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In this work, the dynamical collision process between two miscible/immiscible micro-droplets is simulated by a modified smoothed particle hydrodynamics (C-SPH) method. In order to improve the numerical accuracy and stability of traditional SPH method, a kernel gradient modified scheme without kernel derivative is considered. Meanwhile, an improved surface tension technique based on the van der Waals model is adopted to deal with the moving interface. The reliability of C-SPH method of simulating the deformation process between two droplet collisions is tested through the numerical simulations of coalescence process between two miscible Newtonian droplet collisions. Subsequently, the coalescence process of miscible polymer droplet collision and the deformation process of bouncing and separation between two immiscible droplet collisions are investigated, in which the control equations of droplets are all based on the van der Waals model. The influences of the collision velocity, collision angle and the density ratio on the deformation process of collision are discussed, and the changes of liquid bridge and rotation angle are analyzed.
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Keywords:
- smoothed partical hydrodynamics /
- micro-droplet /
- polymer droplet /
- collision
[1] Pan Y, Suga K 2005 Phys. Fluids 17 082105
[2] Chang J Z, Liu M B, Liu H T 2008 Acta Phys. Sin. 57 3954 (in Chinese) [常建忠, 刘谋斌, 刘汉涛 2008 物理学报 57 3954]
[3] Willis K D, Orme M E 2000 Experim. Fluids 29 347
[4] Mashayek F, Ashgriz N, Minkowycz W J, Shotorban B 2003 Int. J. Heat Mass Transfer 46 77
[5] Bach G A, Koch D L, Gopinath A 2004 J. Fluid Mech. 518 157
[6] Chen R H, Chen C T 2006 Experim. Fluids 41 453
[7] Gao T C, Chen R H, Pu J Y, Lin T H 2005 Experim. Fluids 38 731
[8] Lyu S P, Bates F S, Macosko C W 2002 Fluid Mech. Transport Phenomena 48 7
[9] Eggers J, Lister J, Stone H A 1999 J. Fluid Mech. 401 293
[10] Yao W, Maris H J, Pennington P, Seidel G M 2005 Phys. Rev. E 71 016309
[11] Dai M Z, Schmidt D P 2005 Phys. Fluids 17 041701
[12] Qian J, Law C K 1997 J. Fluid Mech. 331 59
[13] Jiang X, James A J 2007 J. Engineer. Math. 59 99
[14] Motzigemba M, Roth N, Bothe D, Warnecke H J, Pruss J, Wielage K, Weigand B 2002 Proceedings of the 18th Annual Conference Liquid Atomization Spray Systems (ILASS Europe) Zaragoza, Spain September 9–11, 2002 p559
[15] Ashgriz N 2011 Handbook of Atomization and Sprays Theory and Applications (New York: Springer) p157
[16] Zhao Y, Ji Z Z, Feng T 2004 Acta Phys. Sin. 53 671 (in Chinese) [赵颖, 季仲贞, 冯涛 2004 物理学报 53 671]
[17] Zhong C W, Xie J F, Zhuo C S, Xiong S W, Yin D C 2009 Chin. Phys. B 18 4083
[18] Wang J F, Sun F X, Cheng R J 2010 Chin. Phys. B 19 060201
[19] Cheng R J, Cheng Y M, Ge H X 2009 Chin. Phys. B 18 4059
[20] Liu G R, Liu M B 2003 Smoothed Particle Hydrodynamics: A Mesh-free Particle Method (Singapore: World Scientific)
[21] Monaghan J J 1994 J. Comp. Phys. 110 399
[22] Nugent S, Posch H A 2000 Phys. Rev. E 62 4968
[23] Hu X Y, Adams N A 2006 J. Comp. Phys. 213 844
[24] Ellero M, Kröger M, Hess S 2002 J. Non-Newtonian Fluid Mech. 105 35
[25] Fang J, Owens R G, Tacher L, Parriaux A 2006 J. Non-Newtonian Fluid Mech. 13 68
[26] Liu M B, Chang J Z 2010 Acta Phys. Sin. 59 3654 (in Chinese) [刘谋斌, 常建忠 2010 物理学报 59 3654]
[27] Chen J K, Beraun J E 2000 Comp. Meth. Appl. Mech. Eng. 190 225
[28] Yang X Y, Liu M B 2012 Acta Phys. Sin. 61 224701 (in Chinese) [杨秀峰, 刘谋斌 2012 物理学报 61 224701]
[29] Jiang T, Ouyang J, Li X J, Zhang L, Ren J L 2011 Acta Phys. Sin. 60 096206 (in Chinese) [蒋涛, 欧阳洁, 栗雪娟, 张林, 任金莲2011 物理学报 60 096206]
[30] Liu M B, Xie W P, Liu G R 2005 Appl. Math. Model. 29 1252
[31] Jiang T, Ouyang J, Zhao X K, Ren J L 2011 Acta Phys. Sin. 60 054701 (in Chinese) [蒋涛, 欧阳洁, 赵晓凯, 任金莲2011 物理学报 60 054701]
[32] Lopez H, Sigalotti L D G 2006 Phys. Rev. E 73 051201-1
[33] Hopper R W 1990 J. Fluid Mech. 213 349
[34] Jiang Y J, Umemura A, Law C K 1992 J. Fluid Mech. 234 171
[35] Qian J, Law C K 1997 J. Fluid Mech. 331 59
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[1] Pan Y, Suga K 2005 Phys. Fluids 17 082105
[2] Chang J Z, Liu M B, Liu H T 2008 Acta Phys. Sin. 57 3954 (in Chinese) [常建忠, 刘谋斌, 刘汉涛 2008 物理学报 57 3954]
[3] Willis K D, Orme M E 2000 Experim. Fluids 29 347
[4] Mashayek F, Ashgriz N, Minkowycz W J, Shotorban B 2003 Int. J. Heat Mass Transfer 46 77
[5] Bach G A, Koch D L, Gopinath A 2004 J. Fluid Mech. 518 157
[6] Chen R H, Chen C T 2006 Experim. Fluids 41 453
[7] Gao T C, Chen R H, Pu J Y, Lin T H 2005 Experim. Fluids 38 731
[8] Lyu S P, Bates F S, Macosko C W 2002 Fluid Mech. Transport Phenomena 48 7
[9] Eggers J, Lister J, Stone H A 1999 J. Fluid Mech. 401 293
[10] Yao W, Maris H J, Pennington P, Seidel G M 2005 Phys. Rev. E 71 016309
[11] Dai M Z, Schmidt D P 2005 Phys. Fluids 17 041701
[12] Qian J, Law C K 1997 J. Fluid Mech. 331 59
[13] Jiang X, James A J 2007 J. Engineer. Math. 59 99
[14] Motzigemba M, Roth N, Bothe D, Warnecke H J, Pruss J, Wielage K, Weigand B 2002 Proceedings of the 18th Annual Conference Liquid Atomization Spray Systems (ILASS Europe) Zaragoza, Spain September 9–11, 2002 p559
[15] Ashgriz N 2011 Handbook of Atomization and Sprays Theory and Applications (New York: Springer) p157
[16] Zhao Y, Ji Z Z, Feng T 2004 Acta Phys. Sin. 53 671 (in Chinese) [赵颖, 季仲贞, 冯涛 2004 物理学报 53 671]
[17] Zhong C W, Xie J F, Zhuo C S, Xiong S W, Yin D C 2009 Chin. Phys. B 18 4083
[18] Wang J F, Sun F X, Cheng R J 2010 Chin. Phys. B 19 060201
[19] Cheng R J, Cheng Y M, Ge H X 2009 Chin. Phys. B 18 4059
[20] Liu G R, Liu M B 2003 Smoothed Particle Hydrodynamics: A Mesh-free Particle Method (Singapore: World Scientific)
[21] Monaghan J J 1994 J. Comp. Phys. 110 399
[22] Nugent S, Posch H A 2000 Phys. Rev. E 62 4968
[23] Hu X Y, Adams N A 2006 J. Comp. Phys. 213 844
[24] Ellero M, Kröger M, Hess S 2002 J. Non-Newtonian Fluid Mech. 105 35
[25] Fang J, Owens R G, Tacher L, Parriaux A 2006 J. Non-Newtonian Fluid Mech. 13 68
[26] Liu M B, Chang J Z 2010 Acta Phys. Sin. 59 3654 (in Chinese) [刘谋斌, 常建忠 2010 物理学报 59 3654]
[27] Chen J K, Beraun J E 2000 Comp. Meth. Appl. Mech. Eng. 190 225
[28] Yang X Y, Liu M B 2012 Acta Phys. Sin. 61 224701 (in Chinese) [杨秀峰, 刘谋斌 2012 物理学报 61 224701]
[29] Jiang T, Ouyang J, Li X J, Zhang L, Ren J L 2011 Acta Phys. Sin. 60 096206 (in Chinese) [蒋涛, 欧阳洁, 栗雪娟, 张林, 任金莲2011 物理学报 60 096206]
[30] Liu M B, Xie W P, Liu G R 2005 Appl. Math. Model. 29 1252
[31] Jiang T, Ouyang J, Zhao X K, Ren J L 2011 Acta Phys. Sin. 60 054701 (in Chinese) [蒋涛, 欧阳洁, 赵晓凯, 任金莲2011 物理学报 60 054701]
[32] Lopez H, Sigalotti L D G 2006 Phys. Rev. E 73 051201-1
[33] Hopper R W 1990 J. Fluid Mech. 213 349
[34] Jiang Y J, Umemura A, Law C K 1992 J. Fluid Mech. 234 171
[35] Qian J, Law C K 1997 J. Fluid Mech. 331 59
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