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Droplet impact on a solid surface is ubiquitous in daily life and various engineering fields such as ink-jet printing and surface coating. Most of existing studies focused on the droplet impact on flat or convex surface whereas the droplet impact on a concave surface has been less investigated. The purpose of this paper is to investigate the dynamic process of droplet impact on the inner surface of a cylinder numerically by using the phase-field-based lattice Boltzmann method. This method combines the finite-difference solution of the Cahn-Hilliard equation to capture the interface dynamics and the lattice Boltzmann method for the hydrodynamics of the flow. Besides, a recently proposed method is employed to deal with the wetting boundary condition on the curved wall. The method is first verified through the study of the equilibrium contact angle of a droplet on the inner surface of a cylinder and the droplet impact on a thin film, for which good agreement is obtained with theoretical results or other numerical solutions in the literature. Then, different droplet impact velocity, initial height of the droplet, surface wettability and radius of the cylinder are considered for the main problem and their effects on the evolution of the droplet shape are investigated. The physical properties of the droplet including the density and viscosity are also varied to assess their effects on the impact outcome. It is found that the impact Weber number, the liquid/gas density and dynamic viscosity ratios, the wettability of the inner surface of the cylinder, and the radius of the cylinder may have significant effects on the deformation and spreading of the droplet. At low Weber numbers, when the density and dynamic viscosity ratios are sufficiently high, their variations have little effect on the droplet impact process. At high Weber numbers, changes of these two ratios have more noticeable effects. When the Weber number is high enough, droplet splashing appears. When the density and dynamic viscosity ratios are high, the initial height of the droplet only has a minor effect on the impact results. The increment of the cylinder radius not only increases the maximum spreading radius but also enlarges the oscillation period of the droplet after its impact. Rebound of the droplet may be observed when the contact angle of the inner surface of the cylinder is large enough. Besides, the gravity force is found to suppress the oscillation of the droplet on the cylinder's inner surface. This work may broaden our understanding of the droplet impact on curved surfaces.
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Keywords:
- phase-field /
- lattice Boltzmann method /
- spreading radius /
- droplet splitting
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[19] Huang J J, Huang H B, Wang X Z 2015 Int. J. Numer. Meth. Fluids 77 123
[20] Gao Y J, Jiang H Q, Li J J, Zhao Y Y, Hu J C, Chang Y H 2017 Acta Phys. Sin. 66 024702 (in Chinese) [高亚军, 姜汉桥, 李俊键, 赵玉云, 胡锦川, 常元昊 2017 物理学报 66 024702]
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[23] Wen B H, Zhang C Y, Fang H P 2017 Sci. Sin.: Phys. Mech. Astron. 47 070012 (in Chinese) [闻炳海, 张超英, 方海平 2017 中国科学: 物理学 力学 天文学 47 070012]
[24] Shao J Y, Shu C, Huang H B, Chew Y T 2014 Phys. Rev. E 89 033309
[25] Prosperetti A 1981 Phys. Fluids 24 1217
[26] Liu Y, Tan P, Xu L 2015 PNAS 112 3280
[27] Yue P, Zhou C, Feng J J 2007 J. Comput. Phys. 223 1
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[1] Guo Y X, Liu Y Z, Dong W, Lei G L, Zhu J J 2016 Acta Aerodyn. Sin. 34 573 (in Chinese) [郭宇翔, 刘荫泽, 董威, 雷桂林, 朱剑鋆 2016 空气动力学报 34 573]
[2] Liu Q Z, Kou Z M, Han Z N, Gao G J 2013 Acta Phys. Sin. 62 234701 (in Chinese) [刘邱祖, 寇子明, 韩振南, 高贵军 2013 物理学报 62 234701]
[3] Han F H, Zhang C M, Wang Y X 1995 J. Beijing Univ. Aeron. Astron. 21 16 (in Chinese) [韩凤华, 张朝民, 王跃欣 1995 北京航空航天大学学报 21 16]
[4] Li W Z, Zhu W Y, Quan S L, Jiang Y X 2008 J. Therm. Sci. Technol. 7 155 (in Chinese) [李维仲, 朱卫英, 权生林, 姜远新 2008 热科学与技术 7 155]
[5] Fan Y 2016 M. S. Thesis (Chongqing: University of Chongqing) (in Chinese) [范瑶 2016 硕士学位论文 (重庆: 重庆大学)]
[6] Wang Y E, Zhou J H, Qin Y L, Li P L, Yang M M, Han Q, Wang Y B, Wei S M 2012 J. Vib. Shock 31 51 (in Chinese) [汪焰恩, 周金华, 秦琰磊, 李鹏林, 杨明明, 韩琴, 王月波, 魏生民 2012 振动与冲击 31 51]
[7] Li Y P, Wang H R 2009 J. Xi'an Jiaotong Univ. 43 21 (in Chinese) [李彦鹏, 王焕然 2009 西安交通大学学报 43 21]
[8] Huang J J, Wu J, Huang H 2018 Eur. Phys. J. E 41 17
[9] Shen S Q, Bi F F, Guo Y L 2012 Int. J. Heat Mass Tran. 55 6938
[10] Song Y C, Ning Z, Sun C H, L M, Yan K, Fu J 2013 T. CSICE 31 531 (in Chinese) [宋云超, 宁智, 孙春华, 吕明, 阎凯, 付娟 2013 内燃机学报 31 531]
[11] Zheng Z W, Li D S, Qiu X Q, Zhu X L, Cui Y J 2015 CIESC J. 66 1667 (in Chinese) [郑志伟, 李大树, 仇性启, 朱晓丽, 崔运静 2015 化工学报 66 1667]
[12] Ling J 2016 M. S. Thesis (Dalian: Dalian University of Technology) (in Chinese) [凌俊 2016 硕士学位论文 (大连: 大连理工大学)]
[13] Huang J J, Huang H B, Shu C, Chew Y T, Wang S L 2013 J. Phys. A: Math. Theor. 46 55501
[14] Lee T 2009 Compu. Math. Appl. 58 987
[15] Lee T, Liu L 2010 J. Comput. Phys. 229 8045
[16] Lallemand P, Luo L S 2000 Phys. Rev. E 61 6546
[17] Lee H G, Kim J 2011 Comput. Fluids 44 178
[18] Ding H, Spelt P D M 2007 Phys. Rev. E 75 046708
[19] Huang J J, Huang H B, Wang X Z 2015 Int. J. Numer. Meth. Fluids 77 123
[20] Gao Y J, Jiang H Q, Li J J, Zhao Y Y, Hu J C, Chang Y H 2017 Acta Phys. Sin. 66 024702 (in Chinese) [高亚军, 姜汉桥, 李俊键, 赵玉云, 胡锦川, 常元昊 2017 物理学报 66 024702]
[21] Shen S Q, Yu H, Guo Y L, Liang G T 2013 J. Therm. Sci. Technol. 12 20 (in Chinese) [沈胜强, 于欢, 郭亚丽, 梁刚涛 2013 热科学与技术 12 20]
[22] Yue P T, Zhou C F, Feng J J 2010 J. Fluid Mech. 645 279
[23] Wen B H, Zhang C Y, Fang H P 2017 Sci. Sin.: Phys. Mech. Astron. 47 070012 (in Chinese) [闻炳海, 张超英, 方海平 2017 中国科学: 物理学 力学 天文学 47 070012]
[24] Shao J Y, Shu C, Huang H B, Chew Y T 2014 Phys. Rev. E 89 033309
[25] Prosperetti A 1981 Phys. Fluids 24 1217
[26] Liu Y, Tan P, Xu L 2015 PNAS 112 3280
[27] Yue P, Zhou C, Feng J J 2007 J. Comput. Phys. 223 1
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