DOI QR코드

DOI QR Code

Computational Modelling of Droplet Dynamics Behaviour in Polymer Electrolyte Membrane Fuel Cells: A Review

  • Yong, K.W. (Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, Jalan Universiti) ;
  • Ganesan, P.B. (Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, Jalan Universiti) ;
  • Kazi, S.N. (Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, Jalan Universiti) ;
  • Ramesh, S. (Department of Mechanical Engineering, Faculty of Engineering, University of Malaya, Jalan Universiti) ;
  • Sandaran, S.C. (Universiti Teknologi Malaysia)
  • Received : 2019.05.28
  • Accepted : 2019.07.25
  • Published : 2019.12.31

Abstract

Polymer Electrolyte Membrane Fuel Cells (PEMFC) is one of the leading advanced energy conversion technology for the use in transport. It generates water droplets through the catalytic processes and dispenses the water through the gas-flowed microchannels. The droplets in the dispensing microchannel experience g-forces from different directions during the operation in transport. Therefore, this paper reviews the computational modelling topics of droplet dynamics behaviour specifically for three categories, i.e. (i) the droplet sliding down a surface, (ii) the droplet moving in a gas-flowed microchannel, and (iii) the droplet jumping upon coalescence on superhydrophobic surface; in particular for the parameters like hydrophobicity surfaces, droplet sizes, numerical methods, channel sizes, wall conditions, popular references and boundary conditions.

Acknowledgement

Supported by : MOSTI-Science Fund, Newton - Ungku Omar

References

  1. P. Loyselle, K. Prokopius, Proton Exchange Member (PEM) Fuel Cell Engineering Model Powerplant; Ohio, 2011.
  2. S. Byun, D. Kwak, J. Electrochem. Sci. Technol., 2019, 10(2), 104-114. https://doi.org/10.5229/jecst.2019.10.2.104
  3. M. Mortazavi, A. D. Santamaria, V. Chauhan, J. Z. Benner, J. Electrochem. Soc., 2019, 166(7), F3143-F3153. https://doi.org/10.1149/2.0211907jes
  4. V. Palan, S. W. J. Shepard, A. K. Williams, J. Power Sources, 2006, 161(2), 1116-1125. https://doi.org/10.1016/j.jpowsour.2006.06.021
  5. A. Theodorakakos, T. Ous, M. Gavaises, J. M. Nouri, N. Nikolopoulos, H. Yanagihara, J. Colloid Interface Sci., 2006, 300(2), 673-687. https://doi.org/10.1016/j.jcis.2006.04.021
  6. X. Zhu, Q. Liao, P. C. Sui, N. Djilali, J. Power Sources, 2010, 195(3), 801-812. https://doi.org/10.1016/j.jpowsour.2009.08.021
  7. L. Hao, P. Cheng, Int. J. Heat Mass Transf., 2010, 53(5-6), 1243-1246. https://doi.org/10.1016/j.ijheatmasstransfer.2009.11.010
  8. C. Qin, D. Rensink, S. Hassanizadeh, J. Electrochem. Soc., 2012, 159(4), 434-443. https://doi.org/10.1149/2.004205jes
  9. S. C. Cho, Y. Wang, K. S. Chen, J. Power Sources, 2012, 210, 191-197. https://doi.org/10.1016/j.jpowsour.2012.03.033
  10. A. Bazylak, D. Sinton, N. Djilali, J. Power Sources, 2008, 176(1), 240-246. https://doi.org/10.1016/j.jpowsour.2007.10.066
  11. A. Kumar, R. G. Reddy, J. Power Sources, 2003, 114(1), 54-62. https://doi.org/10.1016/S0378-7753(02)00540-2
  12. C. Hartnig, I. Manke, R. Kuhn, S. Kleinau, J. Goebbels, J. Banhart, J. Power Sources, 2009, 188(2), 468-474. https://doi.org/10.1016/j.jpowsour.2008.12.023
  13. S. Cho, M. Cha, M. Kim, Y. Sohn, T. Yang, W. Lee, J. Electrochem. Sci. Technol., 2016, 7(1), 41-51. https://doi.org/10.33961/JECST.2016.7.1.41
  14. P. D. M. Spelt, J. Comput. Phys., 2005, 207(2), 389-404. https://doi.org/10.1016/j.jcp.2005.01.016
  15. L. W. Schwartz, D. Roux, J. J. Cooper White, Phys. D, 2005, 209(July), 236-244. https://doi.org/10.1016/j.physd.2005.07.001
  16. Y. Y. Koh, Y. C. Lee, P. H. Gaskell, P. K. Jimack, H. M. Thompson, Eur. Phys. J. Spec. Top., 2009, 166, 117-120. https://doi.org/10.1140/epjst/e2009-00890-2
  17. J. B. Dupont, D. Legendre, J. Comput. Phys., 2010, 229(7), 2453-2478. https://doi.org/10.1016/j.jcp.2009.07.034
  18. L. de Oliveira, D. Lopes, S. Ramos, J. Mombach, Soft Matter, 2011, 7, 3763-3765. https://doi.org/10.1039/c0sm01178a
  19. A. S. Ravi, J. Y. Murthy, S. V. Garimella, Int. J. Heat Mass Transf., 2012, 55(5-6), 1466-1474. https://doi.org/10.1016/j.ijheatmasstransfer.2011.10.028
  20. G. Ahmed, M. Sellier, Y. C. Lee, M. Jermy, M. Taylor, Colloids Surfaces A Physicochem. Eng. Asp., 2013, 432, 2-7. https://doi.org/10.1016/j.colsurfa.2013.05.015
  21. G. Ahmed, M. Sellier, M. Jermy, M. Taylor, Eur. J. Mech. B/Fluids, 2014, 48, 218-230. https://doi.org/10.1016/j.euromechflu.2014.06.003
  22. C. Lee, S. Lyu, J. W. Park, W. Hwang, Adv. Eng. Softw., 2016, 91, 44-50. https://doi.org/10.1016/j.advengsoft.2015.10.001
  23. K. W. Yong, P. B. Ganesan, S. N. Kazi, S. Ramesh, I. A. Badruddin, N. M. Mubarak, Phys. Fluids, 2018, 30(12), 122006. https://doi.org/10.1063/1.5063857
  24. X. Liu, P. Cheng, X. Quan, Int. J. Heat Mass Transf., 2014, 73, 195-200. https://doi.org/10.1016/j.ijheatmasstransfer.2014.01.060
  25. F. Liu, G. Ghigliotti, J. J. Feng, C. H. Chen, J. Fluid Mech., 2014, 752(2014), 22-38. https://doi.org/10.1017/jfm.2014.319
  26. X. Liu, P. Cheng, Int. Commun. Heat Mass Transf., 2015, 64, 7-13. https://doi.org/10.1016/j.icheatmasstransfer.2015.03.002
  27. S. Farokhirad, J. F. Morris, T. Lee, Phys. Fluids, 2015, 27(10).
  28. Y. Shi, G. H. Tang, H. H. Xia, Int. J. Heat Mass Transf., 2015, 88(4), 445-455. https://doi.org/10.1016/j.ijheatmasstransfer.2015.04.085
  29. Z. Khatir, K. J. Kubiak, P. K. Jimack, T. G. Mathia, Appl. Therm. Eng., 2016, 106, 1337-1344. https://doi.org/10.1016/j.applthermaleng.2016.06.128
  30. L. Zhang, W. Yuan, Appl. Surf. Sci., 2018, 436, 172-182. https://doi.org/10.1016/j.apsusc.2017.11.200
  31. F. Chu, Z. Yuan, X. Zhang, X. Wu, Int. J. Heat Mass Transf., 2018, 121, 315-320. https://doi.org/10.1016/j.ijheatmasstransfer.2018.01.027
  32. Y. Shi, G. H. Tang, Comput. Math. with Appl., 2018, 75(4), 1213-1225. https://doi.org/10.1016/j.camwa.2017.10.024
  33. G. Londe, A. Chunder, A. Wesser, L. Zhai, H. Cho, Sensors Actuators B Chem., 2008, 132(2), 431-438. https://doi.org/10.1016/j.snb.2007.10.052
  34. J. P. La, A. Jonsson, S. Senkbeil, J. P. Kutter, Biosens. Bioelectron., 2016, 76, 213-233. https://doi.org/10.1016/j.bios.2015.08.003
  35. S. H. Jin, H. H. Jeong, B. Lee, S. S. Lee, C. S. Lee, Lab Chip, 2015, 15(18), 3677-3686. https://doi.org/10.1039/C5LC00651A
  36. M. Sakai, J. H. Song, N. Yoshida, S. Suzuki, Y. Kameshima, A. Nakajima, Langmuir, 2006, 22(11), 4906-4909. https://doi.org/10.1021/la060323u
  37. A. Nakajima, K. Hashimoto, T. Watanabe, Monatshefte fuer Chemie, 2001, 132(1), 31-41. https://doi.org/10.1007/s007060170142
  38. V. P. Carey, Liquid-Vapor Phase Change Phenomena, 2nd ed.; Scholl, S., Ed.; Taylor & Francis Group: New York, 2008.
  39. R. N. Wenzel, J. Phys. Colloid Chem., 1949, 53(9), 1466-1467. https://doi.org/10.1021/j150474a015
  40. A. B. D. Cassie, S. Baxter, Trans. Faraday Soc., 1944, 40, 546. https://doi.org/10.1039/tf9444000546
  41. E. Bormashenko, P. Faculty, Adv. Colloid Interface Sci., 2015, 222, 92-103. https://doi.org/10.1016/j.cis.2014.02.009
  42. J. Cui, W. Li, W. H. Lam, Comput. Math. with Appl., 2011, 61(12), 3678-3689. https://doi.org/10.1016/j.camwa.2010.07.037
  43. X. T. Zhu, Z. Z. Zhang, X. h. Xu, X. h. Men, J. Yang, X. y. Zhou, Q. J. Xue, J. Colloid Interface Sci., 2012, 367(1), 443-449. https://doi.org/10.1016/j.jcis.2011.10.008
  44. D. Khojasteh, M. Kazerooni, S. Salarian, R. Kamali, J. Ind. Eng. Chem., 2016, 42(2016), 1-14. https://doi.org/10.1016/j.jiec.2016.07.027
  45. G. Mchale, N. J. Shirtcliffe, M. I. Newton, Langmuir, 2004, 20, 10146-10149. https://doi.org/10.1021/la0486584
  46. B. He, J. Lee, N. A. Patankar, Colloids Surfaces A Physicochem. Eng. Asp., 2004, 248(2004), 101-104. https://doi.org/10.1016/j.colsurfa.2004.09.006
  47. B. He, N. A. Patankar, J. Lee, Langmuir, 2003, 19, 4999-5003. https://doi.org/10.1021/la0268348
  48. N. A. Patankar, Langmuir, 2003, 19, 1249-1253. https://doi.org/10.1021/la026612+
  49. J. Bico, C. Marzolin, D. Qu, Europhys. Lett., 1999, 47(July), 220-226. https://doi.org/10.1209/epl/i1999-00548-y
  50. J. Min, R. L. Webb, Exp. Therm. Fluid Sci., 2000, 22(3-4), 175-182. https://doi.org/10.1016/S0894-1777(00)00024-8
  51. E. Moallem, S. Padhmanabhan, L. Cremaschi, D. E. Fisher, Int. J. Refrig., 2012, 35(1), 171-186. https://doi.org/10.1016/j.ijrefrig.2011.08.010
  52. P. B. Ganesan, S. M. Vanakia, K. K. Thoo, W. M. Chin, Int. Commun. Heat Mass Transf., 2016, 74, 27-35. https://doi.org/10.1016/j.icheatmasstransfer.2016.02.017
  53. F. Chu, X. Wu, Q. Ma, Appl. Therm. Eng., 2017, 115, 1101-1108. https://doi.org/10.1016/j.applthermaleng.2017.01.060
  54. H. W. Hu, G. H. Tang, D. Niu, Appl. Therm. Eng., 2016, 100, 699-707. https://doi.org/10.1016/j.applthermaleng.2016.02.086
  55. D. E. Kim, H. S. Ahn, T. S. Kwon, Appl. Therm. Eng., 2017, 110, 412-423. https://doi.org/10.1016/j.applthermaleng.2016.08.175
  56. J. B. Boreyko, C. P. Collier, ACS Nano, 2013, 7(2), 1618-1627. https://doi.org/10.1021/nn3055048
  57. Q. Zhang, M. He, J. Chen, J. Wang, Y. Song, L. Jiang, Chem. Commun., 2013, 49(40), 4516. https://doi.org/10.1039/c3cc40592c
  58. L. Cao, A. K. Jones, V. K. Sikka, J. Wu, D. Gao, Langmuir, 2009, 25(21), 12444-12448. https://doi.org/10.1021/la902882b
  59. F. Tavakoli, H. P. Kavehpour, Langmuir, 2015, 31, 2120-2126. https://doi.org/10.1021/la503620a
  60. M. Kim, H. Kim, K. Lee, D. R. Kim, Energy Convers. Manag., 2017, 138, 1-11. https://doi.org/10.1016/j.enconman.2017.01.067
  61. X. Li, L. Zhang, X. Ma, H. Zhang, Surf. Coat. Technol., 2016, 307(2016), 243-253. https://doi.org/10.1016/j.surfcoat.2016.08.089
  62. R. Kamali, D. Khojasteh, S. M. Mousavi, In 24th Annual International Conference on Mechanical Engineering; 2016; p 24486.
  63. N. D. Patil, V. H. Gada, A. Sharma, R. Bhardwaj, Int. J. Multiph. Flow, 2016, 81, 54-66. https://doi.org/10.1016/j.ijmultiphaseflow.2016.01.005
  64. N. Patil, R. Bhardwaj, Int. J. Micro-Nano Scale Transp., 2014, 5(2), 51-58. https://doi.org/10.1260/1759-3093.5.2.51
  65. J. R. Moffat, K. Sefiane, M. E. R. Shanahan, J. Nano Res., 2009, 7, 75-80. https://doi.org/10.4028/www.scientific.net/JNanoR.7.75
  66. G. McHale, S. M. Rowan, M. I. Newton, M. K. Banerjee, J. Phys. Chem. B, 1998, 102(11), 1964-1967. https://doi.org/10.1021/jp972552i
  67. W. K. Choi, E. Lebrasseur, M. I. Al-Haq, H. Tsuchiya, T. Torii, H. Yamazaki, E. Shinohara, T. Higuchi, Sensors Actuators, A Phys., 2007, 136(1), 484-490. https://doi.org/10.1016/j.sna.2006.12.028
  68. H. Ren, R. B. Fair, M. G. Pollack, Sensors Actuators B Chem., 2004, 98(2-3), 319-327. https://doi.org/10.1016/j.snb.2003.09.030
  69. P. Onnerfjord, J. Nilsson, L. Wallman, T. Laurell, G. Marko-Varga, Anal. Chem., 1998, 70(22), 4755-4760. https://doi.org/10.1021/ac980207z
  70. S. Suzuki, A. Nakajima, Y. Kameshima, K. Okada, Surf. Sci. Lett., 2004, 557.
  71. N. Yoshida, Y. Abe, H. Shigeta, A. Nakajima, H. Ohsaki, J. Am. Chem. Soc., 2006, 128(13), 743-747. https://doi.org/10.1021/ja050617m
  72. M. Sakai, Surf. Sci., 2006, 600, L204-L208. https://doi.org/10.1016/j.susc.2006.06.039
  73. Z. Yoshimitsu, A. Nakajima, T. Watanabe, Langmuir, 2002, 18, 5818-5822. https://doi.org/10.1021/la020088p
  74. W. Yeong, L. Ling, T. Wah, A. Neild, Q. Zheng, J. Colloid Interface Sci., 2011, 354(2), 832-842. https://doi.org/10.1016/j.jcis.2010.11.027
  75. N. Thanh vinh, H. Takahashi, K. Matsumoto, I. Shimoyama, Sensors Actuators A. Phys., 2015, 231(2015), 35-43. https://doi.org/10.1016/j.sna.2014.09.015
  76. H. Wang, L. Tang, X. Wu, W. Dai, Y. Qiu, Appl. Surf. Sci., 2007, 253(22), 8818-8824. https://doi.org/10.1016/j.apsusc.2007.04.006
  77. Z. Jin, H. Zhang, Z. Yang, Int. J. Heat Mass Transf., 2016, 103(2016), 886-893. https://doi.org/10.1016/j.ijheatmasstransfer.2016.08.012
  78. S. Wang, X. Yu, C. Liang, Y. Zhang, Appl. Therm. Eng., 2018, 137(April), 758-766. https://doi.org/10.1016/j.applthermaleng.2018.04.020
  79. R. P. Garrod, L. G. Harris, W. C. E. Schofield, J. Mcgettrick, L. J. Ward, D. O. H. Teare, J. P. S. Badyal, Langmuir, 2007, 23, 689-693. https://doi.org/10.1021/la0610856
  80. J. B. Marcinichen, J. A. Olivier, V. de Oliveira, J. R. Thome, Appl. Energy, 2012, 92, 147-161. https://doi.org/10.1016/j.apenergy.2011.10.030
  81. K. Ellinas, V. Pliaka, G. Kanakaris, A. Tserepi, L. G. Alexopoulos, E. Gogolides, Microelectron. Eng., 2017, 175, 73-80. https://doi.org/10.1016/j.mee.2017.02.015
  82. K. Ellinas, A. Tserepi, E. Gogolides, Microfluid. Nanofluidics, 2014, 17(3), 489-498. https://doi.org/10.1007/s10404-014-1335-9
  83. A. P. Washe, P. Lozano S., D. Bejarano N., B. Teixeira D., I. Katakis, Microelectron. Eng., 2013, 111, 416-420. https://doi.org/10.1016/j.mee.2013.04.022
  84. T. Onda, S. Shibuichi, N. Satoh, K. Tsujii, Langmuir, 1996, 12(9), 2125-2127. https://doi.org/10.1021/la950418o
  85. W. Fang, H. Mayama, K. Tsujii, Colloids Surfaces A Physicochem. Eng. Asp., 2008, 316(1-3), 258-265. https://doi.org/10.1016/j.colsurfa.2007.09.010
  86. H. Yan, H. Shiga, E. Ito, T. Nakagaki, S. Takagi, T. Ueda, K. Tsujii, Colloids Surfaces A Physicochem. Eng. Asp., 2006, 284-285, 490-494. https://doi.org/10.1016/j.colsurfa.2005.10.083
  87. S. Shibuichi, T. Yamamoto, T. Onda, K. Tsujii, J. Colloid Interface Sci., 1998, 208(1), 287-294. https://doi.org/10.1006/jcis.1998.5813
  88. T. He, Y. Wang, Y. Zhang, Q. lv, T. Xu, T. Liu, Corros. Sci., 2009, 51(8), 1757-1761. https://doi.org/10.1016/j.corsci.2009.04.027
  89. H. Saffari, B. Sohrabi, M. R. Noori, H. R. T. Bahrami, Appl. Surf. Sci., 2018, 435, 1322-1328. https://doi.org/10.1016/j.apsusc.2017.11.188
  90. Y. Wu, M. Bekke, Y. Inoue, H. Sugimura, H. Kitaguchi, C. Liu, O. Takai, Thin Solid Films, 2004, 457(1), 122-127. https://doi.org/10.1016/j.tsf.2003.12.007
  91. Y. Wu, Y. Inoue, H. Sugimura, O. Takai, H. Kato, S. Murai, H. Oda, Thin Solid Films, 2002, 407(1-2), 45-49. https://doi.org/10.1016/S0040-6090(02)00010-X
  92. Y. Wu, Surf. Sci., 2006, 600, 3710-3714. https://doi.org/10.1016/j.susc.2006.01.073
  93. W. Barthlott, C. Neinhuis, Planta, 1997, 202(1), 1-8. https://doi.org/10.1007/s004250050096
  94. E. Ueda, P. A. Levkin, Adv. Mater., 2013, 25(9), 1234-1247. https://doi.org/10.1002/adma.201204120
  95. B. L. Feng, S. H. Li, Y. S. Li, H. J. Li, L. J. Zhang, J. Zhai, Y. L. Song, B. Q. Liu, L. Jiang, ... D. B. Zhu, Adv. Mater., 2002, 14(24), 1857-1860. https://doi.org/10.1002/adma.200290020
  96. S. Gogte, P. Vorobieff, R. Truesdell, A. Mammoli, F. van Swol, P. Shah, C. J. Brinker, Phys. Fluids, 2005, 17(5), 1-4.
  97. H. Matsui, Y. Noda, T. Hasegawa, Langmuir, 2012, 28(2012), 15450-15453. https://doi.org/10.1021/la303717n
  98. J. Drelich, J. L. Wilbur, J. D. Miller, G. M. Whitesides, Langmuir, 1996, 12, 1913-1922. https://doi.org/10.1021/la9509763
  99. S. Suzuki, A. Nakajima, K. Tanaka, Appl. Surf. Sci., 2008, 254, 1797-1805. https://doi.org/10.1016/j.apsusc.2007.07.171
  100. B. Chang, Q. Zhou, R. H. A. Ras, A. Shah, Z. Wu, K. Hjort, Appl. Phys. Lett., 2016, 108(15), 154102. https://doi.org/10.1063/1.4947008
  101. Y. Lin, Z. Wu, Y. Gao, J. Wu, W. Wen, Appl. Surf. Sci., 2018, 442, 189-194. https://doi.org/10.1016/j.apsusc.2018.02.055
  102. J. Huang, R. Fan, S. Connor, P. Yang, Angew. Chemie Int. Ed., 2007, 46(14), 2414-2417. https://doi.org/10.1002/anie.200604789
  103. X. Xu, Y. Di, M. Doi, 2016, 087101.
  104. A. I. ElSherbini, A. M. Jacobi, J. Colloid Interface Sci., 2004, 273(2), 556-565. https://doi.org/10.1016/j.jcis.2003.12.067
  105. A. I. ElSherbini, A. M. Jacobi, J. Colloid Interface Sci., 2004, 273(2), 566-575. https://doi.org/10.1016/j.jcis.2003.12.043
  106. A. I. ElSherbini, A. M. Jacobi, J. Colloid Interface Sci., 2006, 299(2), 841-849. https://doi.org/10.1016/j.jcis.2006.02.018
  107. B. Krasovitski, A. Marmur, Langmuir, 2005, 21, 3881-3885. https://doi.org/10.1021/la0474565
  108. X. G. Yang, F. Y. Zhang, A. L. Lubawy, C. Y. Wang, 2004, 408-411.
  109. B. Peng, S. Wang, Z. Lan, W. Xu, R. Wen, X. Ma, Appl. Phys. Lett., 2013, 102(15).
  110. N. Miljkovic, D. J. Preston, R. Enright, E. N. Wang, ACS Nano, 2013, 7(12), 11043-11054. https://doi.org/10.1021/nn404707j
  111. J. B. Boreyko, C. H. Chen, Phys. Rev. Lett., 2009, 103(18), 184501. https://doi.org/10.1103/PhysRevLett.103.184501
  112. Y. Nam, H. Kim, S. Shin, Appl. Phys. Lett., 2013, 103(16).
  113. L. Z. Zhang, W. Z. Yuan, Appl. Surf. Sci., 2018, 436, 172-182. https://doi.org/10.1016/j.apsusc.2017.11.200
  114. Y. Hou, H. Deng, Q. Du, K. Jiao, J. Power Sources, 2018, 393(February), 83-91. https://doi.org/10.1016/j.jpowsour.2018.05.008
  115. J. Yu, D. Froning, U. Reimer, W. Lehnert, Int. J. Hydrogen Energy, 2018, 43(12), 6318-6330. https://doi.org/10.1016/j.ijhydene.2018.01.168
  116. D. G. Venkateshan, H. V. Tafreshi, Colloids Surfaces A Physicochem. Eng. Asp., 2018, 538(October 2017), 310-319. https://doi.org/10.1016/j.colsurfa.2017.11.003
  117. X. Shang, Z. Luo, E. Ya, O. A. Kabov, B. Bai, Comput. Fluids, 2018, 172, 181-195. https://doi.org/10.1016/j.compfluid.2018.06.021
  118. P. Gopalan, S. G. Kandlikar, Colloids Surfaces A Physicochem. Eng. Asp., 2014, 441, 262-274. https://doi.org/10.1016/j.colsurfa.2013.09.013
  119. P. Gopalan, S. G. Kandlikar, J. Electrochem. Soc., 2013, 160(6), F487-F495. https://doi.org/10.1149/2.030306jes
  120. X. Zhu, P. C. Sui, N. Djilali, J. Power Sources, 2008, 181(1), 101-115. https://doi.org/10.1016/j.jpowsour.2008.03.005
  121. C. W. Hirt, B. D. Nichols, J. Comput. Phys., 1981, 39(1), 201-225. https://doi.org/10.1016/0021-9991(81)90145-5
  122. X. Shan, H. Chen, Phys. Rev. E, 1994, 49(4), 2941-2948. https://doi.org/10.1103/PhysRevE.49.2941
  123. L. W. Schwartz, Lanngmuir, 1998, 14, 3440-3453. https://doi.org/10.1021/la971407t
  124. M. R. Barkhudarov, Semi-Lagrangian VOF Advection Method for FLOW-3D; 2003; Vol. FSI-03-TN6.
  125. D. A. Perumal, A. K. Dass, Alexandria Eng. J., 2015, 54(4), 955-971. https://doi.org/10.1016/j.aej.2015.07.015
  126. X. He, L. Luo, Phys. Rev. E, 1997, 56(6), 6811-6817. https://doi.org/10.1103/PhysRevE.56.6811
  127. Q. Li, K. H. Luo, X. J. Li, Phys. Rev. E, 2013, 87(5), 053301. https://doi.org/10.1103/PhysRevE.87.053301
  128. A. D. Schleizer, R. T. Bonnecaze, J. Fluid Mech., 1999, 383(July), 29-54. https://doi.org/10.1017/S0022112098003462
  129. B. Lavi, A. Marmur, Colloids Surfaces A Physicochem. Eng. Asp., 2004, 250(1-3 SPEC. ISS.), 409-414. https://doi.org/10.1016/j.colsurfa.2004.04.079
  130. S. M. M. Ramos, A. Benyagoub, B. Canut, C. Jamois, Langmuir, 2010, 26(7), 5141-5146. https://doi.org/10.1021/la9036138
  131. T. Podgorski, J. M. Flesselles, L. Limat, Phys. Rev. Lett., 2001, 87(3), 361021-361024.
  132. S. Kulju, L. Riegger, P. Koltay, K. Mattila, J. Hyvaluoma, J. Colloid Interface Sci., 2018, 522(2018), 48-56. https://doi.org/10.1016/j.jcis.2018.03.053
  133. P. T. Yue, C. F. Zhou, J. J. Feng, C. F. Ollivier G., H. H. Hu, J. Comput. Phys., 2006, 219(1), 47-67. https://doi.org/10.1016/j.jcp.2006.03.016
  134. P. Yuan, University of Pittsburgh, 2005.
  135. D. Zhang, K. Papadikis, S. Gu, Int. J. Multiph. Flow., 2014, 64, 11-18. https://doi.org/10.1016/j.ijmultiphaseflow.2014.04.005
  136. C. Lv, P. Hao, Z. Yao, Y. Song, X. Zhang, F. He, Appl. Phys. Lett., 2013, 103(2), 021601. https://doi.org/10.1063/1.4812976
  137. T. Okada, G. Xie, M. Meeg, Electrochim. Acta, 1998, 43(14-15), 2141-2155. https://doi.org/10.1016/S0013-4686(97)10099-8
  138. L. You, H. Liu, Int. J. Heat Mass Transf., 2002, 45(11), 2277-2287. https://doi.org/10.1016/S0017-9310(01)00322-2
  139. Z. H. Wang, C. Y. Wang, K. S. Chen, J. Power Sources, 2001, 94(1), 40-50. https://doi.org/10.1016/S0378-7753(00)00662-5