Issues

 / 

2012

 / 

November

  

Reviews of topical problems


Where is the supercritical fluid on the phase diagram?

 a, b,  a,  a, b,  c,  a,  a
a Institute for High Pressure Physics, Russian Academy of Sciences, Kaluzhskoe shosse 14, Troitsk, Moscow, 108840, Russian Federation
b Moscow Institute of Physics and Technology (National Research University), Institutskii per. 9, Dolgoprudny, Moscow Region, 141701, Russian Federation
c South East Physics Network and School of Physics, Queen Mary University of London, Mile End Road, London, E1 4NS, UK

We discuss the fluid state of matter at high temperature and pressure. We review the existing ways in which the boundary between a liquid and a quasigas fluid above the critical point are discussed. We show that the proposed ’thermodynamic’ continuation of the boiling line, the ’Widom line’, exists as a line near the critical point only, but becomes a bunch of short lines at a higher temperature. We subsequently propose a new ’dynamic’ line separating a liquid and a gas-like fluid. The dynamic line is related to different types of particle trajectories and different diffusion mechanisms in liquids and dense gases. The location of the line on the phase diagram is determined by the equality of the liquid relaxation time and the minimal period of transverse acoustic excitations. Crossing the line results in the disappearance of transverse waves at all frequencies, the diffusion coefficient acquiring a value close to that at the critical point, the speed of sound becoming twice the particle thermal speed, and the specific heat reaching 2kB. In the high-pressure limit, the temperature on the dynamic line depends on pressure in the same way as does the melting temperature. In contrast to the Widom line, the proposed dynamic line separates liquid and gas-like fluids above the critical point at arbitrarily high pressure and temperature. We propose calling the new dynamic line the ’Frenkel line’.

Fulltext pdf (963 KB)
Fulltext is also available at DOI: 10.3367/UFNe.0182.201211a.1137
PACS: 62.10.+s, 62.50.−p, 63.50.−x, 64.60.F−, 64.60.fd, 65.20.De, 66.20.Cy (all)
DOI: 10.3367/UFNe.0182.201211a.1137
URL: https://ufn.ru/en/articles/2012/11/a/
https://youtu.be/z4uAHLiUSmo
https://rutube.ru/video/87a452b31ab611e02222429ddb883d29/
000314808600001
2-s2.0-84873901364
2012PhyU...55.1061B
Citation: Brazhkin V V, Lyapin A G, Ryzhov V N, Trachenko K, Fomin Yu D, Tsiok E N "Where is the supercritical fluid on the phase diagram?" Phys. Usp. 55 1061–1079 (2012)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 20th, September 2011, revised: 31st, October 2011, 2nd, November 2011

Оригинал: Бражкин В В, Ляпин А Г, Рыжов В Н, Траченко К, Фомин Ю Д, Циок Е Н «Где находится область сверхкритического флюида на фазовой диаграмме?» УФН 182 1137–1156 (2012); DOI: 10.3367/UFNr.0182.201211a.1137

References (73) Cited by (152) ↓ Similar articles (20)

  1. Khrapak S A, Khrapak A G Phys. Rev. E 114 (1) (2026)
  2. Torres-Arenas J, Becerra-Zamudio Ju The Journal Of Supercritical Fluids 234 106969 (2026)
  3. Ferracina F, Lu A K A et al J. Phys.: Condens. Matter 38 (20) 205702 (2026)
  4. Khrapak S A Physics of Fluids 38 (5) (2026)
  5. Yan Ch, Luo Zh et al Energy Fuels 40 (16) 8628 (2026)
  6. Yan Sh-F, Zheng X-M et al Organic Geochemistry 213 105128 (2026)
  7. Atamas N, Yablochkova K S et al Chemical Thermodynamics And Thermal Analysis 23 100332 (2026)
  8. Khrapak S A Phys. Rev. E 111 (6) (2025)
  9. Gurrala L, Morais A R C ChemCatChem 17 (7) (2025)
  10. Belyakov M Yu, Kulikov V D The Journal Of Supercritical Fluids 218 106513 (2025)
  11. MUNEOKA Hitoshi IEEJ Journal 145 (8) 468 (2025)
  12. Fomin Yu D, Brazhkin V V Journal Of Molecular Liquids 418 126736 (2025)
  13. Khrapak S A, Wu Y -F, Du C -R Physics of Plasmas 32 (9) (2025)
  14. Fomin Yu D, Tsiok E N et al Phys. Scr. 100 (7) 075914 (2025)
  15. Khrapak S A, Khrapak A G Journal Of Molecular Liquids 425 127263 (2025)
  16. Ghandili A Physics of Fluids 37 (1) (2025)
  17. Brazhkin V V Uspekhi Fizicheskikh Nauk 195 (05) 519 (2025) [Brazhkin V V Phys. Usp. 68 (05) 490 (2025)]
  18. Raj K D, Kwak D et al Separation And Purification Technology 359 130254 (2025)
  19. Khrapak S A, Formisano F, Bove L E Phys. Rev. E 112 (1) (2025)
  20. Asharchuk N M, Yusupov V I, Mareev E I Materials Today 82 49 (2025)
  21. Salim O, Sharma K V, Piri M Journal Of CO2 Utilization 92 103017 (2025)
  22. Demishev S V Uspekhi Fizicheskikh Nauk 194 (01) 23 (2024) [Demishev S V Phys. Usp. 67 (01) 22 (2024)]
  23. Epifanov E O, Asharchuk N M et al Russ. J. Phys. Chem. B 18 (8) 1948 (2024)
  24. Khrapak S A, Khrapak A G Phys. Rev. E 110 (5) (2024)
  25. Zhang W, Kang X et al International Journal Of Greenhouse Gas Control 135 104139 (2024)
  26. Zaika S O, Loburets A T, Fedorus O H Springer Proceedings In Physics Vol. Nanomaterials and Nanocomposites, Nanostructures, and Their ApplicationsPhase Transitions in Anisotropic Submonolayer Adsorbed Films253 Chapter 27 (2024) p. 397
  27. de Oliveira C R S, de Oliveira P V et al Journal Of Environmental Sciences 140 123 (2024)
  28. Khrapak S A, Khrapak A G Physics of Fluids 36 (11) (2024)
  29. Khrapak S A Phys. Rev. E 110 (3) (2024)
  30. Vasin M, Ankudinov V Math Methods In App Sciences 47 (8) 6798 (2024)
  31. Atamas N O, Yablochkova K S et al Fluid Phase Equilibria 576 113951 (2024)
  32. Vasin M, Ankudinov V Phase Transitions 97 (7-8) 432 (2024)
  33. Ghandili A Fluid Phase Equilibria 585 114178 (2024)
  34. Atamas N O, Yablochkova K S et al Journal Of Molecular Liquids 416 126481 (2024)
  35. Khrapak S A, Khrapak A G Jetp Lett. 120 (4) 236 (2024)
  36. Asharchuk N M, Mareev E I Russ. J. Phys. Chem. B 18 (7) 1729 (2024)
  37. Li S, Deng W et al Physics of Fluids 36 (10) (2024)
  38. Apfelbaum E M Journal Of Molecular Liquids 389 122877 (2023)
  39. Atamas N O, Yablochkova K S et al Appl Nanosci 13 (7) 5101 (2023)
  40. Batalin O Yu, Vafina N G The Journal Of Supercritical Fluids 203 106081 (2023)
  41. Tovbin Yu K Russ. J. Phys. Chem. B 17 (8) 1569 (2023)
  42. Brazhkin V V Uspekhi Fizicheskikh Nauk 193 (11) 1227 (2023) [Brazhkin V V Phys. Usp. 66 (11) 1154 (2023)]
  43. Klumov B A Uspekhi Fizicheskikh Nauk 193 (03) 305 (2023) [Klumov B A Phys. Usp. 66 (03) 288 (2023)]
  44. Brazhkin V V, Danilov I V, Tsiok O B Pisʹma V žurnal êksperimentalʹnoj I Teoretičeskoj Fiziki 117 (11-12 (6)) 840 (2023)
  45. Brazhkin V V, Danilov I V, Tsiok O B Jetp Lett. 117 (11) 834 (2023)
  46. Voloshin V P, Naberukhin Yu I J Struct Chem 64 (2) 208 (2023)
  47. He R, Yi P, Li T Fuel 331 125729 (2023)
  48. Khrapak S A The Journal of Chemical Physics 156 (11) (2022)
  49. Mozafar O, Denniston C Phys. Rev. E 105 (6) (2022)
  50. Apfelbaum E M, Vorob’ev V S High Temp 60 (S3) S339 (2022)
  51. Ghandili A, Moeini V Fluid Phase Equilibria 555 113355 (2022)
  52. Tsiok E N, Fomin Yu D et al The Journal of Chemical Physics 156 (11) (2022)
  53. Ghandili A, Moeini V Fluid Phase Equilibria 562 113564 (2022)
  54. Vasin M G Phys. Rev. E 106 (4) (2022)
  55. Liu M, Tang J et al The Journal Of Supercritical Fluids 183 105554 (2022)
  56. Apfelbaum E M J. Phys. Chem. B 126 (15) 2912 (2022)
  57. Khrapak S A, Khrapak A G The Journal of Chemical Physics 157 (1) (2022)
  58. Volkov N B, Lipchak A I Condensed Matter 7 (4) 61 (2022)
  59. Mareev E I, Sviridov A P, Gordienko V M IJMS 22 (18) 9813 (2021)
  60. Cockrell C, Brazhkin V V, Trachenko K Physics Reports 941 1 (2021)
  61. Khrapak S A, Khrapak A G Phys. Rev. E 103 (4) (2021)
  62. Ghandili A, Moeini V Physics And Chemistry Of Liquids 59 (1) 113 (2021)
  63. Khrapak S A, Yurchenko S O The Journal of Chemical Physics 155 (13) (2021)
  64. Tovbin Yu K Russ. J. Phys. Chem. 95 (3) 429 (2021)
  65. Atamas N, Yablochkova K S, Lazarenko M M Journal Of Molecular Liquids 332 115900 (2021)
  66. Tolias P, Lucco C F Physics of Plasmas 28 (3) (2021)
  67. Khrapak S A, Khrapak A G Phys. Rev. E 104 (4) (2021)
  68. Fomin Yu D, Tsiok E N et al Journal Of Molecular Liquids 337 116450 (2021)
  69. Maxim F, Poenaru I et al Energies 14 (21) 7399 (2021)
  70. Abdulagatov I M, Skripov P V Russ. J. Phys. Chem. B 15 (7) 1171 (2021)
  71. Maxim F, Karalis K et al Advanced Science 8 (3) (2021)
  72. Atamas N, Gavryushenko D et al Journal Of Molecular Liquids 340 117201 (2021)
  73. Atamas N A, Lazarenko M M et al RSC Adv. 11 (59) 37307 (2021)
  74. Khomkin A L, Shumikhin A S Uspekhi Fizicheskikh Nauk 191 (11) 1187 (2021)
  75. Fomin Yu D J. Phys.: Condens. Matter 32 (39) 395101 (2020)
  76. Pestryaev E M Polym. Sci. Ser. A 62 (6) 766 (2020)
  77. Bell I H, Galliero G et al The Journal of Chemical Physics 152 (19) (2020)
  78. Ryzhov V N, Tareyeva E E et al Uspekhi Fizicheskikh Nauk 190 (05) 449 (2020) [Ryzhov V N, Tareyeva E E et al Phys.-Usp. 63 (5) 417 (2020)]
  79. Cockrell C, Dicks O A et al J. Phys.: Condens. Matter 32 (38) 385102 (2020)
  80. Cockrell C J, Dicks O et al Phys. Rev. E 101 (5) (2020)
  81. Ghandili A, Moeini V AIChE Journal 66 (9) (2020)
  82. Walker P J, Haslam A J J. Chem. Eng. Data 65 (12) 5809 (2020)
  83. Uwineza P A, Waśkiewicz A Molecules 25 (17) 3847 (2020)
  84. Fomin YuD, Tsiok E N et al Fluid Phase Equilibria 498 45 (2019)
  85. Fomin Yu D, Tsiok E N et al Journal Of Molecular Liquids 287 110992 (2019)
  86. Kats E I J. Exp. Theor. Phys. 129 (4) 751 (2019)
  87. Kryuchkov N P, Mistryukova L A et al Sci Rep 9 (1) (2019)
  88. Pipich V, Schlenstedt K et al Journal Of Membrane Science 573 167 (2019)
  89. Fomin Yu D Physics And Chemistry Of Liquids 57 (1) 67 (2019)
  90. Fomin Yu D Molecular Physics 117 (20) 2786 (2019)
  91. Khomkin A L, Shumikhin A S Plasma Phys. Rep. 44 (10) 958 (2018)
  92. Pipich V, Schwahn D Phys. Rev. Lett. 120 (14) (2018)
  93. Brazhkin V V, Prescher C et al J. Phys. Chem. B 122 (22) 6124 (2018)
  94. Khomkin A L, Shumikhin A S High Temp 56 (4) 467 (2018)
  95. Kats E I J. Exp. Theor. Phys. 127 (5) 939 (2018)
  96. Mareev E, Aleshkevich V et al Opt. Express 26 (10) 13229 (2018)
  97. Tareyeva E E, Fomin Yu D et al Theor Math Phys 194 (1) 148 (2018)
  98. Brazhkin V V, Fomin Yu D et al Physica A: Statistical Mechanics And Its Applications 509 690 (2018)
  99. Fomin Yu D, Ryzhov V N et al J. Phys.: Condens. Matter 30 (13) 134003 (2018)
  100. Lazarev A V, Tatarenko P A, Tatarenko K A Russ. J. Phys. Chem. B 12 (7) 1152 (2018)
  101. Artemenko S, Krijgsman P, Mazur V Journal Of Molecular Liquids 238 122 (2017)
  102. Khomkin A L, Shumikhin A S J. Exp. Theor. Phys. 125 (6) 1189 (2017)
  103. Brazhkin V V Uspekhi Fizicheskikh Nauk 187 (09) 1028 (2017) [Brazhkin V V Phys.-Usp. 60 (9) 954 (2017)]
  104. Wang L, Yang C et al Phys. Rev. E 95 (3) (2017)
  105. Prescher C, Fomin Yu D et al Phys. Rev. B 95 (13) (2017)
  106. Baldock R J N Classical Statistical Mechanics with Nested Sampling Springer Theses Chapter 8 (2017) p. 61
  107. Khomkin A L, Shumikhin A S J. Exp. Theor. Phys. 124 (1) 70 (2017)
  108. Fomin Yu D, Ryzhov V N et al J. Phys.: Condens. Matter 29 (34) 345401 (2017)
  109. Khrapak S, Klumov B, Couëdel L Sci Rep 7 (1) (2017)
  110. Khomkin A L, Shumikhin A S J. Exp. Theor. Phys. 124 (6) 1001 (2017)
  111. Wang L, Dove M T et al Phys. Rev. E 96 (1) (2017)
  112. Baldock R J N Classical Statistical Mechanics with Nested Sampling Springer Theses Chapter 5 (2017) p. 31
  113. Khusnutdinoff R M Colloid J 78 (2) 225 (2016)
  114. Khomkin A L, Shumikhin A S J. Exp. Theor. Phys. 123 (5) 891 (2016)
  115. Norman G E, Saitov I M J. Phys.: Conf. Ser. 774 012015 (2016)
  116. Fomin Yu D, Ryzhov V N et al Physica A: Statistical Mechanics And Its Applications 444 890 (2016)
  117. Fomin Yu D, Ryzhov V N et al J. Phys.: Condens. Matter 28 (43) 43LT01 (2016)
  118. Tareeva E E, Tareeva E E i dr Teoreticheskaya Matematicheskaya Fizika 189 (3) 464 (2016) [Tareyeva E E, Ryzhov V N Theor Math Phys 189 (3) 1806 (2016)]
  119. Dyre Je C J. Phys.: Condens. Matter 28 (32) 323001 (2016)
  120. Desgranges C, Delhommelle Je The Journal of Chemical Physics 145 (18) (2016)
  121. Trachenko K, Brazhkin V V Rep. Prog. Phys. 79 (1) 016502 (2016)
  122. Desgranges C, Margo A, Delhommelle Je Chemical Physics Letters 658 37 (2016)
  123. Vorob’ev V S, Apfelbaum E M High Temp 54 (2) 175 (2016)
  124. Gaiduk E A, Fomin Yu D et al Fluid Phase Equilibria 417 237 (2016)
  125. Khomkin A L, Shumikhin A S J. Phys.: Conf. Ser. 653 012083 (2015)
  126. Apfelbaum E, Vorob’ev V Springer Proceedings In Physics Vol. Physics of Liquid Matter: Modern ProblemsThe Generalized Similarity Laws and Isocontours in the Thermodynamics of Simple Liquids171 Chapter 6 (2015) p. 139
  127. Fomin Yu D, Ryzhov V N et al Sci Rep 5 (1) (2015)
  128. Armstrong G Eur. J. Phys. 36 (6) 063001 (2015)
  129. Fomin Yu D, Ryzhov V N et al Phys. Rev. E 91 (2) (2015)
  130. Khomkin A L, Shumikhin A S J. Exp. Theor. Phys. 121 (3) 521 (2015)
  131. Trachenko K, Brazhkin V V Phys. Rev. E 91 (3) (2015)
  132. Maslov V P, Maslov V P Teoreticheskaya Matematicheskaya Fizika 180 (3) 394 (2014) [Maslov V P Theor Math Phys 180 (3) 1096 (2014)]
  133. Maslov V P Russ. J. Math. Phys. 21 (1) 99 (2014)
  134. Fedyaeva O N, Vostrikov A A et al Russ. J. Phys. Chem. B 8 (8) 1054 (2014)
  135. Bryk T, Gorelli F et al Phys. Rev. E 90 (4) (2014)
  136. Leonov S B, Adamovich I V, Lempert W R 52nd Aerospace Sciences Meeting, (2014)
  137. Brazhkin V V, Lyapin A G et al Russ. J. Phys. Chem. B 8 (8) 1087 (2014)
  138. Khusnutdinoff R M, Mokshin A V Jetp Lett. 100 (1) 39 (2014)
  139. Maslov V P Russ. J. Math. Phys. 21 (2) 256 (2014)
  140. Maslov V P Math Notes 95 (5-6) 670 (2014)
  141. Brazhkin V V, Fomin Yu D et al Phys. Rev. E 89 (4) (2014)
  142. Fomin Yu D, Ryzhov V N et al Sci Rep 4 (1) (2014)
  143. Ryltsev R E, Chtchelkatchev N M The Journal of Chemical Physics 141 (12) (2014)
  144. Maslov V P Math Notes 96 (3-4) 403 (2014)
  145. Maslov V P Math Notes 95 (1-2) 91 (2014)
  146. Brazhkin V V, Fomin Yu D et al Phys. Rev. Lett. 111 (14) (2013)
  147. Maslov V P Math Notes 94 (1-2) 231 (2013)
  148. Apfelbaum E M, Vorob’ev V S J. Phys. Chem. B 117 (25) 7750 (2013)
  149. Maslov V P Math Notes 94 (5-6) 722 (2013)
  150. Maslov V P Math Notes 94 (3-4) 532 (2013)
  151. Nikolaev P N Moscow Univ. Phys. 68 (3) 196 (2013)
  152. Maslov, Maslov Matematicheskie Zametki 94 (2) 237 (2013)

© 1918–2026 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions