Surface tension coefficient and thickness measurements in planar soap-film flows
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摘要: 在流体力学实验中，平面流动皂膜得到大量应用（如用于模拟两维湍流流动或超声速流动），对皂膜的测量手段也得到了极大发展，但对流动皂膜特性参数的测量尚有可提高之处。本文给出了两根平行弹性线之间在重力驱动下稳定流动的皂膜的表面张力系数及厚度的非接触测量实例。对于表面张力系数测量，针对新近文献中提出的一种基于皂膜边缘的力平衡测量表面张力系数的半经验方法给出了严格推导，并采用两种方法验证了推导结论，证实了该半经验方法的正确性，同时还得出了一种新的、更简便的表面张力系数测量方法；对于皂膜厚度测量，结合传统的皂膜流动速度测量方法（如粒子图像测速法），提出了一种基于单色激光干涉的测量方法，可以通过普通单色相机摄像来获取稳定流动皂膜的厚度剖面。Abstract: Steady planar soap-film flows have been used widely in experimental investigations of fluid mechanics, e.g., as models for two-dimensional flows or supersonic flows. Despite the significant advances in the measurement techniques for soap films over the years, there is still room for improvement, especially for flowing soap films. Here we present two developments in measuring the surface tension coefficient and the film thickness of flowing soap films. For a vertically flowing soap film between two elastic wires, based on the force balance of the boundary wires, we derived an exact solution for the curve shape of the boundary wires. We verified our solution by direct measurement of the wire shape in our flowing soap film. Our exact solution thus provides support to a recently proposed semi-empirical method. Moreover, based on our solution, we proposed a new, easy-to-implement method for measuring the surface tension coefficient of flowing soap films. For film thickness measurement, we proposed a new method based on the interference of the incident light with a single-wavelength. When coupled with a conventional vertical velocity profile measurement, such as particle image velocimetry (PIV), the interference method can provide the film thickness profile using a single monochrome camera.
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图 1 竖直平面流动皂膜实验装置图
Fig. 1 Schematic drawing of the vertical planar soap-film flow experimental device
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图 2 流道边界实测值(红色点)与理论分析(蓝色线)对比
Fig. 2 Comparison of the measured channel boundary (red dots) and the theoretical prediction (blue line)
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图 3 流道中点O在有/无皂膜流动时的位移量随砝码质量的变化
Fig. 3 Horizontal shift of the middle point of the channel with the inverse of the hanging weight: measurements (red stars) vs. theoretical prediction (blue line)
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图 4 表面张力系数随皂液流量的变化
Fig. 4 Change of the surface tension coefficient with the flow rate of the soap film
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图 5 皂膜表面干涉条纹
Fig. 5 Interference fringes produced by a laser beam reflected from the soap-film
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图 6 皂膜横剖面内的光路图
Fig. 6 Incident and reflected laser light paths in a horizontal cross-section of the soap-film
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[1] COHEN C, TEXIER B D, REYSSAT E, et al. On the shape of giant soap bubbles[J]. PNAS, 2017, 114(10):2515-2519. DOI: 10.1073/pnas.1616904114
[2] COUDER Y, CHOMAZ J M, RABAUD M. On the hydrodynamics of soapfilms[J]. Physica D:Nonlinear Phenomena, 1989, 37(1-3):384-405. DOI: 10.1016/0167-2789(89)90144-9
[3] CHOMAZ J M, CATHALAU B. Soap films as two-dimensional classical fluids[J]. Physical Review A (Atomic, Molecular, and Optical Physics), 1990, 41(4):2243-2245. DOI: 10.1103/PhysRevA.41.2243
[4] VOROBIEFF P, ECKE R E. Cylinder wakes in flowing soapfilms[J]. Physical Review E, 1999, 60(3):2953-2956. DOI: 10.1103/PhysRevE.60.2953
[5] ROUSHAN P, WU X L. Universal wake structures ofKármán vortex streets in two-dimensional flows[J]. Physics of Fluids, 2005, 17(7):073601. DOI: 10.1063/1.1943469
[6] KIM I, WU X L. Unified Strouhal-Reynolds number relationship for laminar vortex streets generated by different-shaped obstacles[J]. Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 2015, 92(4):043011. DOI: 10.1103/PhysRevE.92.043011
[7] RUTGERS M A, WU X L, BHAGAVATULA R, et al. Two-dimensional velocity profiles and laminar boundary layers in flowing soap films[J]. Physics of Fluids, 1996, 8(11):2847-2854. DOI: 10.1063/1.869105
[8] PARET J, TABELING P. Intermittency in the two-dimensional inverse cascade of energy:Experiment alobservations[J]. Physics of Fluids, 1998, 10(12):3126-3136. DOI: 10.1063/1.869840
[9] RIVERA M, VOROBIEFF P, ECKE R E. Turbulence in flowing soap films:velocity, vorticity, and thickness fields[J]. Physical Review Letters, 1998, 81(7):1417-1420. DOI: 10.1103/PhysRevLett.81.1417
[10] MARTIN B K, WU X L, GOLDBURG W I, et al. Spectra of decaying turbulence in a soap film[J]. Physical Review Letters, 1998, 80(18):3964-3967. DOI: 10.1103/PhysRevLett.80.3964
[11] VOROBIEFF P, RIVERA M, ECKE R E. Soap film flows:Statistics of two-dimensionalturbulence[J]. Physics of Fluids, 1999, 11(8):2167-2177. DOI: 10.1063/1.870078
[12] RUTGERS M A, WU X L, DANIEL W B. Conducting fluid dynamics experiments with vertically falling soap films[J]. Review of Scientific Instruments, 2001, 72(7):3025-3037. DOI: 10.1063/1.1379956
[13] KELLAY H, GOLDBURG W I. Two-dimensional turbulence:a review of some recentexperiments[J]. Reports on Progress in Physics, 2002, 65(5):845-894. DOI: 10.1088/0034-4885/65/5/204
[14] TABELING P. Two-dimensional turbulence:a physicistapproach[J]. Physics Reports, 2002, 362(1):1-62. DOI: 10.1016/S0370-1573(01)00064-3
[15] RIVERA M K, DANIEL W B, CHEN S Y, et al. Energy andenstrophy transfer in decaying two-dimensional turbulence[J]. Physical Review Letters, 2003, 90(10):104502. DOI: 10.1103/PhysRevLett.90.104502
[16] TRAN T, CHAKRABORTY P, GUTTENBERG N, et al. Macroscopic effects of the spectral structure in turbulent flows[J]. Nature Physics, 2010, 6(6):438-441. DOI: 10.1038/nphys1674
[17] CERBUS R T, GOLDBURG W I. Intermittency in 2D soap film turbulence[J]. Physics of Fluids, 2013, 25(10):105111. DOI: 10.1063/1.4824658
[18] ZHANG J, CHILDRESS S, LIBCHABER A, et al. Flexible filaments in a flowing soap film as a model for one-dimensionalflags in a two-dimensional wind[J]. Nature, 2000, 408(6814):835-839. DOI: 10.1038/35048530
[19] WEN C, LAI J. Analogy between soap film and gas dynamics. I. Equations and shock jumpconditions[J]. Experiments in Fluids, 2003, 34(1):107-114. DOI: 10.1007/s00348-002-0539-z
[20] WEN C Y, CHANG-JIAN S K, CHUANG M C. Analogy between soap film and gas dynamics. II. Experiments on one-dimensional motion of shock waves in soapfilms[J]. Experiments in Fluids, 2003, 34(2):173-180. DOI: 10.1007/s00348-002-0540-6
[21] TRAN T, CHAKRABORTY P, GIOIA G, et al.Marangoni shocks in unobstructed soap-film flows[J]. Physical Review Letters, 2009, 103(10):104501. DOI: 10.1103/PhysRevLett.103.104501
[22] KIM I D, MANDRE S. Marangoni elasticity of flowing soap films[J]. Physical Review Fluids, 2017, 2(8):082001. DOI: 10.1103/PhysRevFluids.2.082001
[23] 杨义红, 尹协振, 陆夕云.肥皂膜水洞实验技术[J].实验流体力学, 2005, 19(4):36-41. DOI: 10.3969/j.issn.1672-9897.2005.04.007 YANG Y H, YIN X Z, LU X Y. Experimental methods in a soap film tunnel[J]. Journal of Experiments in Fluid Mechanics, 2005, 19(4):36-41. DOI: 10.3969/j.issn.1672-9897.2005.04.007
[24] 高宗海, 王思莹, 贾来兵, 等.用于小Re数流动显示研究的水平式肥皂膜水洞[J].实验流体力学, 2009, 23(3):80-84. DOI: 10.3969/j.issn.1672-9897.2009.03.017 GAO Z H, WANG S Y, JIA L B, et al. A horizontal soap film tunnel for studying two-dimensional flow at small Reynolds number[J]. Journal of Experiments in Fluid Mechanics, 2009, 23(3):80-84. DOI: 10.3969/j.issn.1672-9897.2009.03.017
[25] JIA L B, YIN X Z. Passive oscillations of two tandem flexible filaments in a flowing soapfilm[J]. Physical Review Letters, 2008, 100(22):228104. DOI: 10.1103/PhysRevLett.100.228104
[26] 沙勇, 李樟云, 江桂仙, 等.竖直流动皂膜中解吸导致的Marangoni对流观察[J].化工学报, 2010, 61(5):1123-1126. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=hgxb201005009 SHA Y, LI Z Y, JIANG G X, et al. Observation on Marangoni convection induced by desorption in falling soap film[J]. Ciesc Journal, 2010, 61(5):1123-1126. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=hgxb201005009
[27] GAO P, LU X Y. Effect of surfactants on the long-wave stability of oscillatory filmflow[J]. Journal of Fluid Mechanics, 2006, 562:345-354. DOI: 10.1017/S002211200600139X
[28] GAO P, LU X Y. Instability of an oscillatory fluid layer with insolublesurfactants[J]. Journal of Fluid Mechanics, 2008, 595:461-490. DOI: 10.1017/S0022112007009512
[29] 罗喜胜, 王显圣, 陈模军, 等.可控肥皂膜气柱界面与激波相互作用的实验研究[J].实验流体力学, 2014, 28(2):7-13, 26. http://www.syltlx.com/CN/abstract/abstract10711.shtml LUO X S, WANG X S, CHEN M J, et al. Experimental study of shock interacting with well-controlled gas cylinder generated by soap film[J]. Journal of Experiments in Fluid Mechanics, 2014, 28(2):7-13, 26. http://www.syltlx.com/CN/abstract/abstract10711.shtml
[30] WU X L, LEVINE R, RUTGERS M, et al. Infrared technique for measuring thickness of a flowing soap film[J]. Review of Scientific Instruments, 2001, 72(5):2467-2471. DOI: 10.1063/1.1366634
[31] DE GENNES P G, BROCHARD-WYART F, QUERE D. Capillarity and wetting phenomena:drops, bubbles, pearls, waves[M]. Berlin:Springer, 2004.
[32] DRELICH J, FANG C, WHITE C L. Measurement of interfacial tension in fluid-fluid systems[M]//Somasundaran P. Encyclopedia of Surface and Colloid Science. 3rd ed. New York: Marcel Dekker Inc, 2002.
[33] WAN D M, XIANG H S, XU H T. A laminar-jet-discharging method for measuring the interfacial tension of deformablesurfaces[J]. Measurement Science and Technology, 2020, 31(3):035302. DOI: 10.1088/1361-6501/ab5b1e
[34] SANE A, MANDRE S, KIM I D. Surface tension of flowing soap films[J]. Journal of Fluid Mechanics, 2018, 841:R2. DOI: 10.1017/jfm.2018.28
[35] LIANG N Y, CHAN C K. Fast thickness profile measurement of a thin film by using a line scan charge coupled device camera[J]. Review of Scientific Instruments, 1997, 68(12):4525-4530. DOI: 10.1063/1.1148425
[36] SEIWERT J, KERVIL R, NOU S, et al. Velocity field in a vertical foamfilm[J]. Physical Review Letters, 2017, 118(4):048001. DOI: 10.1103/PhysRevLett.118.048001
[37] ZHANG J, WU X L, RASHIDNIA N. Thermal radiation and thickness fluctuations in freely suspended liquid films[J]. Physics of Fluids, 2006, 18(8):085110. DOI: 10.1063/1.2337997
[38] OUELLETTE N T, XU H T, BODENSCHATZ E. A quantitative study of three-dimensionalLagrangian particle tracking algorithms[J]. Experiments in Fluids, 2006, 40(2):301-313. DOI: 10.1007/s00348-005-0068-7
[39] 姚启钧原著, 华东师大光学教材编写组改编.光学教程[M]. 5版.北京: 高等教育出版社, 2014.
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