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Theoretical and computational approaches to predicting the viscosity of liquids

†  a, b, c, ‡  a, b, c
a Joint Institute for High Temperatures, Russian Academy of Sciences, ul. Izhorskaya 13/19, Moscow, 127412, Russian Federation
b HSE University, ul. Myasnitskaya 20, Moscow, 101000, Russian Federation
c Moscow Institute of Physics and Technology (National Research University), Institutskii per. 9, Dolgoprudny, Moscow Region, 141701, Russian Federation

Predictive models for the shear viscosity of liquids and gases along with exact equations of state are of great practical importance for hydrodynamic modeling of processes occurring in nature, industrial plants, and machinery. We consider currently proposed theoretical, including atomistic modeling, and semi-empirical approaches to predicting the viscosity of liquids, gases, and their mixtures in a wide range of thermodynamic conditions. Viscosity models of homogeneous liquids in a thermodynamically stable state are described. The dynamics of supercooled and vitrescent liquids and dispersed systems (colloids, emulsions) remain beyond the scope of this review. We discuss the area of applicability of correlation methods for predicting viscosity and the accuracy of various methods in the pressure range up to 1 GPa. Application examples of various approaches for hydrocarbons — model oil and gas, fuel, and lubrication systems — are given.

Fulltext pdf (1.4 MB)
Fulltext is also available at DOI: 10.3367/UFNe.2021.11.039102
Keywords: shear viscosity, liquids, theoretical models, empirical models, molecular modeling, atomistic modeling
PACS: 66.20.Cy
DOI: 10.3367/UFNe.2021.11.039102
URL: https://ufn.ru/en/articles/2023/4/d/
001099929700006
2-s2.0-85137744289
2023PhyU...66..410K
Citation: Kondratyuk N D, Pisarev V V "Theoretical and computational approaches to predicting the viscosity of liquids" Phys. Usp. 66 410–432 (2023)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 26th, August 2021, revised: 17th, November 2021, 18th, November 2021

Оригинал: Кондратюк Н Д, Писарев В В «Теоретические и вычислительные подходы к предсказанию вязкости жидкостей» УФН 193 437–461 (2023); DOI: 10.3367/UFNr.2021.11.039102

References (228) ↓ Cited by (8) Similar articles (20)

  1. Batschinski A J Z. Phys. Chem. 84 643 (1913)
  2. van der Gulik P S, Mostert R, van den Berg H R Physica A 151 153 (1988)
  3. van der Gulik P S, Mostert R, van den Berg H R Fluid Phase Equilib. 79 301 (1992)
  4. Hildebrand J H Science 174 490 (1971)
  5. Hanley H J M Cryogenics 16 643 (1976)
  6. Rowlinson J S, Watson I D Chem. Eng. Sci. 24 1565 (1969)
  7. Ely J F, Hanley H J M Ind. Eng. Chem. Fundamen. 20 323 (1981)
  8. Ely J F, Hanley H J M "A computer program for the prediction of viscosity and thermal conductivity in hydrocarbon mixtures" NBS Technical Note 1039 (Boulder, CO: US Department of Commerce, National Bureau of Standards, 1981); Ely J F, Hanley H J M nvlpubs.nist.gov/nistpubs/Legacy/TN/nbstechnicalnote1039.pdf
  9. Leach J W, Chappelear P S, Leland T W AIChE J. 14 568 (1968)
  10. Huber M L, Hanley H J M Transport Properties Of Fluids (Eds J Millat, J H Dymond, C A Nieto de Castro) (Cambridge: IUPAC, Cambridge Univ. Press, 1996) p. 283
  11. Hanley H J M, McCarty R D, Haynes W M Cryogenics 15 413 (1975)
  12. Ely J F, Marrucho I M F "The corresponding-states principle" Equations Of State For Fluids And Fluid Mixtures (Experimental Thermodynamics) Vol. 5 (Eds J V Sengers et al) (Amsterdam: Elsevier, 2000) p. 289
  13. Huber M L, Ely J F Fluid Phase Equilib. 80 239 (1992)
  14. Klein S A, McLinden M O, Laesecke A Int. J. Refrigerat. 20 208 (1997)
  15. McCarty R D Cryogenics 14 276 (1974)
  16. Younglove B A, Ely J F J. Phys. Chem. Ref. Data 16 577 (1987)
  17. Pedersen K S et al Chem. Eng. Sci. 39 1011 (1984)
  18. Pedersen K S, Fredenslund A Chem. Eng. Sci. 42 182 (1987)
  19. Assael M J, Dymond J H, Tselekidou V Int. J. Thermophys. 11 863 (1990)
  20. Mulero A (Ed.) Theory And Simulation Of Hard-Sphere Fluids And Related Systems (Lecture Notes in Physics) Vol. 753 (Berlin: Springer, 2008)
  21. Assael M J et al Int. J. Thermophys. 13 269 (1992)
  22. Ciotta F, Trusler J P M, Vesovic V Fluid Phase Equilib. 363 239 (2014)
  23. Nguyen T-B, Vesovic V Fluid Phase Equilib. 487 58 (2019)
  24. Wang X, Teja A S Fluid Phase Equilib. 425 47 (2016)
  25. Baylaucq A et al Petroleum Sci. Technol. 23 143 (2005)
  26. Nguyen T-B, Riesco N, Vesovic V Fuel 208 363 (2017)
  27. Malta J A M S C et al Fluid Phase Equilib. 505 112343 (2020)
  28. Galliéro G, Boned C, Baylaucq A Ind. Eng. Chem. Res. 44 6963 (2005)
  29. Baylaucq A et al Int. J. Thermophys. 24 621 (2003)
  30. Galliéro G et al Phys. Rev. E 73 061201 (2006)
  31. Rosenfeld Y Phys. Rev. A 15 2545 (1977)
  32. Dzugutov M Nature 381 137 (1996)
  33. Lötgering-Lin O, Gross J Ind. Eng. Chem. Res. 54 7942 (2015)
  34. Pasturel A, Jakse N J. Phys. Condens. Matter 28 485101 (2016)
  35. Dyre J C J. Chem. Phys. 149 210901 (2018)
  36. Carnahan N F, Starling K E J. Chem. Phys. 51 635 (1969)
  37. Bell I H, Dyre J C, Ingebrigtsen T S Nat. Commun. 11 4300 (2020)
  38. Fomin Yu D, Ryzhov V N, Gribova N V Phys. Rev. E 81 061201 (2010)
  39. Chopra R, Truskett T M, Errington J R J. Phys. Chem. B 114 10558 (2010)
  40. Soave G Chem. Eng. Sci. 27 1197 (1972)
  41. Peng D-Y, Robinson D B Ind. Eng. Chem. Fundamen. 15 59 (1976)
  42. Brusilovskii A I Fazovye Prevrashcheniya Pri Razrabotke Mestorozhdenii Nefti I Gaza (Phase Transformations In The Development Of Oil And Gas Fields) (Moscow: Graal, 2002)
  43. Chapman W G et al Fluid Phase Equilib. 52 31 (1989)
  44. Gross J, Sadowski G Ind. Eng. Chem. Res. 40 1244 (2001)
  45. Polishuk I Ind. Eng. Chem. Res. 53 14127 (2014)
  46. Gerasimov A, Alexandrov I, Grigoriev B Fluid Phase Equilib. 418 204 (2016)
  47. Grigor’ev B A, Gerasimov A A, Aleksandrov I S Aktual’nye Voprosy Issledovanii Plastovykh Sistem Mestorozhdenii Uglevodorodov (Topical Issues Of Research Of Bedded Systems Of Hydrocarbon Fields, Vesti Gazovoi Nauki (Gas Science Bulletin), No. 1(12), Ed. B A Grigor’ev) (Moscow: Gazprom VNIIGAZ, 12) p. 1
  48. Levashov P et al AIP Conf. Proc. 505 89 (2000)
  49. Baled H O et al Fuel 218 89 (2018)
  50. Taib M B M, Trusler J P M J. Chem. Phys. 152 164104 (2020)
  51. Rokni H B et al Fuel 241 1203 (2019)
  52. Abramson E H, West-Foyle H Phys. Rev. E 77 041202 (2008)
  53. Abramson E H J. Phys. Chem. B 118 11792 (2014)
  54. Abramson E H Phys. Rev. E 80 021201 (2009)
  55. Abramson E H High Pressure Res. 31 544 (2011)
  56. Bell I H Proc. Natl. Acad. Sci. USA 116 4070 (2019)
  57. Quiñones-Cisneros S E, Zéberg-Mikkelsen C K, Stenby E H Fluid Phase Equilib. 169 249 (2000)
  58. Quiñones-Cisneros S E, Zéberg-Mikkelsen C K, Stenby E H Fluid Phase Equilib. 178 1 (2001)
  59. Quiñones-Cisneros S E, Zéberg-Mikkelsen C K, Stenby E H Int. J. Thermophys. 23 41 (2002)
  60. Quiñones-Cisneros S E et al AIChE J. 52 1600 (2006)
  61. Bair S High Temp. High Press. 44 415 (2015)
  62. Kondratyuk N D, Pisarev V V, Ewen J P J. Chem. Phys. 153 154502 (2020)
  63. Allal A, Boned C, Baylaucq A Phys. Rev. E 64 011203 (2001)
  64. Llovell F, Marcos R M, Vega L F J. Phys. Chem. B 117 8159 (2013)
  65. Llovell F, Marcos R M, Vega L F J. Phys. Chem. B 117 5195 (2013)
  66. Polishuk I, Yitzhak A Ind. Eng. Chem. Res. 53 959 (2014)
  67. Yarranton H W, Satyro M A Ind. Eng. Chem. Res. 48 3640 (2009)
  68. Hildebrand J H, Lamoreaux R H Proc. Natl. Acad. Sci. USA 69 3428 (1972)
  69. Motahhari H, Satyro M A, Yarranton H W Ind. Eng. Chem. Res. 50 12831 (2011)
  70. Polishuk I Ind. Eng. Chem. Res. 51 13527 (2012)
  71. Polishuk I Ind. Eng. Chem. Res. 54 6999 (2015)
  72. Abolala M, Peyvandi K, Varaminian F Fluid Phase Equilib. 394 61 (2015)
  73. Ryshkova O S, Postnikov E B, Polishuk I Ind. Eng. Chem. Res. 58 20116 (2019)
  74. Oliveira C M B P, Wakeham W A Int. J. Thermophys. 13 773 (1992)
  75. Audonnet F, Pádua A A H Fluid Phase Equilib. 181 147 (2001)
  76. Dymond J H, Robertson J, Isdale J D Int. J. Thermophys. 2 133 (1981)
  77. Canet X, Baylaucq A, Boned C Int. J. Thermophys. 23 1469 (2002)
  78. Battezzati L, Greer A Acta Metallurg. 37 1791 (1989)
  79. Kaptay G Z. Metallkd 96 24 (2005)
  80. Budai I, Benkõ M Z, Kaptay G Mater. Sci. Forum 537-538 489 (2007)
  81. Gasior W Calphad 44 119 (2014)
  82. Chen W et al Philos. Mag. 94 1552 (2014)
  83. Beltyukov A, Olyanina N, Ladyanov V J. Mol. Liq. 281 204 (2019)
  84. Kozlov L Ya, Romanov L M, Petrov N N Izv. Vyssh. Uchebn. Zaved. Chernaya Metallurg. (3) 7 (1983)
  85. Golubev I F Viscosity Of Gases And Gas Mixtures (Jerusalem: Israel Program for Scientific Translations, 1970); Translated from Russian, Golubev I F Vyazkost’ Gazov I Gazovykh Smesei (Moscow: Fizmatgiz, 1959)
  86. Hirschfelder J O, Curtiss C F, Bird R B Molecular Theory Of Gases And Liquids (New York: Wiley, 1954); Translated into Russian, Hirschfelder J O, Curtiss C F, Bird R B Molekulyarnaya Teoriya Gazov I Zhidkostei (Moscow: IL, 1961)
  87. Golubev I F, Gnezdilov N E Vyazkost’ Gazovykh Smesei (Viscosity Of Gas Mixtures) (Moscow: Izd. Standartov, 1971)
  88. Neufeld P D, Janzen A R, Aziz R A J. Chem. Phys. 57 1100 (1972)
  89. Chung T H, Lee L L, Starling K E Ind. Eng. Chem. Fundamen. 23 8 (1984)
  90. Wilke C R J. Chem. Phys. 18 517 (1950)
  91. Palmer G E, Wright M J J. Thermophys. Heat Transfer 17 232 (2003)
  92. Herning F, Zipperer L Gas Wasserfach 79 69 (1936)
  93. Davidson T A "A simple and accurate method for calculating viscosity of gaseous mixtures" Report of Investigations 9456 (Spokane, WA: US Department of the Interior, Bureau of Mines, 1993)
  94. Norman G E, Stegailov V V Math. Models Comput. Simul. 5 305 (2013); Norman G E, Stegailov V V Matem. Modelirovanie 24 (6) 3 (2012)
  95. Tuckerman M E Statistical Mechanics: Theory And Molecular Simulation (Oxford: Oxford Univ. Press, 2010)
  96. Frenkel D, Smit B Understanding Molecular Simulation: From Algorithms To Applications (Computational Science Series) Vol. 1 2nd ed. (San Diego, CA: Academic Press, 2002)
  97. Ewen J P et al Materials 9 651 (2016)
  98. Kondratyuk N D, Norman G E, Stegailov V V J. Chem. Phys. 145 204504 (2016)
  99. Glova A D et al RSC Adv. 9 38834 (2019)
  100. Orekhov N, Ostroumova G, Stegailov V Carbon 170 606 (2020)
  101. Belashchenko D K Phys. Usp. 63 1161 (2020); Belashchenko D K Usp. Fiz. Nauk 190 1233 (2020)
  102. Nazarychev V M et al Int. J. Heat Mass Transf. 165 120639 (2021)
  103. Zabaloy M S, Machado J M V, Macedo E A Int. J. Thermophys. 22 829 (2001)
  104. Brazhkin V V Phys. Usp. 62 623 (2019); Brazhkin V V Usp. Fiz. Nauk 189 665 (2019)
  105. Lv X et al J. Fluorine Chem. 241 109675 (2021)
  106. Galamba N, Nieto de Castro C A, Ely J F J. Phys. Chem. B 108 3658 (2004)
  107. Galamba N, Nieto de Castro C A, Ely J F J. Chem. Phys. 122 224501 (2005)
  108. Janz G J J. Phys. Chem. Ref. Data 17 (Suppl. 2) 1 (1988)
  109. Belashchenko D K Phys. Usp. 56 1176 (2013); Belashchenko D K Usp. Fiz. Nauk 183 1281 (2013)
  110. Daw M S, Baskes M I Phys. Rev. B 29 6443 (1984)
  111. Finnis M W, Sinclair J E Philos. Mag. A 50 45 (1984)
  112. Canales M, González L E, Padró J À Phys. Rev. E 50 3656 (1994)
  113. Meyer N, Xu H, Wax J-F Phys. Rev. B 93 214203 (2016)
  114. Demmel F, Tani A Phys. Rev. E 97 062124 (2018)
  115. Metya A K, Hens A, Singh J K Fluid Phase Equilib. 313 16 (2012)
  116. Kirova E M, Norman G E, Pisarev V V JETP Lett. 110 359 (2019); Kirova E M, Norman G E, Pisarev V V Pis’ma Zh. Eksp. Teor. Fiz. 110 343 (2019)
  117. Cherne F J (III), Deymier P A Scr. Mater. 39 1613 (1998)
  118. Cherne F J, Baskes M I, Deymier P A Phys. Rev. B 65 024209 (2001)
  119. Mendelev M et al Philos. Mag. 88 1723 (2008)
  120. Smirnova D et al Modelling Simul. Mater. Sci. Eng. 21 035011 (2013)
  121. O’Connor T C, Andzelm J, Robbins M O J. Chem. Phys. 142 024903 (2015)
  122. Jorgensen W L et al J. Chem. Phys. 79 926 (1983)
  123. Horn H W et al J. Chem. Phys. 120 9665 (2004)
  124. Abascal J L F, Vega C J. Chem. Phys. 123 234505 (2005)
  125. Mitchell P J, Fincham D J. Phys. 5 1031 (1993)
  126. Ponder J W, Case D A Adv. Protein Chem. 66 27 (2003)
  127. Wang J et al J. Comput. Chem. 25 1157 (2004)
  128. MacKerell A D (Jr.) et al J. Phys. Chem. B 102 3586 (1998)
  129. Jorgensen W L, Maxwell D S, Tirado-Rives J J. Am. Chem. Soc. 118 11225 (1996)
  130. Allen W, Rowley R L J. Chem. Phys. 106 10273 (1997)
  131. Liu H et al Ind. Eng. Chem. Res. 51 7242 (2012)
  132. Siu S W I, Pluhackova K, Böckmann R A J. Chem. Theory Comput. 8 1459 (2012)
  133. Dodda L S et al J. Phys. Chem. B 121 3864 (2017)
  134. Martin M G, Siepmann J I J. Phys. Chem. B 102 2569 (1998)
  135. Moore J D et al J. Chem. Phys. 113 8833 (2000)
  136. Dysthe D K, Fuchs A H, Rousseau B J. Chem. Phys. 112 7581 (2000)
  137. Nieto-Draghi C, Ungerer P, Rousseau B J. Chem. Phys. 125 044517 (2006)
  138. Ungerer P et al J. Chem. Phys. 112 5499 (2000)
  139. Nieto-Draghi C et al Mol. Simul. 34 211 (2008)
  140. Sun H J. Phys. Chem. B 102 7338 (1998)
  141. Kondratyuk N D, Pisarev V V Fluid Phase Equilib. 498 151 (2019)
  142. Kondratyuk N, Lenev D, Pisarev V J. Chem. Phys. 152 191104 (2020)
  143. Kondratyuk N D, Pisarev V V Fluid Phase Equilib. 544-545 113100 (2021)
  144. Orekhov N, Ostroumova G, Stegailov V Carbon 170 606 (2020)
  145. Car R, Parrinello M Phys. Rev. Lett. 55 2471 (1985)
  146. Kohn W Rev. Mod. Phys. 71 1253 (1999); Kohn W Usp. Fiz. Nauk 172 336 (2002)
  147. Levashov P R et al J. Phys. 22 505501 (2010)
  148. French M et al Astrophys. J. Suppl. 202 5 (2012)
  149. Wang W Y et al Acta Mater. 97 75 (2015)
  150. Weber H et al Phys. Rev. B 96 054204 (2017)
  151. Rong Z et al Renewable Energy 163 579 (2021)
  152. Harada A, Shimojo F, Hoshino K J. Phys. Soc. Jpn. 74 2017 (2005)
  153. Ohmura S, Shimojo F Phys. Rev. B 80 020202 (2009)
  154. Ohmura S, Shimojo F Phys. Rev. B 84 224202 (2011)
  155. Koura A, Ohmura S, Shimojo F J. Chem. Phys. 138 134504 (2013)
  156. Ohmura S, Shimojo F Phys. Rev. B 83 134206 (2011)
  157. Lopanitsyna N, Ben Mahmoud C, Ceriotti M Phys. Rev. Mater. 5 043802 (2021)
  158. Kamaeva L V et al J. Phys. 32 224003 (2020)
  159. Ryltsev R, Chtchelkatchev N J. Mol. Liq.
  160. Behler J, Parrinello M Phys. Rev. Lett. 98 146401 (2007)
  161. Wang H et al Comput. Phys. Commun. 228 178 (2018)
  162. Yeh I-C, Hummer G J. Phys. Chem. B 108 15873 (2004)
  163. Green M S J. Chem. Phys. 22 398 (1954)
  164. Kubo R J. Phys. Soc. Jpn. 12 570 (1957)
  165. Helfand E Phys. Rev. 119 1 (1960)
  166. Alder B J, Wainwright T E Phys. Rev. A 1 18 (1970)
  167. Anikeenko A V, Malenkov G G, Naberukhin Yu I J. Chem. Phys. 148 094508 (2018)
  168. Orekhov M A J. Mol. Liq. 322 114554 (2021)
  169. Moultos O A et al J. Chem. Phys. 145 074109 (2016)
  170. Volkov N A, Posysoev M V, Shchekin A K Colloid J. 80 248 (2018); Volkov N A, Posysoev M V, Shchekin A K Kolloid. Zh. 80 264 (2018)
  171. Jamali S H et al J. Chem. Theor. Comput. 14 2667 (2018)
  172. Tazi S et al J. Phys. Condens. Matter 24 284117 (2012)
  173. Humphrey W, Dalke A, Schulten K J. Mol. Graph. 14 33 (1996)
  174. Lee A L, Ellington R T J. Chem. Eng. Data 10 101 (1965)
  175. Belonoshko A B et al Nat. Commun. 10 2483 (2019)
  176. Adjaoud O, Steinle-Neumann G, Jahn S Earth Planet. Sci. Lett. 312 463 (2011)
  177. Gordon P A Ind. Eng. Chem. Res. 44 5828 (2005)
  178. Kondratyuk N D, Orekhov M A J. Phys. Conf. Ser. 1556 012048 (2020)
  179. Brazhkin V V, Lyapin A G Phys. Usp. 43 493 (2000); Brazhkin V V, Lyapin A G Usp. Fiz. Nauk 170 535 (2000)
  180. Khrapak S A, Khrapak A G JETP Lett. 114 540 (2021); Khrapak S A, Khrapak A G Pis’ma Zh. Eksp. Teor. Fiz. 114 615 (2021)
  181. Viscardy S, Servantie J, Gaspard P J. Chem. Phys. 126 184512 (2007)
  182. Allen M P, Brown D, Masters A J Phys. Rev. E 49 2488 (1994)
  183. Nevins D, Spera F J Mol. Simul. 33 1261 (2007)
  184. Fomin Yu D, Brazhkin V V, Ryzhov V N JETP Lett. 95 320 (2012); Fomin Yu D, Brazhkin V V, Ryzhov V N Pis’ma Zh. Eksp. Teor. Fiz. 95 349 (2012)
  185. Fomin Yu D, Brazhkin V V, Ryzhov V N Phys. Rev. E 86 011503 (2012)
  186. Rudyak V Ya, Krasnolutskii S L Phys. Lett. A 378 1845 (2014)
  187. Rudyak V Ya, Krasnolutskii S L Tech. Phys. 60 798 (2015); Rudyak V Ya, Krasnolutskii S L Zh. Tekh. Fiz. 85 (6) 9 (2015)
  188. Brazhkin V V et al Physica A 509 690 (2018)
  189. Zhang Y, Otani A, Maginn E J J. Chem. Theory Comput. 11 3537 (2015)
  190. Maginn E J et al Living J. Comput. Mol. Sci. 1 6324 (2019)
  191. Hess B J. Chem. Phys. 116 209 (2002)
  192. Rey-Castro C, Vega L F J. Phys. Chem. B 110 14426 (2006)
  193. Kondratyuk N J. Chem. Phys. 151 074502 (2019)
  194. Zhang Y et al J. Phys. Chem. B 119 14934 (2015)
  195. Messerly R A et al Fluid Phase Equilib. 495 76 (2019)
  196. Kondratyuk N, Lenev D, Pisarev V J. Chem. Phys. 152 191104 (2020)
  197. Liesen N T et al J. Chem. Phys. 153 024502 (2020)
  198. Heyes D M, Smith E R, Dini D J. Chem. Phys. 150 174504 (2019)
  199. Heyes D M, Dini D, Smith E R J. Chem. Phys. 154 074503 (2021)
  200. Müller-Plathe F Phys. Rev. E 59 4894 (1999)
  201. Bordat P, Müller-Plathe F J. Chem. Phys. 116 3362 (2002)
  202. Evans D J, Morriss G P Statistical Mechanics Of Nonequilibrium Liquids (London: Academic Press, 1990)
  203. Tuckerman M E et al J. Chem. Phys. 106 5615 (1997)
  204. Daivis P J, Todd B D J. Chem. Phys. 124 194103 (2006)
  205. Ewen J P, Spikes H A, Dini D Tribol. Lett. 69 24 (2021)
  206. McCabe C et al J. Chem. Phys. 114 1887 (2001)
  207. Jadhao V, Robbins M O Proc. Natl. Acad. Sci. USA 114 7952 (2017)
  208. Jadhao V, Robbins M O Tribol. Lett. 67 66 (2019)
  209. Liu P et al J. Chem. Phys. 147 084904 (2017)
  210. Carreau P J Trans. Soc. Rheology 16 99 (1972)
  211. Prentice I J et al J. Chem. Phys. 152 074504 (2020)
  212. Lee S H, Cummings P T Mol. Simulat. 16 229 (1996)
  213. Travis K P, Searles D J, Evans D J Mol. Phys. 95 195 (1998)
  214. Kelkar M S et al Fluid Phase Equilib. 260 218 (2007)
  215. Galvani Cunha M A, Robbins M O Fluid Phase Equilib. 495 28 (2019)
  216. Bair S, McCabe C, Cummings P T Phys. Rev. Lett. 88 058302 (2002)
  217. Chen T, Smit B, Bell A T J. Chem. Phys. 131 246101 (2009)
  218. Simonnin P et al J. Chem. Theory Comput. 13 2881 (2017)
  219. Bair S, Martinie L, Vergne P Tribol. Lett. 63 37 (2016)
  220. Bair S Fluid Phase Equilib. 488 9 (2019)
  221. Zhang J, Spikes H Tribol. Lett. 68 42 (2020)
  222. Tropin T V, Schmelzer Ju W P, Aksenov V L Phys. Usp. 59 42 (2016); Tropin T V, Schmelzer Ju W P, Aksenov V L Usp. Fiz. Nauk 186 47 (2016)
  223. "Industrial Fluid Properties Simulation Challenge", Industrial Fluid Properties Simulation Collective, Accessed: 2021-03-24, fluidproperties.org
  224. Weiß H et al Annu. Rev. Chem. Biomol. Eng. 7 65 (2016)
  225. Lowitz D A et al J. Chem. Phys. 30 73 (1959)
  226. "Benchmarks for the 11th Challenge", Industrial Fluid Properties Simulation Collective, fluidproperties.org/11th-benchmarks
  227. Stegailov V et al Int. J. High Perform. Comput. Appl. 33 507 (2019)
  228. Kostenetskiy P S, Chulkevich R A, Kozyrev V I J. Phys. Conf. Ser. 1740 012050 (2021)
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