【作者】 王德明；

【导师】 曾丹苓；

【作者基本信息】 重庆大学 ， 工程热物理， 2004， 博士

【摘要】 气液界面现象的研究不仅在基础理论研究上极为重要而且在工程应用上也受到广泛的重视。从宏观上讲,气液界面层通常比较薄,在一般工程应用中常把它当作没有厚度的几何面来处理。Gibbs利用所谓表面“剩余量”的方法赋予表面一定的折合能量和张力。但是界面现象在微尺度空间以及某些特殊场合(如对吸附现象、蒸发与凝结、以及界面张力的研究),这样的处理会带来困难。为此,本文利用分子动力学模拟并应用分形理论对气液界面特性进行了较为系统的研究。从分子动力学模拟中发现气-液两相间有一实际的过渡层存在,其厚度约为几个分子直径大小。本文经统计找出了过渡层中密度及温度分布,计算还发现对于同一种工质系统温度越高,虽然气相与液相间的密度差减小,但气液界面层却反而越厚。而温度分布在气相区域和液相区域中都围绕着平均值上下涨落,但由于气相区的分子密度较小,其涨落幅度比液相区稍大。另外,在气液界面层的外边缘,存在一个温度谷值,而在靠近界面附近存在一温度峰值。本文从微观的角度对上述现象作出了解释。本文认为,气液界面并不是一个规则几何面,它随着时间的变化而起伏涨落,它是一个分形面,其构形随着所处条件(如压力、温度等)的不同而变化。1919年,Hausdorff提出了连续空间的概念,也就是空间的维数不是跃变的,而是可以连续变化的,既可以是整数,也可以是分数。建立在此概念基础上的分形理论近年来得到了迅速的发展,但分形理论在工程实践中的应用还不很多,特别是利用它来研究气液界面的性质尚未见诸报导。在研究了界面层中物理量分布的基础上,利用分形理论对界面的几何特征进行了研究。根据分形理论,提出了计算气液界面分形维数的方法,获得了气液界面的分形图像及其分形维数,验证了气液界面具有分形这一特征。计算还发现,气液界面的分形维数随温度压力不同而变化,但其值均在2 ~ 3的范围内。在界面分形特征研究中本文根据大量数据统计及分析制定了如下规则以确定处于界面的分子:在气液界面层区域内,以1.2倍液相分子间的平均距离为标准,对于其中的某个分子,如果在该标准距离内的其它分子数小于2则视为气相分子,在2 ~ 5之间视为气液界面上的分子,大于5视为液相分子。这种规则称为(2 ~ 5)/1.2rm规则。为了确定界面的分形维数,在气液过渡区中作出不同回转半径的结构,利用(2 ~ 5)/1.2rm规则找出其中所包含的气液界面上的分子数,然后将这些分子数与回转半径关联,在双对数坐标中此关联曲线的渐近斜率便是气液界面的分形维数。<WP=6>对于气液界面的分形图像的获得,也采用了这种确定界面分子的规则。从热力学角度看,气液界面张力乃是其Gibbs折合面单位面积上的过剩自由能。作为分形面本没有面积的概念,但界面分形维数不同,显然过渡区界面上分子的总过剩自由能是不同的。本文提出了确定Gibbs折合面的位置及折合面分子面数密度的方法,以及该数密度与界面分形维数间的关系,计算了折合表面单位面积上的过剩自由能,从而算出了气液界面的张力。并将所得结果与用MDS方法和实验方法得到的界面张力的数据进行了比较,结果十分吻合,最大相对误差不超过5%。这不仅证明了本文提出的界面的分形描述的正确性,而且还可望由此发展出通过测定界面分形维数以确定界面张力的新的实验方法,其在理论和应用上的价值是显见的。综上所述,本论文提出气液界面是一个分形面,通过计算机分子动力学模拟方法,获得了气液界面的分形图像,提取出了反映气液界面特征的分形维数,以界面张力为例,从理论上导出了气液界面特性与分形维数之间的关系,并借助于计算机分子动力学模拟方法算出了界面张力,结果与MDS方法及实验法得到的结果十分吻合,充分证明所提出方法的可行性。在此基础上,还可望发展通过实验获得微观信息而得到宏观信息的新的热物性测试方法和热过程研究方法。更多还原

【Abstract】 The study on liquid-vapor interface is important not only in the fundamental research but also in engineering applications. From macroscopic point of view, the layer of interface is regarded as a geometric surface. Gibbs assigned certain equivalent energy and surface tension to the interface by using “surplus parameter” method. But in so doing, some difficulties will occur in microscopic space and under some special conditions. Therefore, a systematic study on the characteristics of liquid-vapor interface was conducted in the dissertation by using fractal theory and molecular dynamics simulation.In molecular dynamics simulation, distributions of temperature and density of the system are computed statistically. It was found from computation that for the same fluid, the higher the temperature, the thicker the liquid-vapor interface layer, and the temperatures both in vapor and in liquid region are fluctuating around the average, but the fluctuation in the vapor region is larger than that in the liquid. Also, there exist a valley and a peak in the temperature profile. Explanations on above phenomena are given in the dissertation from microscopic point of view.The dissertation asserts that the interface of liquid-vapor is not a regular geometric surface, but a fractal one fluctuating with time and changing with the conditions (such as the pressure, temperature, and so on). It is known that the concept of continuous space was proposed by Hausdorff in 1919. It is asserted that the spatial dimension may vary continuously, i.e., the dimension may either be an integer or a fraction. Fractal theory based on such a concept was well developed in recent years, but its application in engineering was not so much, especially in the study of the characteristics of liquid-vapor interface. By the aid of computer molecular dynamics simulation, this study applies the fractal theory to investigate the characteristics of liquid-vapor interface.On the basis of the study on distributions of the parameters in interface layer, fractal theory is introduced to study the geometric characteristics of the interface, and the method for computing the fractal dimension of liquid-vapor interface was advanced. By using molecular dynamics simulation, fractal representation and dimension of the interface are obtained. It is demonstrated that the liquid-vapor interface is really fractal. Calculation also shows that the fractal dimension of the <WP=8>interface changes with temperature and pressure, the values of it are between 2 to 3.During the study of the fractal interface, based on the statistics and analysis on a vast amount of data, a rule for making the judgment of the molecules locating on the interface was proposed which is described as follows: in the interface area, we define 1.2 times of the averaged distance between the molecules of liquid as a reference distance, to a certain molecule, if the number of molecules is 2 ~ 5 inside the region within the reference distance to it, we regard it as a surface molecule, if the number is less than 2, we regard it as a vapor molecule, and if the number is more than 5, we regard it as a liquid molecule. Such a rule is called (2 ~ 5)/1.2rm rule.In order to determine the fractal dimension of the interface, structures with different rotation radii are set in the transition region. By using above regulation, the number of surface molecules of each rotation structure with certain radius can be obtained, then correlate these molecule numbers with the corresponding radii, in a logarithmic coordinate system the asymptotic slope of the correlated curve is the fractal dimension of the liquid-vapor interface. Also the fractal representation of interface is obtained by using this regulation.According to thermodynamics, the surface tension of interface is the surplus free energy on a unit area of Gibbs surface. Fractal interface has no concept of area, but it is obvious that different fractal dimension of surface should have different molecular surplus free energy. In this dissertation, a method of deter更多还原