低频液体表面波激光衍射条纹的特征及表面波物理参量的测量
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摘要
液体表面无论组成、结构、分子所处的能量状态，还是受力情况等与体相相比，各方面都有差别，这些差别使得液体表面具有某些特殊的性质。而液体表面波蕴含着液体表面的一些性质，通过研究液体表面波，就可以获得液体的某些参数。
液体表面波是沿着液体表面传播的一种弹性波。要获得液体及液体表面波的一些特性，就需要建立有效的测量方法。光学方法来探测物质的性质，它具有无损、非接触、实时快捷等特点，因此备受人们关注。自上世纪60年代激光问世以后，激光就被用于研究表面波性质。对于高频的表面波，绝大部分研究是建立在声波光衍射的基础上。根据声光衍射原理，如果表面波的频率越大，则引起的衍射光角分离越大，所以这类实验大多针对超声表面波进行。1979年，G．Weisbuch等人首次提出了利用液体表面波来实现光衍射，并以此建立了表面张力的光学测量方法。对于低频液体表面波，我们曾进行过专门的研究。在这些研究中，激光衍射法把表面波频率下延到几十赫兹。
本文运用激光衍射法，研究低频液体表面波的特性。通过对低频液体表面波光衍射的分析，得到了衍射光场的分布和表面波之间的解析关系。根据这一关系，可以测量液体表面张力，表面波的波长、振幅等一些物理参量。本文的研究主要内容和结论如下：
1．对表面波的分类进行了归纳，对表面波的声光效应进行了分析归类。光通过声场作用下的晶体的衍射效应可以分为两类：拉曼—奈斯衍射和布拉格衍射。声波场作用下晶体的拉曼—奈斯衍射现象，不但可以看到零级和一级条纹，而且可以高于一级的衍射条纹。布拉格衍射的特点是仅有零级和一级衍射光，其他各级的衍射光已不明显存在。
2．由流体力学的动量守恒方程，推导出了牛顿流体的运动方程即纳维—斯托克斯方程(Navier-Stokes equation)，简称N-S方程。由N-S方程，再根据低频液体表面波的回复力主要为面积力的特点，简化N-S方程，求解该方程，得到低频液体表面波的波动方程。由拉普拉斯公式出发，再利用势函数的性质，推导出液体的色散关系。
3．低频液体表面波的激光衍射。对于频率高于几十赫兹的液体表面波，我们观察到了清晰的、对比度非常高的激光衍射条纹。在实验中观察到了衍射条纹的缺级，包括零级条纹的缺级，并且发现各级条纹的强度分布和表面波的振幅相关。运用傅里叶光学的理论对此衍射现象进行了分析，讨论了低频液体表面波激光衍射条纹的特征，并与实验现象进行对比，理论和实验吻合。
4．液体表面波的检测和测量。测量表面波的方法需根据测量要求和表面波频段而定。我们利用表面波的激光衍射法对表面波进行了检测，测量了液体表面波的波长、振幅，液体样品的表面张力系数等。测试了油酸钠水溶液、乙醇水溶液、NaCl水溶液的表面张力与溶液浓度的关系，为表面活性剂的研究提供了一种光学实验方法。此外，还对液体表面波的衰减特性进行了测定，发现表面波的衰减系数具有色散效应，衰减系数随着表面波的频率增大而线性增大，并通过数学检验，这一规律成立。
Compared with the bulk, the liquid surface has much difference in composition, structure, energy state, and so on. It is the difference that makes the liquid surface take on some special characteristics. These characteristics will be involved in the liquid surface waves. So, we can get the parameters through detecting the liquid surface waves.
The liquid surface wave is a kind of elastic wave which travels along the liquid surface. An effective measure must be set up if you want to obtain the characters of the liquid or liquid surface waves. Researchers are favor of the optic means which possess the lossless, no contacted, real-time and prompt characters. Since the laser has been invented, it was been widely used in studying the surface waves. The research of high frequencies surface waves are mostly based on acoustic-optic diffraction theory. Based on the theory, the diffraction angle will be widening along with the surface waves frequencies accretion. So, this kind of experiment is focused on Ultrasonic wave mainly.
In 1979, G.Weisbuch put forward the idea that liquid surface waves was detected by laser diffraction, and an optic way of detecting liquid surface tension has been come true. We have taken special research on the liquid surface waves at low frequencies. In these experiments, we declined the surface wave's frequencies to tens Hz in our experiments and achieved the goal well.
The liquid surface wave's characters have been studied by laser diffraction in this paper. Through the analysis of the laser diffraction field, the dependence of the diffraction intensity upon the surface wave amplitude and the relation of fringes distribution with surface wavelength were derived. We can measure the liquid surface wavelength,amplitude and liquid surface tension base on the relation. In our research, the major phenomena and conclusions were obtained as follow:
1. We class the surface waves and sum up the acoustic-optic effect. There are two kinds of diffraction when the light incidence on the crystal which was acted by sound wave, Raman-Nath diffraction and bragg diffraction. The phenomenon of Raman-Nath diffraction can be observed higher order fringes rather than the bragg's in which you only can find the zero and the first order diffraction fringes obviously.
2. Making use of the momentum conservation equation, Navier-Stokes equation (N-S equation) was deducted. The N-S equation was simplified based on the reversion force traits of the surface waves at low frequencies. The surface wave's equation has been obtained through answering equation N-S equation. From the laplace equation and the potential function, the liquid dispersion relation also has been obtained at the same time.
3. Light diffraction effect from the low frequencies liquid surface waves. Highly visible stationary laser diffraction patterns from liquid surface waves at a few tens Hertz were obtained experimentally, and the disappearance of diffraction spot was also observed, including zero fringes. The dependence of the diffracted field upon the surface waves were derived by theory of Fourier optics. Based on the relations of the diffraction field and the surface wave, some relations were conformed such as: The diffraction fringes spatial distribution versus surface wavelength, diffraction intensity versus surface wave amplitude, and so on.
4. Measurement in the parameters of the low frequencies surface waves by means of laser diffraction. In order to detect the liquid surface waves validly, an appropriate way should be chosen. We measure the liquid surface tension, surface wave's amplitude, surface wavelength by means of laser diffraction. In our experiment, we test the liquor surface tension of sodium oleate liquor, ethanol liquor and sodium chloride liquor and get the relation of surface tension versus the liquor concentration; the result will be helpful for studying surfactant. The experimental results indicate another result that the liquid surface wave amplitude declined exponentially with the spreading distance and the damping coefficient, which varied lineally with frequency, has dispersion characteristics.
液体表面波是沿着液体表面传播的一种弹性波。要获得液体及液体表面波的一些特性，就需要建立有效的测量方法。光学方法来探测物质的性质，它具有无损、非接触、实时快捷等特点，因此备受人们关注。自上世纪60年代激光问世以后，激光就被用于研究表面波性质。对于高频的表面波，绝大部分研究是建立在声波光衍射的基础上。根据声光衍射原理，如果表面波的频率越大，则引起的衍射光角分离越大，所以这类实验大多针对超声表面波进行。1979年，G．Weisbuch等人首次提出了利用液体表面波来实现光衍射，并以此建立了表面张力的光学测量方法。对于低频液体表面波，我们曾进行过专门的研究。在这些研究中，激光衍射法把表面波频率下延到几十赫兹。
本文运用激光衍射法，研究低频液体表面波的特性。通过对低频液体表面波光衍射的分析，得到了衍射光场的分布和表面波之间的解析关系。根据这一关系，可以测量液体表面张力，表面波的波长、振幅等一些物理参量。本文的研究主要内容和结论如下：
1．对表面波的分类进行了归纳，对表面波的声光效应进行了分析归类。光通过声场作用下的晶体的衍射效应可以分为两类：拉曼—奈斯衍射和布拉格衍射。声波场作用下晶体的拉曼—奈斯衍射现象，不但可以看到零级和一级条纹，而且可以高于一级的衍射条纹。布拉格衍射的特点是仅有零级和一级衍射光，其他各级的衍射光已不明显存在。
2．由流体力学的动量守恒方程，推导出了牛顿流体的运动方程即纳维—斯托克斯方程(Navier-Stokes equation)，简称N-S方程。由N-S方程，再根据低频液体表面波的回复力主要为面积力的特点，简化N-S方程，求解该方程，得到低频液体表面波的波动方程。由拉普拉斯公式出发，再利用势函数的性质，推导出液体的色散关系。
3．低频液体表面波的激光衍射。对于频率高于几十赫兹的液体表面波，我们观察到了清晰的、对比度非常高的激光衍射条纹。在实验中观察到了衍射条纹的缺级，包括零级条纹的缺级，并且发现各级条纹的强度分布和表面波的振幅相关。运用傅里叶光学的理论对此衍射现象进行了分析，讨论了低频液体表面波激光衍射条纹的特征，并与实验现象进行对比，理论和实验吻合。
4．液体表面波的检测和测量。测量表面波的方法需根据测量要求和表面波频段而定。我们利用表面波的激光衍射法对表面波进行了检测，测量了液体表面波的波长、振幅，液体样品的表面张力系数等。测试了油酸钠水溶液、乙醇水溶液、NaCl水溶液的表面张力与溶液浓度的关系，为表面活性剂的研究提供了一种光学实验方法。此外，还对液体表面波的衰减特性进行了测定，发现表面波的衰减系数具有色散效应，衰减系数随着表面波的频率增大而线性增大，并通过数学检验，这一规律成立。
Compared with the bulk, the liquid surface has much difference in composition, structure, energy state, and so on. It is the difference that makes the liquid surface take on some special characteristics. These characteristics will be involved in the liquid surface waves. So, we can get the parameters through detecting the liquid surface waves.
The liquid surface wave is a kind of elastic wave which travels along the liquid surface. An effective measure must be set up if you want to obtain the characters of the liquid or liquid surface waves. Researchers are favor of the optic means which possess the lossless, no contacted, real-time and prompt characters. Since the laser has been invented, it was been widely used in studying the surface waves. The research of high frequencies surface waves are mostly based on acoustic-optic diffraction theory. Based on the theory, the diffraction angle will be widening along with the surface waves frequencies accretion. So, this kind of experiment is focused on Ultrasonic wave mainly.
In 1979, G.Weisbuch put forward the idea that liquid surface waves was detected by laser diffraction, and an optic way of detecting liquid surface tension has been come true. We have taken special research on the liquid surface waves at low frequencies. In these experiments, we declined the surface wave's frequencies to tens Hz in our experiments and achieved the goal well.
The liquid surface wave's characters have been studied by laser diffraction in this paper. Through the analysis of the laser diffraction field, the dependence of the diffraction intensity upon the surface wave amplitude and the relation of fringes distribution with surface wavelength were derived. We can measure the liquid surface wavelength,amplitude and liquid surface tension base on the relation. In our research, the major phenomena and conclusions were obtained as follow:
1. We class the surface waves and sum up the acoustic-optic effect. There are two kinds of diffraction when the light incidence on the crystal which was acted by sound wave, Raman-Nath diffraction and bragg diffraction. The phenomenon of Raman-Nath diffraction can be observed higher order fringes rather than the bragg's in which you only can find the zero and the first order diffraction fringes obviously.
2. Making use of the momentum conservation equation, Navier-Stokes equation (N-S equation) was deducted. The N-S equation was simplified based on the reversion force traits of the surface waves at low frequencies. The surface wave's equation has been obtained through answering equation N-S equation. From the laplace equation and the potential function, the liquid dispersion relation also has been obtained at the same time.
3. Light diffraction effect from the low frequencies liquid surface waves. Highly visible stationary laser diffraction patterns from liquid surface waves at a few tens Hertz were obtained experimentally, and the disappearance of diffraction spot was also observed, including zero fringes. The dependence of the diffracted field upon the surface waves were derived by theory of Fourier optics. Based on the relations of the diffraction field and the surface wave, some relations were conformed such as: The diffraction fringes spatial distribution versus surface wavelength, diffraction intensity versus surface wave amplitude, and so on.
4. Measurement in the parameters of the low frequencies surface waves by means of laser diffraction. In order to detect the liquid surface waves validly, an appropriate way should be chosen. We measure the liquid surface tension, surface wave's amplitude, surface wavelength by means of laser diffraction. In our experiment, we test the liquor surface tension of sodium oleate liquor, ethanol liquor and sodium chloride liquor and get the relation of surface tension versus the liquor concentration; the result will be helpful for studying surfactant. The experimental results indicate another result that the liquid surface wave amplitude declined exponentially with the spreading distance and the damping coefficient, which varied lineally with frequency, has dispersion characteristics.
引文
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[5] 林航友，宁继平，胡鸿璋,王顺权，耿凡．高频补偿倾斜电极型宽带声光叉指换能器[J]．中国激光,2004,31(1)：33-36
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[2] 武以立，邓盛刚，王永德．声表面波原理及其在电子技术上的应用[M]．北京：科学出版社．1984：1-5
[3] 杨晓东，周雪峰．声表面波器件在雷达对抗技术中的应用[J]．压电与声光，1994,21(2)：87-91
[4] 卢文科，朱长纯，刘君华，文常保，鲁坚丘．小波变换式小电流传感器的研究[J]．西安 交通大学学报,2003,37(8)：791-794
[5] 林航友，宁继平，胡鸿璋,王顺权，耿凡．高频补偿倾斜电极型宽带声光叉指换能器[J]．中国激光,2004,31(1)：33-36
[6] MIAO R C, YANG Z L, ZHU J T, Visualization of low-frequency liquid surface acoustic waves by means of optical diffraction[J].Appl.Phys.Lett,2002,80(17):3033-3035
[7] 苗润才 杨宗立。液体表面波物理特性及其光学效应的研究[J]。物理学报,1996,45(9)：1521-1525
[8] 朱若谷．激光应用技术[M]，北京：国防工业出版社,2006：82
[9] 董曾南，章梓雄．非粘性流体力学[M]．北京：清华大学出版社．2003：44
[10] W.M.Klipstein,J.s.Radnich,S.K.Lamoreaux.Thermally excited liquid surface waves and their study through the quasi-elastic scattering of light[J].Am.J.Phys,1996, 64(6):758-765
[11] 沈钟，赵振国，王国庭．胶体与表面化学[M]．第三版．北京：化学工业出版社．2004：193
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