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Research on the droplet impact on a hydrophobic surface is of important theoretical significance and engineering value, both in mesoscopic fluid mechanics and interactions between microfluid and special materials. The van der Waals (vdW) equation of state relates the pressure to the temperature and the density of the fluid, and gives the long-range attractive force and short-range repulsive force between particles. The van der Waals equation of state can be used to describe the surface tension between liquid and vapor. As a pure meshless particle method, the smoothed particle hydrodynamic (SPH) method can use the vdW equation of state written in SPH form of N-S equations to describe the surface tension. The vdW surface tension mode is validated by simulating the coalescence of two equally sized static droplets in vacuum. Repellant of the hydrophobic surface is derived from a core potential. By combining the vdW surface tension and the repulsive force of the surface, the phenomenon of a liquid droplet impact with a certain initial velocity on the hydrophobic surface is studied. The SPH model is not only capable to describe the spreading of the droplet after it contacts the surface, but also clearly reproduces the springback, bouncing and secondary impact of the droplet. During the deformation of the droplet, the inertia force impels the spreading process of the droplet whilst the springback and bouncing behavior is dominated by the surface tension. The simulated results are in good agreement with the published experimental observations and VOF simulated results, indicating that the way we treat the surface tension and the repulsive force of the hydrophobic surface is effective and applicable in droplet impact surface problems. The impact velocity and liquid viscosity are considered to be two important factors that affect the deformation of the droplet after it contacts the surface. By varying the impact velocity within a certain range it is concluded that the maximum liquid-solid contact area increases as the impact velocity grows, and the bounced droplet will leave the surface when the velocity is big enough. Another comparison between different liquid viscosities shows that the maximum contact area decreases as the liquid viscosity increases because of the viscous dissipation, and the droplet barely rebound when the liquid viscosity is big enough.
[1] Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P 1996 Comput. Method Appl. M. 139 3
[2] Vinh Phu N, Timon R, Stéphane B, Marc D 2008 Math. Comput. Simulat. 79 763
[3] Cheng R J, Ge H X 2012 Chin. Phys. B 21 040203
[4] Cheng Y M, Li R X, Peng M J 2012 Chin. Phys. B 21 090205
[5] Feng Z, Wang X D, Ouyang J 2013 Chin. Phys. B 22 074704
[6] Chen L, Ma H P, Cheng Y M 2013 Chin. Phys. B 22 050202
[7] Qin Y X, Liu Y Y, Li Z H, Yang M 2014 Chin. Phys. B 23 070207
[8] Weng Y J, Cheng Y M 2013 Chin. Phys. B 22 090204
[9] Xia M H, Li J 2007 Chin. Phys. B 16 3067
[10] Chen L, Cheng Y M 2008 Acta Phys. Sin. 57 6047 (in Chinese) [陈丽, 程玉民 2008 物理学报 57 6047]
[11] Ghou A, Malfreyt P 2011 Phys. Rev. E. 83 051601
[12] Liu X L, Cheng P 2013 Int. J. Heat Mass Tran. 64 1041
[13] Feng S D, Tsutahara M, Ji Z Z 2001 Chin. Phys. B 10 587
[14] Liu M B, Liu G R 2010 Arch. Comput. Method E S. 17 25
[15] Li Q, Cai T M, He G Q, Hu C B 2006 Appl. Math. Mech-Engl. 27 67
[16] Zhang M Y, Zhang H, Zheng L L 2007 Numer. Heat Tr. A-Appl. 52 299
[17] Zhang M Y, Zhang H, Zheng L L 2008 Int. J. Heat Mass Tran. 51 3410
[18] Morris J P 2000 Int. J. Numer. Meth Fl. 33 333
[19] Nugent S, Posch H A 2000 Phys. Rev. E 62 4968
[20] Meleán Y, Sigalotti L D G, Hasmy A 2004 Comput. Phys. Commun. 157 191
[21] Zhou G Z, Wen G, Li J H 2008 Powder Technol. 183 21
[22] Li D M, Wang Z C, Bai L, Wang X 2013 Acta Phys. Sin. 62 194704 (in Chinese) [李大鸣, 王志超, 白玲, 王笑 2013 物理学报 62 194704]
[23] Monaghan J J 2000 J. Comput. Phys. 159 290
[24] López H, Sigalotti L D G 2006 P hys. Rev. E 73 1201
[25] Meleán Y, Sigalotti L D G 2005 Int. J. Heat. Mass. Tran. 48 4041
[26] Fang H S, Bao K, Wei J A, Zhang H, Wu E H, Zheng L L 2009 Numer. Heat Tr. A.-Appl. 55 124
[27] Jiang T, Ouyang J, Yang B, Ren J 2010 Comput. Mech. 45 573
[28] Liu M B, Shao J R, Chang J Z 2012 Sci. China Tech. Sci. 55 244
[29] Tartakovsky A, Meakin P 2005 Phys. Rev. E 72 026301
[30] Shirtcliffe N J, McHale G, Atherton S, Newton M I 2010 Adv Colloid Interfac 161 124
[31] Lafuma A, Quere D 2003 Nat Mater 2 457
[32] Hoover W G 2006 Smooth particle applied mechanics:the state of the art (Singapore:World Scientific) p94
[33] Charles A N 2014 Ph. D. Dissertation (Melbourne, Australia:RMIT University)
[34] Charles A N, Daivis P 2011 19th International Congress on Modelling and Simulation Perth, Australia, December 12-16, 2011 p516
[35] Charles A, Daivis P 2009 18th World IMACS/MODSIM Congress Cairns, Australia July 13-17 2009 p303
[36] Lattanzio J C, Monaghan J J, Pongracic H, Schwarz M P 1986 SIAM J. Sci. Stat. Comp. 7 591
[37] Yang X F, Liu M B 2012 Acta Phys. Sin. 61 224701 (in Chinese) [杨秀峰, 刘谋斌 2012 物理学报 61 224701]
[38] Liu D 2013 Ph. D. Dissertation (Beijing:Tsinghua University) (in Chinese) [刘栋 2013 博士学位论文 (北京:清华大学)]
[39] Menchaca-Rocha A, Martínez-Dávalos A, Núñez R, Popinet S, Zaleski S 2001 Phys. Rev. E 63 046309
[40] Mao T, Kuhn D C S, Tran H 1997 AIChE J 43 2169
[41] Li Y 2008 Master Dissertation ( Dalian:Dalian University of Technology) (in Chinese) [李燕 2008 硕士学位论文 (大连:大连理工大学)]
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[1] Belytschko T, Krongauz Y, Organ D, Fleming M, Krysl P 1996 Comput. Method Appl. M. 139 3
[2] Vinh Phu N, Timon R, Stéphane B, Marc D 2008 Math. Comput. Simulat. 79 763
[3] Cheng R J, Ge H X 2012 Chin. Phys. B 21 040203
[4] Cheng Y M, Li R X, Peng M J 2012 Chin. Phys. B 21 090205
[5] Feng Z, Wang X D, Ouyang J 2013 Chin. Phys. B 22 074704
[6] Chen L, Ma H P, Cheng Y M 2013 Chin. Phys. B 22 050202
[7] Qin Y X, Liu Y Y, Li Z H, Yang M 2014 Chin. Phys. B 23 070207
[8] Weng Y J, Cheng Y M 2013 Chin. Phys. B 22 090204
[9] Xia M H, Li J 2007 Chin. Phys. B 16 3067
[10] Chen L, Cheng Y M 2008 Acta Phys. Sin. 57 6047 (in Chinese) [陈丽, 程玉民 2008 物理学报 57 6047]
[11] Ghou A, Malfreyt P 2011 Phys. Rev. E. 83 051601
[12] Liu X L, Cheng P 2013 Int. J. Heat Mass Tran. 64 1041
[13] Feng S D, Tsutahara M, Ji Z Z 2001 Chin. Phys. B 10 587
[14] Liu M B, Liu G R 2010 Arch. Comput. Method E S. 17 25
[15] Li Q, Cai T M, He G Q, Hu C B 2006 Appl. Math. Mech-Engl. 27 67
[16] Zhang M Y, Zhang H, Zheng L L 2007 Numer. Heat Tr. A-Appl. 52 299
[17] Zhang M Y, Zhang H, Zheng L L 2008 Int. J. Heat Mass Tran. 51 3410
[18] Morris J P 2000 Int. J. Numer. Meth Fl. 33 333
[19] Nugent S, Posch H A 2000 Phys. Rev. E 62 4968
[20] Meleán Y, Sigalotti L D G, Hasmy A 2004 Comput. Phys. Commun. 157 191
[21] Zhou G Z, Wen G, Li J H 2008 Powder Technol. 183 21
[22] Li D M, Wang Z C, Bai L, Wang X 2013 Acta Phys. Sin. 62 194704 (in Chinese) [李大鸣, 王志超, 白玲, 王笑 2013 物理学报 62 194704]
[23] Monaghan J J 2000 J. Comput. Phys. 159 290
[24] López H, Sigalotti L D G 2006 P hys. Rev. E 73 1201
[25] Meleán Y, Sigalotti L D G 2005 Int. J. Heat. Mass. Tran. 48 4041
[26] Fang H S, Bao K, Wei J A, Zhang H, Wu E H, Zheng L L 2009 Numer. Heat Tr. A.-Appl. 55 124
[27] Jiang T, Ouyang J, Yang B, Ren J 2010 Comput. Mech. 45 573
[28] Liu M B, Shao J R, Chang J Z 2012 Sci. China Tech. Sci. 55 244
[29] Tartakovsky A, Meakin P 2005 Phys. Rev. E 72 026301
[30] Shirtcliffe N J, McHale G, Atherton S, Newton M I 2010 Adv Colloid Interfac 161 124
[31] Lafuma A, Quere D 2003 Nat Mater 2 457
[32] Hoover W G 2006 Smooth particle applied mechanics:the state of the art (Singapore:World Scientific) p94
[33] Charles A N 2014 Ph. D. Dissertation (Melbourne, Australia:RMIT University)
[34] Charles A N, Daivis P 2011 19th International Congress on Modelling and Simulation Perth, Australia, December 12-16, 2011 p516
[35] Charles A, Daivis P 2009 18th World IMACS/MODSIM Congress Cairns, Australia July 13-17 2009 p303
[36] Lattanzio J C, Monaghan J J, Pongracic H, Schwarz M P 1986 SIAM J. Sci. Stat. Comp. 7 591
[37] Yang X F, Liu M B 2012 Acta Phys. Sin. 61 224701 (in Chinese) [杨秀峰, 刘谋斌 2012 物理学报 61 224701]
[38] Liu D 2013 Ph. D. Dissertation (Beijing:Tsinghua University) (in Chinese) [刘栋 2013 博士学位论文 (北京:清华大学)]
[39] Menchaca-Rocha A, Martínez-Dávalos A, Núñez R, Popinet S, Zaleski S 2001 Phys. Rev. E 63 046309
[40] Mao T, Kuhn D C S, Tran H 1997 AIChE J 43 2169
[41] Li Y 2008 Master Dissertation ( Dalian:Dalian University of Technology) (in Chinese) [李燕 2008 硕士学位论文 (大连:大连理工大学)]
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