摘要
本论文的主要目的是利用分子动力学模拟方法(Molecular Dynamic Simulation,简称MD)从微观上系统地研究相变及界面现象。
相变是工程中常见的物理现象,相界面是不同相间的边界面。由于界面非常薄,在许多场合下仅有几个分子直径厚,因而常被忽略而将其想像为一个没有厚度的几何面。但正是这一薄薄的界面的存在,对界面区的热力学特性及其附近的流动和输运、化学过程产生了重要的影响。近几年来,国内外对界面性质及相间输运现象的研究非常活跃,界面现象的探索长期以来都是科学研究的一个重点领域。
本论文借助分子动力学模拟方法,从微尺度上全面系统地研究界面层的物理特性和流体宏观特性与微观特性之间的关系,找出了宏观现象对应的微观图象,使我们能更好地把握现象的本质,以丰富理论、指导实践。
本论文所作的主要工作如下:
①详细阐述了分子动力学模拟的原理和关键技术,构造了分子动力学模拟方法的计算程序。以LJ流体氩、甲烷和强极性物质水为例,计算了流体的饱和特性,确定了饱和压力与温度的相互关系。并通过与实际气体状态方程的计算结果及相应的实验值进行了比较,证明了分子动力学模拟方法在模拟气体物性上是成功的,并对现有实际气体状态的正确性利用MD方法进行了对比、验证。另外,运用曾丹苓教授提出的用分数布朗函数作为描写实际流体分子无规则运动的概率密度函数的理论,获取了分子动力学模拟中大量的分子运动的微观信息,定量描述了实际气体偏离理想气体的程度。
②用MD方法研究了气-液相平衡。发现此时除气、液两相外,还存在一个各向异性的界面相。本文仔细地研究了界面相中流体粒子的数密度分布、温度分布及法向切向应力分布,计算了表面张力。在气-液界面特性的分子动力学模拟方法研究中,由于界面层存在各向异性,本文特别分析了势能截断半径的选取对均匀相中饱和气体和饱和液体的密度以及非均匀相中表面张力的影响,提出了一种能够同时满足均匀相中饱和气体、饱和液体密度和非均匀相中表面张力计算要求的截断半径选取方法-变截断半径算法。此算法克服了传统模拟方法中统一的截断半径不可能同时满足均匀相中和非均匀相中相关参数的计算精度要求的缺点,提高了计算精度,节约了计算时间;并将该算法运用在分子动力学模拟中,进一步分析了涨落现象对非均匀相的影响。
③在相变过程界面现象的研究中,本论文从平界面的相平衡发展到球界面的相平衡研究,从微观尺度上分析研究了纳米液滴蒸发、冷却凝固的微观过程。以径向分布函数理论为基础,更为详细地探究了纳米液滴在蒸发和冷却凝固过程中界面现象及过程的微观机制。并从微尺度液滴的模拟中获取了相应的宏观性质,这将为探索宏观系统尚未知或未确定的物理性质打下基础。
④本论文研究了分子动力学模拟中固壁对流体分子的影响。在固-液界面特性的分子动力学模拟研究中,本文提出了修正的半经验固-液分子作用势函数,引入了固-液分子作用力耦合参数α和β,分析了耦合参数α和β对作用势函数的影响;建立了固体壁面对液体分子作用的数学模型;发现在紧靠壁面处存在一个兼有固体和液体特征的一层,我们称之为“拟有序层”。本论文研究了固体和液体不同的物性参数对固体近表面流体拟有序层的影响,进而研究了拟有序层中的分子排布、分子双体分布函数及分子的运动特征,为研究相关现象提供了必要的微观分析基础。最后,结合工程需要研究了由两个固壁构成的纳米通道中受限流体的特性、输运和流动行为并与其相应的宏观特性进行了比较。文中绘出了窄通道内分子排布规律,双体分布函数的变化,分子运动情况的空间轨迹及时间谱分析,得到一些具有鲜明物理意义的有趣的结论。为研究窄通道内物质的特殊行为例如其所表现的尺度效应等提供了依据,在此基础上本文还研究了窄通道内的输运系数(扩散系数),并以其间的泊松流为例,研究了纳米通道内的流动特性,绘出了微通道中的泊松流的速度分布,可以明显地看出在微尺度下N-S方程将不再适用。这不仅在理论上表明了流体宏观特性及微观特性之间的差异,也为实际工程运用提供了依据。
The main purpose of the present dissertation is to systematically study the interfacial phenomena and phase transition in microscopic level by means of molecular dynamics simulation (MDS).
It is well known that phase transition is a physical phenomenon which appears frequently in engineering and the interface is a face between different phases. Generally speaking, the thickness of the interface is about several diameters of a molecule. The interface is so thin that it could be considered as a geometric surface without thickness. But this thin interface has an important influence on flow, transport properties and chemical process of the fluids nearby it. In recent years, there are many researches on properties of the interface and transportation phenomena among phases. The exploration of the interfacial phenomena is a remarkable field of scientific study for a long time. By using molecular dynamics simulation, the relation between the microscopic properties and the macroscopic properties of a system is investigated on the microscopic scale. The microscopic picture of macroscopic phenomenon is clearly unfolded. It makes a better grasp of the essence of a phenomenon, so that to enrich the theory and direct the practice.
The main contributions of the present dissertation are as follows:
①The saturated properties of fluids were calculated to determine the correlation between saturated temperature and saturated pressure. In which, argon, methane and water with strong polarity were chosen as the working substances. Then, the simulated results were compared with the calculated data by using the state equation of real gases and the corresponding experimental values. It was proved that the molecular dynamics simulation method was very successful and efficient for real gas to determine its properties. Meanwhile, the validity of the existing state equations of real gas was contrasted and verified using MD. In addition, the microscopic information was withdrawn during the simulation according to the theory proposed by Prof. Danling Zeng, in which the fractional Brownian function was adopted to describe the probability density function of the molecule’s random motion. This could be indicated quantitively the derivation degree of a perfect gas from a real gas.
②The phase equilibrium between two phases of liquid and vapor were performed by MD. It is found that except bulk liquid and bulk vapor, there exists an anisotropic interfacial phase. In this section, the profiles of number density, temperature, normal and tangential pressure tensors were studied in detailed for the fluids in the interfacial phase. Because of the anisotropic characteristics in the interface, the effect of the potential cutoff radius was estimated particularly on the densities of saturated vapor and saturated liquid in the homogenous phases and on the surface tension in heterogeneous phase. Then, the new algorithm of choosing the cutoff radius, so called“variable cutoff radius method”, was proposed, which satisfies both the calculation of the densities of saturated vapor and saturated liquid in the homogenous phase as well as the surface tension in heterogeneous phase, so as to overcome the disadvantages of the uniform cutoff radius and increase the calculation precision. Furthermore, the influence of fluctuation phenomena on heterogeneous phase was investigated by the new method proposed.
③From the plane interface extended to spherical one, the microscopic process of the evaporation and solidification for liquid droplets was analyzed and investigated on the basis of the theory of radial distribution functions. So that the mechanisms of interface phenomena in the phase transition would be explored in detail. Then the corresponding macroscopic properties were derived during the simulation of microscale liquid droplets, which will lay a solid foundation for predicting the unknown or undetermined properties of macroscopic system.
④The effect of solid wall on the fluid molecules was investigated by MD. In the study of interfacial properties of solid-liquid system, a modified and semi-experimental potential function was brought out in the dissertation. In which, two parameters coupling the intermolecular force were introduced. Firstly, the effect of coupling parameters on the interaction potential function was analyzed. Moreover, the mathematical model was established for the interaction between solid wall and liquid molecules. It is found that there exists a layer with properties of both bulk solid and bulk liquid at the same time in the vicinity of the solid wall, named“quasi-ordered layer”by us. In the dissertation, the effect of physical parameters of liquid and solid, respectively, on the quasi-ordered liquid layer was investigated. In addition, the distribution of molecules, the motion of a molecule and pair distribution functions in the quasi-ordered layer were shown in the paper, respectively, which provided a necessary basis of microscopical analysis for the corresponding research. In order to make a whole sight into the properties of fluids constrained in the micro and nanochannel, the transport properties of fluids and Poiseuille flow in a nanochannel were investigated and compared with the corresponding macroscopic properties. In the paper, the distribution of molecules, the change of pair distribution functions, the motion of molecules and its trace images and frequency spectrum chart for fluid constrained in the nanochannel were investigated in detail. Some interesting and significant results were obtained, which provided the basis for studying the properties of the fluids in a nanochannel and investigating the special properties, such as the size effect etc.. Based on the foregoing study, the transport coefficient (diffusivity) of fluids in the nanochannel and the velocity profiles were plotted for the Poeseuille flow. It was seen evidently that the simulated results under some conditions would deviated from the N-S solution. On one hand it shows that there exists the unnegligible difference of fluid properties between microscopic and macroscopic scale from the viewpoint of theory, on the other hand it could provided some references for the practical applications.
引文
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