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微重力条件下内角处液体行为的研究对于认识表面张力主导的液体行为, 预测和控制空间微重力条件下的液体位置、瞬时状态, 以及对空间流体进行有效的管理等方面都非常重要. 通过分析接触角与流体界面在容器内角处的接触线方向之间的关系, 并与Concus-Finn理论进行比较, 提出了内角处接触线、接触角和几何形状之间相互关联的机理, 并探讨了Concus和Finn等 的相关理论结果的物理内涵. 在此基础上, 进一步将内角处的相关理论结果与Surface Evolver程序得出的数值结果进行了比较, 指出当容器中的内角小于180°时, Surface Evolver程序通过自动划分网格即可比较准确地预言内角处的接触线和液面行为, 但是当内角大于180°时, 自动划分网格得到的数值结果有较大的误差, 需要通过手动划分网格减少网格奇异才能减小误差. 因此, 对于具有复杂几何形状的容器, 需注意网格的奇异性, 并对内角处的液面进行定量的验证, 才能有效判断Surface Evolver程序结果的正确性. 本工作对于深入认识内角处的液面特性和机理, 理解Surface Evolver程序的适用条件, 以及分析微重力条件下容器内角处的液体行为等方面都具有明显意义.
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关键词:
- 接触线 /
- 接触角 /
- 内角 /
- Surface Evolver
The study on the fluid behavior under microgravity condition is of great importance for the investigation of the fluid behavior caused by surface tension, the prediction and control of the liquid location at microgravity, the fluid management in space, etc. In this study, we analyze the relationship between the contact angle and the direction of the contact line in interior corner of container, and compare it with the Concus-Finn theory. The mechanism of mutual correlation among the direction of contact line, the contact angle and the geometric shape of container, and the physical meaning of relevant theory by Concus and Finn etc. are also analyzed. By comparing the theoretical results with the numerical results calculated by Surface Evolver, we find that the Surface Evolver program can predict the contact line and the liquid surface in interior corner with angle smaller than 180°, simply by the automatically partitioned grid. However, when the angle of the interior corner is larger than 180°, the results given by Surface Evolver can have a remarkable error with the automatically partitioned grid. In order to reduce the error, it is necessary to manually partition the surface to reduce the singularity of grid. And the results from Surface Evolver should be tested quantitatively at the interior corners for complicated containers. The theoretical analysis and the numerical results calculated by Surface Evolver in this study will be helpful for understanding the characteristics and mechanism of liquid surface in interior corner, choosing the applicable parameters for Surface Evolver program, and the future study on the behavior of liquid in interior corner, especially under microgravity condition.-
Keywords:
- contact line /
- contact angle /
- interior corner /
- Surface Evolver
[1] Ostrach S 1982 Ann. Rev. Fluid Mech. 14 313
[2] Stange M, Dreyer M E, Rath H J 2003 Phys. Fluids 15 2587
[3] Finn R 1999 Not. AMS 46 770
[4] Young T 1805 Philos. Trans. R. Soc. London 95 65
[5] Liu Y X, German R M 1996 Acta Mater. 44 1657
[6] Wang C X, Xu S H, Sun Z W, Hu W R 2010 AIAA J. 47 2642
[7] Weislogel M M, Lichter S 1998 J. Fluid Mech. 373 349
[8] Chen Y K, Collicott S H 2004 AIAA J. 42 305
[9] Bolleddula D A, Chen Y K, Semerjian B, Weislogel M M 2010 Microgravity Sci. Technol. 22 475
[10] Concus P, Finn R 1969 Appl. Math. Sci. 63 292
[11] Concus P, Finn R 1974 Acta Math. 132 177
[12] Simon L 1980 Pacific J. Math. 88 363
[13] Tam L F 1986 Pacific J. Math. 124 469
[14] Shi D Z 2006 Pacific J. Math. 224 321
[15] Lancaster K, Athanassenas M 2008 Pacific J. Math. 234 201
[16] Wang C X, Xu S H, Sun Z W, Hu W R 2010 Int. J. Heat Mass Transer 53 1801
[17] Concus P, Finn R, Weislogel M 2000 Exp. Fluids 28 197
[18] Xu S H, Wang C X, Sun Z W, Hu W R 2011 Int. J. Heat Mass Transfer 54 2222
[19] Brakke K A 1992 Exp. Math. 1 141
[20] Huang J, Sun Q C 2007 Acta Phys. Sin. 56 6124 (in Chinese) [黄晋, 孙其诚 2007 物理学报 56 6124]
[21] Zhou X H, Zhang S G, Yang J Q, Qu X M, Liu Y S, Wang S G 2007 Acta Phys. Sin. 56 6137 (in Chinese) [周晓华, 张劭光,杨继庆,屈学民, 刘渊声,王斯刚 2007 物理学报 56 6137]
[22] Wearire D, Mcuurry S 1996 Solid State Phys. 50 1
[23] Zhou X H 2010 Chin. Phys. B 19 058702
[24] Brakke K A 1996 Philos. Trans. R. Soc. A 354 2143
[25] Weislogel M M, Jenson R, Chen Y K, Collicott S H, Klatte J, Dreyer M 2009 Acta Astronat. 65 861
[26] Kamali M E, Schotté J S, Ohayon R 2010 Comput. Mech. 46 169
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[1] Ostrach S 1982 Ann. Rev. Fluid Mech. 14 313
[2] Stange M, Dreyer M E, Rath H J 2003 Phys. Fluids 15 2587
[3] Finn R 1999 Not. AMS 46 770
[4] Young T 1805 Philos. Trans. R. Soc. London 95 65
[5] Liu Y X, German R M 1996 Acta Mater. 44 1657
[6] Wang C X, Xu S H, Sun Z W, Hu W R 2010 AIAA J. 47 2642
[7] Weislogel M M, Lichter S 1998 J. Fluid Mech. 373 349
[8] Chen Y K, Collicott S H 2004 AIAA J. 42 305
[9] Bolleddula D A, Chen Y K, Semerjian B, Weislogel M M 2010 Microgravity Sci. Technol. 22 475
[10] Concus P, Finn R 1969 Appl. Math. Sci. 63 292
[11] Concus P, Finn R 1974 Acta Math. 132 177
[12] Simon L 1980 Pacific J. Math. 88 363
[13] Tam L F 1986 Pacific J. Math. 124 469
[14] Shi D Z 2006 Pacific J. Math. 224 321
[15] Lancaster K, Athanassenas M 2008 Pacific J. Math. 234 201
[16] Wang C X, Xu S H, Sun Z W, Hu W R 2010 Int. J. Heat Mass Transer 53 1801
[17] Concus P, Finn R, Weislogel M 2000 Exp. Fluids 28 197
[18] Xu S H, Wang C X, Sun Z W, Hu W R 2011 Int. J. Heat Mass Transfer 54 2222
[19] Brakke K A 1992 Exp. Math. 1 141
[20] Huang J, Sun Q C 2007 Acta Phys. Sin. 56 6124 (in Chinese) [黄晋, 孙其诚 2007 物理学报 56 6124]
[21] Zhou X H, Zhang S G, Yang J Q, Qu X M, Liu Y S, Wang S G 2007 Acta Phys. Sin. 56 6137 (in Chinese) [周晓华, 张劭光,杨继庆,屈学民, 刘渊声,王斯刚 2007 物理学报 56 6137]
[22] Wearire D, Mcuurry S 1996 Solid State Phys. 50 1
[23] Zhou X H 2010 Chin. Phys. B 19 058702
[24] Brakke K A 1996 Philos. Trans. R. Soc. A 354 2143
[25] Weislogel M M, Jenson R, Chen Y K, Collicott S H, Klatte J, Dreyer M 2009 Acta Astronat. 65 861
[26] Kamali M E, Schotté J S, Ohayon R 2010 Comput. Mech. 46 169
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