. Phys. Chem. Ref. Data, 4(4), pp. 871–1178. [CrossRef]
Sele, T. , 1977, “Instabilities of the Metal Surface in Electrolytic Alumina Reduction Cells,” Metall. Trans. B, 8B(4), pp. 613–618. [CrossRef]
Davidson, P. A. , 2000, “Overcoming Instabilities in Aluminium Reduction Cells: A Route to Cheaper Aluminium,” Mater. Sci. Technol., 16(5), pp. 475–479. [CrossRef]
Evans, J. W. , and Ziegler, D. P. , 2007, “The Electrolytic Production of Aluminum,” Electrochemical Engineering (Encyclopedia of Electrochemistry), Vol. 5, A. Bard and M. Stratmann , eds., Wiley-VCH, Weinheim, Germany, pp. 224–265. [CrossRef]
Molokov, S. , El, G. , and Lukyanov, A. , 2011, “Classification of Instability Modes in a Model of Aluminium Reduction Cells With a Uniform Magnetic Field,” Theor. Comput. Fluid Dyn., 25(5), pp. 261–279. [CrossRef]
Øye, H. A. , Mason, N. , Peterson, R. D. , Richards, N. E. , Rooy, E. L. , Stevens McFadden, F. J. , Zabreznik, R. D. , Williams, F. S. , and Wagstaff, R. B. , 1999, “Aluminum: Approaching the New Millennium,” J. Metals, 51(2), pp. 29–42.
Bojarevičs, V. , and Romerio, V. , 1994, “Long Waves Instability of Liquid Metal-Electrolyte Interface in Aluminum Electrolysis Cells: A Generalization of Sele's Criterion,” Eur. J. Mech. B, 13(1), pp. 33–56.
Davidson, P. A. , and Lindsay, R. I. , 1998, “Stability of Interfacial Waves in Aluminium Reduction Cells,” J. Fluid Mech., 362, pp. 273–295. [CrossRef]
Sneyd, A. D. , 1985, “Stability of Fluid Layers Carrying a Normal Electric Current,” J. Fluid Mech., 156(1), pp. 223–236. [CrossRef]
Zikanov, O. , 2015, “Metal Pad Instabilities in Liquid Metal Batteries,” Phys. Rev. E, 92(6) p. 063021. [CrossRef]
Weber, N. , Beckstein, P. , Herreman, W. , Horstmann, G. M. , Nore, C. , Stefani, F. , and Weier, T. , 2017, “Sloshing Instability and Electrolyte Layer Rupture in Liquid Metal Batteries,” Phys. Fluids, 29(5), p. 054101. [CrossRef]
Weber, N. , Beckstein, P. , Galindo, V. , Herreman, W. , Nore, C. , Stefani, F. , and Weier, T. , 2017, “Metal Pad Role Instability in Liquid Metal Batteries,” Magnetohydrodynamics, 53(1), pp. 3–13. https://perso.limsi.fr/nore/Weber_MHD_2017.pdf
Weller, H. G. , Tabor, G. , Jasak, H. , and Fureby, C. , 1998, “A Tensorial Approach to Computational Continuum Mechanics Using Object-Oriented Techniques,” Comput. Phys., 12(6), pp. 620–631. [CrossRef]
Horstmann, G. M. , Weber, N. , and Weier, T. , 2017, “Coupling and Stability of Interfacial Waves in Liquid Metal Batteries,” e-print arXiv:1708.02159. https://arxiv.org/abs/1708.02159
Zikanov, O. , 2017, “Shallow Water Modeling of Rolling Pad Instability in Liquid Metal Batteries,” e-print arXiv:1706.08589. https://arxiv.org/abs/1706.08589
Tayler, R. J. , 1957, “Hydromagnetic Instabilities of an Ideally Conducting Fluid,” Proc. Phys. Soc. Lond. B, 70(1), p. 31. [CrossRef]
Tayler, R. J. , 1973, “The Adiabatic Stability of Stars Containing Magnetic Fields—I: Toroidal Fields,” Mon. Not. R. Astron. Soc., 161(4), pp. 365–380. [CrossRef]
Vandakurov, Y. V. , 1972, “Theory for the Stability of a Star With a Toroidal Magnetic Field,” Sov. Astron., 16(2), pp. 265–272. http://adsabs.harvard.edu/full/1972SvA....16..265V
Spruit, H. C. , 2002, “Dynamo Action by Differential Rotation in a Stably Stratified Stellar Interior,” Astron. Astrophys., 381(3), pp. 923–932. [CrossRef]
Rosenbluth, M. N. , 1973, “Nonlinear Properties of the Internal m = 1 Kink Instability in the Cylindrical Tokamak,” Phys. Fluids, 16(11), pp. 1894–1902. [CrossRef]
Freidberg, J. P. , 1982, “Ideal Magnetohydrodynamic Theory of Magnetic Fusion Systems,” Rev. Mod. Phys, 54(3), pp. 801–902. [CrossRef]
Stefani, F. , Weier, T. , Gundrum, T. , and Gerbeth, G. , 2011, “How to Circumvent the Size Limitation of Liquid Metal Batteries Due to the Tayler Instability,” Energ. Convers. Manage, 52(8–9), pp. 2982 –2986. [CrossRef]
Weber, N. , Galindo, V. , Stefani, F. , and Weier, T. , 2014, “Current-Driven Flow Instabilities in Large-Scale Liquid Metal Batteries, and How to Tame Them,” J. Power Sources, 265, pp. 166–173. [CrossRef]
Shumlak, U. , and Hartman, C. W. , 1995, “Sheared Flow Stabilization of the m=1 Kink Mode in Z Pinches,” Phys. Rev. Lett., 75(18), pp. 3285–3288. [CrossRef] [PubMed]
Weber, N. , Galindo, V. , Stefani, F. , Weier, T. , and Wondrak, T. , 2013, “Numerical Simulation of the Tayler Instability in Liquid Metals,” New. J. Phys., 15(4), p. 043034. [CrossRef]
Seilmayer, M. , Stefani, F. , Gundrum, T. , Weier, T. , Gerbeth, G. , Gellert, M. , and Rüdiger, G. , 2012, “Experimental Evidence for a Transient Tayler Instability in a Cylindrical Liquid-Metal Column,” Phys. Rev. Lett., 108(24), p. 244501. [CrossRef] [PubMed]
Rüdiger, G. , Schultz, M. , and Gellert, M. , 2011, “The Tayler Instability of Toroidal Magnetic Fields in a Columnar Gallium Experiment,” Astron. Nachr, 332(1), pp. 17–23. [CrossRef]
Weber, N. , Galindo, V. , Stefani, F. , and Weier, T. , 2015, “The Tayler Instability at Low Magnetic Prandtl Numbers: Between Chiral Symmetry Breaking and Helicity Oscillations,” New. J. Phys., 17(11), p. 113013. [CrossRef]
Stefani, F. , Galindo, V. , Kasprzyk, C. , Landgraf, S. , Seilmayer, M. , Starace, M. , Weber, N. , and Weier, T. , 2016, “Magnetohydrodynamic Effects in Liquid Metal Batteries,” IOP Conf. Ser.: Mater. Sci. Eng., 143(1), p. 012024. [CrossRef]
Stefani, F. , Giesecke, A. , Weber, N. , and Weier, T. , 2016, “Synchronized Helicity Oscillations: A Link Between Planetary Tides and the Solar Cycle?,” Solar Phys., 291(8), pp. 2197–2212. [CrossRef]
Priede, J. , 2016, “Electromagnetic Pinch-Type Instabilities in Liquid Metal Batteries,” Tenth PAMIR International Conference—Fundamental and Applied MHD, DIEE, Cagliari, Italy, June 20–24, pp. 268–273.
Herreman, W. , Nore, C. , Cappanera, L. , and Guermond, J.-L. , 2015, “Tayler Instability in Liquid Metal Columns and Liquid Metal Batteries,” J. Fluid Mech., 771, pp. 79–114. [CrossRef]
Bojarevičs, V. , Freibergs, Y. , Shilova, E. I. , and Shcherbinin, E. V. , 1989, Electrically Induced Vortical Flows, Kluwer Academic Publishers, Dordrecht, The Netherlands. [CrossRef]
Davidson, P. A. , 1999, “Magnetohydrodynamics in Materials Processing,” Annu. Rev. Fluid Mech., 31(1), pp. 273–300. [CrossRef]
Kolesnichenko, I. , and Khripchenko, S. , 2002, “Mathematical Simulation of Hydrodynamic Processes in the Centrifugal MHD-Pump,” Magnetohydrodynamics, 38(4), pp. 391–398.
Kolesnichenko, I. , Khripchenko, S. , Buchenau, D. , and Gerbeth, G. , 2005, “Electro-Vortex Flows in a Square Layer of Liquid Metal,” Magnetohydrodynamics, 41, pp. 39–51.
Denisov, S. , Dolgikh, V. , Mann, M. É. , and Khripchenko, S. , 1999, “Electrical Vortex Generation of Transit Flows Across Plane MHD Channels,” Magnetohydrodynamics, 35(1), pp. 52–58.
Khripchenko, S. , Kolesnichenko, I. , Dolgikh, V. , and Denisov, S. , 2008, “Pumping Effect in a Flat MHD Channel With an Electrovortex Flow,” Magnetohydrodynamics, 44(3), pp. 303–314. http://adsabs.harvard.edu/abs/2008MHD....44..303K
Denisov, S. , Dolgikh, V. , Khalilov, R. , Kolesnichenko, I. , and Khripchenko, S. , 2012, “Pumping Effect in Y- and Ψ-Shaped Channels With Π − shaped Cores,” Magnetohydrodynamics, 48(1), pp. 197–202. http://mhd.sal.lv/contents/2012/1/MG.48.1.22.R.html
Dolgikh, V. , and Khalilov, R. , 2014, “Investigation of a Model of the Winding-Free MHD Pump With Liquid Metal Electrodes,” Magnetohydrodynamics, 50(2), pp. 187–192. http://mhd.sal.lv/contents/2014/2/MG.50.2.7.R.html
Denisov, S. , Dolgikh, V. , Khripchenko, S. , and Kolesnichenko, I. , 2016, “The Electrovortex Centrifugal Pump,” Magnetohydrodynamics, 52(1–2), pp. 25–33. https://www.tib.eu/de/suchen/id/BLSE%3ARN606096378/The-electrovortex-centrifugal-pump/
Kazak, O. V. , and Semko, A. N. , 2011, “Electrovortex Motion of a Melt in Dc Furnaces With a Bottom Electrode,” J. Eng. Phys. Thermophys., 84(1), pp. 223–231. [CrossRef]
Starace, M. , Weber, N. , Seilmayer, M. , Kasprzyk, C. , Weier, T. , Stefani, F. , and Eckert, S. , 2015, “Ultrasound Doppler Flow Measurements in a Liquid Metal Column Under the Influence of a Strong Axial Electric Field,” Magnetohydrodynamics, 51(2), pp. 249–256. http://pamir.sal.lv/2014/mhd/51.2/mahyd-Riga-51.2-249.pdf
Takeda, Y. , 1995, “Velocity Profile Measurement by Ultrasonic Doppler Method,” Exp. Therm. Fluid Sci., 10(4), pp. 444–453. [CrossRef]
Eckert, S. , Cramer, A. , and Gerbeth, G. , 2007, “Velocity Measurement Techniques for Liquid Metal Flows,” Magnetohydrodynamics, Springer, Dordrecht, The Netherlands, pp. 275–294. [CrossRef]
Büttner, L. , Nauber, R. , Burger, M. , Räbiger, D. , Franke, S. , Eckert, S. , and Czarske, J. , 2013, “Dual-Plane Ultrasound Flow Measurements in Liquid Metals,” Meas. Sci. Technol., 24(5), p. 055302. [CrossRef]
Räbiger, D. , Zhang, Y. , Galindo, V. , Franke, S. , Willers, B. , and Eckert, S. , 2014, “The Relevance of Melt Convection to Grain Refinement in Al-Si Alloys Solidified Under the Impact of Electric Currents,” Acta Mater., 79, pp. 327–338. [CrossRef]
Franke, S. , Räbiger, D. , Galindo, V. , Zhang, Y. , and Eckert, S. , 2016, “Investigations of Electrically Driven Liquid Metal Flows Using an Ultrasound Doppler Flow Mapping System,” Flow Meas. Instrum., 48, pp. 64–73. [CrossRef]
Nauber, R. , Beyer, H. , Mäder, K. , Kupsch, C. , Thieme, N. , Büttner, L. , and Czarske, J. , 2016, “Modular Ultrasound Velocimeter for Adaptive Flow Mapping in Liquid Metals,” IEEE International Ultrasonics Symposium (IUS), Tours, France, Sept. 18–21, pp. 1–4.
Eckert, S. , Gerbeth, G. , and Melnikov, V. I. , 2003, “Velocity Measurements at High Temperatures by Ultrasound Doppler Velocimetry Using an Acoustic Wave Guide,” Exp. Fluids, 35(6), pp. 381–388. [CrossRef]
Ashour, R. F. , Yin, H. , Ouchi, T. , Kelley, D. H. , and Sadoway, D. R. , 2017, “Molten Amide-Hydroxide-Iodide Electrolyte for a Low-Temperature Sodium-Based Liquid Metal Battery,” J. Electrochem. Soc., 164(2), pp. A535–A537. [CrossRef]
Lalau, C.-C. , Ispas, A. , Weier, T. , and Bund, A. , 2015, “Sodium-Bismuth-Lead Low Temperature Liquid Metal Battery,” J. Electrochem. Plating Technol., p. 4808.
Lalau, C.-C. , Dimitrova, A. , Himmerlich, M. , Ispas, A. , Weier, T. , Krischok, S. , and Bund, A. , 2016, “An Electrochemical and Photoelectron Spectroscopy Study of a Low Temperature Liquid Metal Battery Based on an Ionic Liquid Electrolyte,” J. Electrochem. Soc., 163(10), pp. A2488–A2493. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Sketch of a liquid metal cell with discharge current and density profile for fully charged state and isothermal conditions (a) and schematic discharge process (b) from Ref. [12]

Grahic Jump Location
Fig. 2

Cross sections of prototype LMBs. Both are enclosed in a stainless steel casing that also serves as the positive current collector, and both have a foam negative current collector attached to a copper conductor that exits the top of the battery. In the discharged state (left), the foam is nearly filled with electrolyte, and a dark Li–Bi intermetallic layer is visible at bottom. In the charged state (right), lithium metal is visible in the foam, and the positive electrode at bottom has been restored to nearly pure bismuth. Because these photographs were taken at room temperature, the electrolyte does not fill the volume between the electrodes, but during operation, it would. The space above the negative current collector is filled with inert gas during operation. Adapted from Ref. [13], with permission.

Grahic Jump Location
Fig. 3

Aluminum refinement cells adapted from Hoopes [26] (a), Betts [25] (b), and Drossbach [24] (c)

Grahic Jump Location
Fig. 4

Closed cycle battery system suggested by Yeager in 1957, adapted from Roberts [50]

Grahic Jump Location
Fig. 5

Sketch of a differential density cell

Grahic Jump Location
Fig. 6

Sketch of a liquid metal cell featuring a retainer (metal foam) to contain the negative electrode

Grahic Jump Location
Fig. 7

Sketch of a liquid metal cell with thermal convection

Grahic Jump Location
Fig. 8

A simulation of thermal convection in a three-layer liquid metal battery. A vertical cross section through the center of the battery (a) shows that the temperature is much higher in the electrolyte than in either electrode. A horizontal cross section above the electrolyte (b) shows vigorous flow. Here, uz is the vertical velocity component, the radius and thickness of the battery are 52 mm, and the LiCl–KCl electrolyte makes up 10% of the thickness. Adapted from Ref. [123], with permission.

Grahic Jump Location
Fig. 9

Marangoni flow occurs when surface tension at a fluid interface varies spatially. Variation along the interface always drives flow, as shown. Variation across the interface, however, causes an instability that drives flow only if the variation is sufficiently large, as quantified by the Marangoni number Ma.

Grahic Jump Location
Fig. 10

A simulation of Marangoni flow in a three-layer liquid metal battery. Temperature is indicated in color, and velocity is indicated by arrows. The horizontal top surface of the electrolyte shows Marangoni cells (a) with downwellings where the temperature is lowest. A vertical cross section through the center of the battery, (b) also shows downwellings and indicates that the temperature is much higher in the electrolyte than in either electrode. Here, a LiCl–KCl electrolyte separates a Li negative electrode from a PbBi positive electrode. The temperature unit is 6.59 K, the velocity unit is 6.46 × 10−6 m/s, and the length unit is 20 mm. Adapted from Ref. [131], with permission.

Grahic Jump Location
Fig. 11

Sketch of a liquid metal cell undergoing an interfacial instability

Grahic Jump Location
Fig. 12

Characteristic dimensions and notations for an aluminum electrolysis cell (left) and a liquid metal battery (right)

Grahic Jump Location
Fig. 13

Minimum electrolyte layer height hmin depending on β according to Eq. (16) for the Mg|KCl–MgCl2–NaCl|Sb system,determined in simulations. For each curve, only the parameter named in the legend is varied, the other ones stay constant (j = 1 A/cm2, Bz = 10 mT, HA = 4.5 cm, HE = 1 cm, and ρA = 1577 kg/m3). By definition, ΔρEA = ρEρA. The inset shows a snapshot of the anode-electrolyte interface for β = 2.5. Adapted from Ref. [167].

Grahic Jump Location
Fig. 14

In phase and antiphase sloshing waves. Simulated interface shapes (top) and idealized circumferential wave contours (bottom). Adapted from Ref. [170].

Grahic Jump Location
Fig. 15

Sketch of a liquid metal cell susceptible to the Tayler instability

Grahic Jump Location
Fig. 16

Critical current for the Tayler instability depending onthe aspect ratio of a cuboid with square cross section(96 × 96 mm3) filled with InGaSn (σ = 3.29 × 106 S/m, ρ = 6403 kg/m3, and ν = 3.4 × 10−7 m2/s), determined in simulations. The insets show contours of the induced vertical magnetic field component. Adapted from Ref. [181].

Grahic Jump Location
Fig. 17

Reynolds number based on the mean velocity in a cylindrical liquid metal column versus time in viscous units. The applied current density corresponds to Ha = 100, column diameter and height are (D = 1 m, H = 2.4 m). The material parameters correspond to Na at 580 °C. hCC denotes the height of the current collectors, their conductivity is five times that of sodium. The centered area with fixed potential has a diameter d = 0.5D. The insets show velocity snapshots in a meridional plane. Adapted from Ref. [137].

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In