液体表面的光学效应及其应用
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摘要
与体相相比，液体表面无论在组成、结构、分子所处的能量状态，以及受力情况等方面都有差别，这些差别使得液体表面具有某些特殊的性质，通过研究这些特性，可以获得液体的某些参数。
光学方法是研究物质性质的重要手段，通过研究光在液体表面的衍射、反射、折射等行为，可以测量液体的某些参数。该方法广泛应用于流体力学，海洋光学等领域。本文运用光学手段研究液体表面：一方面研究动态液体表面，即利用液体表面波对光的衍射效应，根据衍射光强分布与液体表面波的关系，研究液体表面张力、表面相、表面共振等物理特性；另一方面研究静态液体表面，即利用静态液面对光的反射和透射，根据反射光和透射光的光强分布，研究润湿效应、表面张力等表面性质以及折射率和浓度等液体性质。
通过研究，得到以下新的实验现象和结论：
1．在低频液体表面声波的研究中，不但观察到了表面波的衍射效应，而且得到了几乎100％的衍射效率；并运用傅立叶光学理论给出了解释。
2．当光束倾斜入射在平静的液体表面上时，在液体表面观察到一个环形暗场。运用几何光学理论对此现象的形成机理进行了分析；同时确定了环形暗场半径与液体介质折射率之间的定量关系。基于这一发现，建立了一种测量液体折射率的新方法。另外，又根据溶液浓度与其折射率之间存在的定量关系，提出了通过测量溶液折射率间接测量溶液浓度的新方法。
3．由于液体与固体之间的润湿效应，液体表面出现局域弯曲：当液体与固体之间润湿时，液面向上弯曲；当液体与固体之间非润湿时，液面向下弯曲。实验发现：当强度均匀分布的平行入射光束照射到局域弯曲的液面上时，其反射光场的光强分布出现不均匀的现象：对上弯液面，反射光场为均匀分布的亮场中心出现了近似椭圆形的暗场，并且在暗场的边缘，出现衍射条纹和干涉条纹；对下弯液面，反射光场为均匀分布的亮场中心出现了强度分布不均匀的星形亮场，并且星形亮场的边缘也有条纹出现；当采用不同的固体棒或液体时，椭圆形暗场和星形亮场分布的大小不同。进一步研究发现，椭圆形暗场的大小与液体的表面张力有关，对同一固体棒，表面张力大的液体形成的椭圆形暗场的面
积大。利用这一现象，提出了用光学方法测量液体的表面张力。基于杨一拉普
拉斯（Yong－Laplace）方程，推导出了本次实验条件下杨一拉普拉斯方程的具
体形式，并用数值积分方法求解得出了弯曲液面的曲线方程，最后把数值解与
实验测量结果进行了对比分析。
基于液体表面光学特性的研究，再结合现代电子和计算机技术，建立了液体
参数的测量技术，为液体表面张力、折射率、溶液浓度的测量提供了光学无损。
智能化的测量方法。这些测量技术具有精度高、不受人为主观因素干扰、软件重
构性强、相关仪器易于升级等优点。
Compared with the bulk, the liquid surface has much difference in composition, structure, force, energy state, and so on. It is the difference that makes the liquid surface take on some characteristics. One can obtain some parameters of liquid by means of researching them.
Optical method is an important technique to detect the substance properties. Of course, this method is a good choice for the surface research as well. When the optical effects, including diffraction, reflection, refraction, occur on the liquid surface, many fantastic phenomena will emerge, which may be used to measure some parameters of liquid, such as surface tension, contact angle, refraction index, consistence, and so on. Therefore, optical methods have been adopted extensively in many fields, for example, Fluid Mechanics, Ocean Optics.
In this thesis, we studied liquid surface using optical methods: When a capillary wave propagating along the air-liquid interface, a grating will form on the surface under certain condition. When a collimated-beam illuminated upon the liquid surface, diffraction patterns may be observed. Based on the relationship between the distribution of diffraction intensity and the surface wave, we can study the liquid properties. On the other hand, we also investigated the static liquid surface. In principle, the distribution of the reflection or refraction intensity relates to the shapes of the liquid surface, so the liquid properties can be studied by means of analyzing the distribution. In our research, the major phenomena and conclusions were obtained as follows:
1. The high visibility diffraction patterns were observed experimentally in the case of the Low-Frequency Liquid Surface Acoustic Wave (LFLSAW). Furthermore, the disappearance of zero-order diffraction was obtained, which was corresponding to the 100% diffraction efficiency. The phenomena were explained very well using the theory of Fourier Optics.
2. When a light beam illuminated upon the static liquid surface, a dark ring appeared on the surface, which was named the Effect of Light-Obstructed in the thesis. The mechanism of the phenomenon was discussed using the theory of Geometrical Optics. In addition, the relationship between the radius of dark ring and the refraction index of liquid was derived. Based on the discovery and our analysis, a new method was established to measure the refraction index of transparence liquid.
ill
Furthermore, owing to the quantitative correspondence relationship between the consistence and its refraction index, the consistence of solution was also measured by this method.
3. When a needle was inserted into a liquid, a symmetric meniscus appeared around the needle, that is to say, a local-curved surface formed on the liquid surface, which was caused by the effect of the liquid wetting the needle. An ellipse-shape dark area or a star-shape bright area was formed on the observation plane, when a collimated-beam illuminated upon the symmetric meniscus surface. The phenomena were explained using the critical reflection on the local-curved liquid surface. The approximate curve of the symmetric meniscus was obtained by means of the numerical integrating the Young-Laplace Equation.
光学方法是研究物质性质的重要手段，通过研究光在液体表面的衍射、反射、折射等行为，可以测量液体的某些参数。该方法广泛应用于流体力学，海洋光学等领域。本文运用光学手段研究液体表面：一方面研究动态液体表面，即利用液体表面波对光的衍射效应，根据衍射光强分布与液体表面波的关系，研究液体表面张力、表面相、表面共振等物理特性；另一方面研究静态液体表面，即利用静态液面对光的反射和透射，根据反射光和透射光的光强分布，研究润湿效应、表面张力等表面性质以及折射率和浓度等液体性质。
通过研究，得到以下新的实验现象和结论：
1．在低频液体表面声波的研究中，不但观察到了表面波的衍射效应，而且得到了几乎100％的衍射效率；并运用傅立叶光学理论给出了解释。
2．当光束倾斜入射在平静的液体表面上时，在液体表面观察到一个环形暗场。运用几何光学理论对此现象的形成机理进行了分析；同时确定了环形暗场半径与液体介质折射率之间的定量关系。基于这一发现，建立了一种测量液体折射率的新方法。另外，又根据溶液浓度与其折射率之间存在的定量关系，提出了通过测量溶液折射率间接测量溶液浓度的新方法。
3．由于液体与固体之间的润湿效应，液体表面出现局域弯曲：当液体与固体之间润湿时，液面向上弯曲；当液体与固体之间非润湿时，液面向下弯曲。实验发现：当强度均匀分布的平行入射光束照射到局域弯曲的液面上时，其反射光场的光强分布出现不均匀的现象：对上弯液面，反射光场为均匀分布的亮场中心出现了近似椭圆形的暗场，并且在暗场的边缘，出现衍射条纹和干涉条纹；对下弯液面，反射光场为均匀分布的亮场中心出现了强度分布不均匀的星形亮场，并且星形亮场的边缘也有条纹出现；当采用不同的固体棒或液体时，椭圆形暗场和星形亮场分布的大小不同。进一步研究发现，椭圆形暗场的大小与液体的表面张力有关，对同一固体棒，表面张力大的液体形成的椭圆形暗场的面
积大。利用这一现象，提出了用光学方法测量液体的表面张力。基于杨一拉普
拉斯（Yong－Laplace）方程，推导出了本次实验条件下杨一拉普拉斯方程的具
体形式，并用数值积分方法求解得出了弯曲液面的曲线方程，最后把数值解与
实验测量结果进行了对比分析。
基于液体表面光学特性的研究，再结合现代电子和计算机技术，建立了液体
参数的测量技术，为液体表面张力、折射率、溶液浓度的测量提供了光学无损。
智能化的测量方法。这些测量技术具有精度高、不受人为主观因素干扰、软件重
构性强、相关仪器易于升级等优点。
Compared with the bulk, the liquid surface has much difference in composition, structure, force, energy state, and so on. It is the difference that makes the liquid surface take on some characteristics. One can obtain some parameters of liquid by means of researching them.
Optical method is an important technique to detect the substance properties. Of course, this method is a good choice for the surface research as well. When the optical effects, including diffraction, reflection, refraction, occur on the liquid surface, many fantastic phenomena will emerge, which may be used to measure some parameters of liquid, such as surface tension, contact angle, refraction index, consistence, and so on. Therefore, optical methods have been adopted extensively in many fields, for example, Fluid Mechanics, Ocean Optics.
In this thesis, we studied liquid surface using optical methods: When a capillary wave propagating along the air-liquid interface, a grating will form on the surface under certain condition. When a collimated-beam illuminated upon the liquid surface, diffraction patterns may be observed. Based on the relationship between the distribution of diffraction intensity and the surface wave, we can study the liquid properties. On the other hand, we also investigated the static liquid surface. In principle, the distribution of the reflection or refraction intensity relates to the shapes of the liquid surface, so the liquid properties can be studied by means of analyzing the distribution. In our research, the major phenomena and conclusions were obtained as follows:
1. The high visibility diffraction patterns were observed experimentally in the case of the Low-Frequency Liquid Surface Acoustic Wave (LFLSAW). Furthermore, the disappearance of zero-order diffraction was obtained, which was corresponding to the 100% diffraction efficiency. The phenomena were explained very well using the theory of Fourier Optics.
2. When a light beam illuminated upon the static liquid surface, a dark ring appeared on the surface, which was named the Effect of Light-Obstructed in the thesis. The mechanism of the phenomenon was discussed using the theory of Geometrical Optics. In addition, the relationship between the radius of dark ring and the refraction index of liquid was derived. Based on the discovery and our analysis, a new method was established to measure the refraction index of transparence liquid.
ill
Furthermore, owing to the quantitative correspondence relationship between the consistence and its refraction index, the consistence of solution was also measured by this method.
3. When a needle was inserted into a liquid, a symmetric meniscus appeared around the needle, that is to say, a local-curved surface formed on the liquid surface, which was caused by the effect of the liquid wetting the needle. An ellipse-shape dark area or a star-shape bright area was formed on the observation plane, when a collimated-beam illuminated upon the symmetric meniscus surface. The phenomena were explained using the critical reflection on the local-curved liquid surface. The approximate curve of the symmetric meniscus was obtained by means of the numerical integrating the Young-Laplace Equation.
引文
[1]陆家和，陈长彦，《表面分析技术》，电子工业出版社，1988，1-2．
[2]Q. Li, M. Zhao, S. Tang, S. Sun, and J. Wu, Two-dimensional scanning laser slope gauge: measurements of ocean-ripple structures, Appl. Opt., 1993, 32, 4590-4597.
[3]D.S.W. Kwoh, B.M. Lake, A deterministic, coherent, and dual-polarized laboratory study of microwave backscattering from water waves, part I: short gravity waves with(?)ut wind, IEEE J. Oceanic Eng., 1984, OE-9, 291-308.
[4]苗润才，杨宗立，液体表面波物理特性及其光学效应的研究，物理学报，1996，45(9)，1521-1525．
[5]R.C. Miao,Z.L. Yang, J.T. Zhu and C.Y. Shen, Visualization of low-frequency liquid surface acoustic waves by means of optical diffraction, Appl. Phys. Lett., 2002,80(17).
[6]苗润才，杨宗立，局域弯曲液体表面反射光的黑洞效应，光子学报，1995，24(24)，18-21．
[7]R.C. Miao, G. Xu, The distribution variation of reflection light field of the local curve surface, SPIE, 1999,3862, 68-69.
[8]苗润才，朱京涛，杨宗立，时坚，液体表面的遮光效应及其应用，光子学报，2002，31(4)．
[9]J.D. Barter, P.H.Y. Lee, Real-time wave-amplitude spectrum analyzer for air-liquid interfaces, Appl. Phys. Lett., 1994, 64, 1896-1898.
[10]J.D. Barter, P.H.Y. Lee, Imaging surface-wave analyzer for liquid surfaces, Appl. Opt., 1997, 36(12), 2630-2635.
[11]B.D. Duncan, Visualization of surface acoustic waves by means of synchronous amplitude-modulated illumination, Appl. Opt., 2000,39(17), 2888-2895.
[12]G. Weisbuch, F. Garbay, Light scattering by surface tension waves, Am. J. Phys., 1979, 47, 355.
[13]J.W. Goodman, Introduction to Fourier Optics, McGraw-Hill, 1968, 62.
[14]L.E. Kinsler, A.R. Frey, A.B. Coppens and J.V. sanders, Fundmentals of acoustics, Johnwiley & sons, 1982, 141-162.
[15]吴崇试，《数学物理方法》，北京大学出版社，1999，407．
[16]林敏，黄建军，光栅衍射表面张力系数测试系统，计量与测试技术，2000，No．4，
[17]铫启均，《光学教程》，高等教育出版社，1989，81-84．
[18]苏和，王文亮，《基础物理手册》，内蒙古出版社，1981，543-544．
[19]R.C. Weast, M.J. Astle, W.H. Beyer, A Ready-Reference Book of Chemical and Physical Data, CRC Press Inc, 1998, E-382.
[20]R.C. Weast, M.J. Astle, W.H. Beyer, A Ready-Reference Book of Chemical and Physical Data, CRC Press Inc, 1998, E-384.
[21]R.C. Weast, M.J. Astle, W.H. Beyer, A Ready-Reference Book of Chemical and Physical Data, CRC Press Inc, 1998, D-232.
[22]R.C. Weast, M.J. Astle, W.H. Beyer, A Ready-Reference Book of Chemical and Physical Data, CRC Press Inc, 1998, D-231.
[23]R.C. Weast, M.J. Astle, W.H. Beyer, A Ready-Reference Book of Chemical and Physical Data, CRC Press Inc, 1998, D-253-254.
[24]陈怀琛，《MATLAB及其在理工课程的应用指南》，西安电子科技大学，2000，1-8．
[25]李兰友，庄国俞，秦卫光，《Visual Basic绘图与图像处理》，人民邮电出版社，1999，91，195．
[26]上海师大，河北师大，华中师大，华南师大，河南师大合编，《物理化学》，高等教育出版社，1991，482．
[27]徐光，液体表面特性光学智能化检测技术研究，陕西师范大学硕士学位论文，2000，10．
[28]杜清枝，杨继舜，《物理化学》，重庆大学出版社，1997，273．
[29]程传煊，《表面物理化学》，科学技术文献出版社，1995，7．
[30]淡慕华，黄蕴元，《表面物理化学》，中国建筑工业出版社，1995，8．
[31]F. Bashforth, J.C. Adams, An Attempt to Test the Theory of Capillary Attraction, Cambridge Univ. Press, 1883.
[32]J. F. Padday, Tables of the Profiles of Axisymmetric Menisci, J. Electroanal. Interfacial Electrochem, 1972, 37, 313.
[33]J. F Padday, Pitt, Axisymmetric Meniscus Profiles, J. Coll. Int. Sci., 1969, 38(2), 323-334.
[34]J. F. Padday, A. R. Pitt, and R. M. Pashley, Axisymmetric Meniscus Profiles, J. Chem. Soc. Faraday Trans., 1975, 71, 1919-1931.
[35]张开明，顾昌鑫，《计算物理学》，复旦大学出版社，1987，11-13．
[36]施吉林，刘淑珍，陈桂芝，《计算机数值方法》，高等教育出版社，1999，136-207．
[2]Q. Li, M. Zhao, S. Tang, S. Sun, and J. Wu, Two-dimensional scanning laser slope gauge: measurements of ocean-ripple structures, Appl. Opt., 1993, 32, 4590-4597.
[3]D.S.W. Kwoh, B.M. Lake, A deterministic, coherent, and dual-polarized laboratory study of microwave backscattering from water waves, part I: short gravity waves with(?)ut wind, IEEE J. Oceanic Eng., 1984, OE-9, 291-308.
[4]苗润才，杨宗立，液体表面波物理特性及其光学效应的研究，物理学报，1996，45(9)，1521-1525．
[5]R.C. Miao,Z.L. Yang, J.T. Zhu and C.Y. Shen, Visualization of low-frequency liquid surface acoustic waves by means of optical diffraction, Appl. Phys. Lett., 2002,80(17).
[6]苗润才，杨宗立，局域弯曲液体表面反射光的黑洞效应，光子学报，1995，24(24)，18-21．
[7]R.C. Miao, G. Xu, The distribution variation of reflection light field of the local curve surface, SPIE, 1999,3862, 68-69.
[8]苗润才，朱京涛，杨宗立，时坚，液体表面的遮光效应及其应用，光子学报，2002，31(4)．
[9]J.D. Barter, P.H.Y. Lee, Real-time wave-amplitude spectrum analyzer for air-liquid interfaces, Appl. Phys. Lett., 1994, 64, 1896-1898.
[10]J.D. Barter, P.H.Y. Lee, Imaging surface-wave analyzer for liquid surfaces, Appl. Opt., 1997, 36(12), 2630-2635.
[11]B.D. Duncan, Visualization of surface acoustic waves by means of synchronous amplitude-modulated illumination, Appl. Opt., 2000,39(17), 2888-2895.
[12]G. Weisbuch, F. Garbay, Light scattering by surface tension waves, Am. J. Phys., 1979, 47, 355.
[13]J.W. Goodman, Introduction to Fourier Optics, McGraw-Hill, 1968, 62.
[14]L.E. Kinsler, A.R. Frey, A.B. Coppens and J.V. sanders, Fundmentals of acoustics, Johnwiley & sons, 1982, 141-162.
[15]吴崇试，《数学物理方法》，北京大学出版社，1999，407．
[16]林敏，黄建军，光栅衍射表面张力系数测试系统，计量与测试技术，2000，No．4，
[17]铫启均，《光学教程》，高等教育出版社，1989，81-84．
[18]苏和，王文亮，《基础物理手册》，内蒙古出版社，1981，543-544．
[19]R.C. Weast, M.J. Astle, W.H. Beyer, A Ready-Reference Book of Chemical and Physical Data, CRC Press Inc, 1998, E-382.
[20]R.C. Weast, M.J. Astle, W.H. Beyer, A Ready-Reference Book of Chemical and Physical Data, CRC Press Inc, 1998, E-384.
[21]R.C. Weast, M.J. Astle, W.H. Beyer, A Ready-Reference Book of Chemical and Physical Data, CRC Press Inc, 1998, D-232.
[22]R.C. Weast, M.J. Astle, W.H. Beyer, A Ready-Reference Book of Chemical and Physical Data, CRC Press Inc, 1998, D-231.
[23]R.C. Weast, M.J. Astle, W.H. Beyer, A Ready-Reference Book of Chemical and Physical Data, CRC Press Inc, 1998, D-253-254.
[24]陈怀琛，《MATLAB及其在理工课程的应用指南》，西安电子科技大学，2000，1-8．
[25]李兰友，庄国俞，秦卫光，《Visual Basic绘图与图像处理》，人民邮电出版社，1999，91，195．
[26]上海师大，河北师大，华中师大，华南师大，河南师大合编，《物理化学》，高等教育出版社，1991，482．
[27]徐光，液体表面特性光学智能化检测技术研究，陕西师范大学硕士学位论文，2000，10．
[28]杜清枝，杨继舜，《物理化学》，重庆大学出版社，1997，273．
[29]程传煊，《表面物理化学》，科学技术文献出版社，1995，7．
[30]淡慕华，黄蕴元，《表面物理化学》，中国建筑工业出版社，1995，8．
[31]F. Bashforth, J.C. Adams, An Attempt to Test the Theory of Capillary Attraction, Cambridge Univ. Press, 1883.
[32]J. F. Padday, Tables of the Profiles of Axisymmetric Menisci, J. Electroanal. Interfacial Electrochem, 1972, 37, 313.
[33]J. F Padday, Pitt, Axisymmetric Meniscus Profiles, J. Coll. Int. Sci., 1969, 38(2), 323-334.
[34]J. F. Padday, A. R. Pitt, and R. M. Pashley, Axisymmetric Meniscus Profiles, J. Chem. Soc. Faraday Trans., 1975, 71, 1919-1931.
[35]张开明，顾昌鑫，《计算物理学》，复旦大学出版社，1987，11-13．
[36]施吉林，刘淑珍，陈桂芝，《计算机数值方法》，高等教育出版社，1999，136-207．