关于一种开尔文方程推导方法的讨论

不同版次物理化学教材对开尔文方程推导的方法不同。本文通过对吉布斯界面热力学基本方程中球状液滴压强的分析,并依据对于弯曲液滴,附加压力本质上就是由弯曲液面表面张力引起的,得出某物理化学教材中,对小液滴的气液两相平衡过程,其吉布斯自由能的变化为零。对于恒温下,把处于外压为p0的平面液滴分割为处于外压为p_r的小液滴的过程,其吉布斯自由能的变化为2σM/ρr。     

关于等温循环方法推导开尔文公式的讨论

等温循环方法是物理化学教材中推导开尔文公式的一个经典方法。本文从热力学基本原理出发,明确指出其中小液滴可逆相变为气体的吉布斯自由能变化值应由吉布斯自由能判据求解,并对温度恒定、两相压强分别恒定时的判据进行了重新推导。同时,本文还提出了一种对推导开尔文公式的等温循环法的新理解方式,该方式在建立的"箱管模型"辅助下,意义明确,便于理解,更适宜教学使用。     

活用dF=δW'推导热力学公式

应用dF=δW'推导了拉普拉斯方程、开尔文方程、毛细管液柱高度计算公式、杨方程、贝林方程和大气分布定律等热力学公式,给出了这类推导的一般思路。     

关于球形小液滴热力学公式及其气液平衡条件的讨论

依据热力学第一和第二定律,从不同角度导出了球形小液滴的热力学基本公式。明确指出公式中的压力为液体相的压力,不是气相压力。分别用熵判据和Gibbs自由能判据证明了小液滴的气液相平衡条件为物质在两体相的化学势相等。强调指出:相平衡条件具有普适性,与是否为孤立体系或封闭体系及其类型无关,不仅适于球形液滴,对其他形状的液体也适用。对文献中存在的相关问题进行了较详细的讨论,澄清了一些容易模糊的认识。     

关于开尔文公式推导的讨论

应用弯曲界面存在的气液平衡条件和界面热力学方法,分析讨论了物理化学教材中开尔文公式的推导方法和过程,指出了存在的一些容易产生误解的问题。明确指出:等温下小液滴饱和蒸气压相对于平面液体饱和蒸气压的增大是由弯曲液面下液体的附加压力引起的,而不是界面自由能变化所致。并提出了一些教学建议。     

如何理解热力学基本方程dG=-SdT+Vdp的适用条件*

从热力学第一定律和热力学第二定律出发推导了热力学基本方程dG=-SdT+Vdp;然后围绕 dG=-SdT+Vdp的适用条件做细致分析,分别从简单pVT变化、相变化和化学变化等3个方面着手,逐一举例并详细解题、分析,探讨对该公式的应用条件,得出相应的结论。为学生在热力学基本方程应用过程中的问题提供新思路。     

Levelset方法数值模拟单液滴传质中的Marangoni效应

用Levelset方法捕获界面建立了数值模拟变形单液滴萃取传质过程中Marangoni效应的控制方程。将浓度场和流场相耦合计算,数值模拟了变形单液滴传质中的Marangoni效应,描述了Marangoni效应的发生和发展过程,结果同Sternling ＆ Scriven的经典理论分析和前期数值模拟相吻合。     

微小液滴化学势及其在界面化学中的应用

推导了微小液滴化学势的关系式及其在界面化学中建立和推导相平衡关系的应用。     

基于吉布斯弯曲界面相平衡判据的开尔文方程推导

对两种界面热力学处理方法(古根海姆法与吉布斯法)进行了介绍。采用吉布斯界面热力学方法建立了存在界面相时两相平衡的热力学判据,并以此为基础提出了一种新的开尔文方程推导方法。     

函数的单调性和导数在物理化学教学中的运用

分析了函数的单调性在阿伦尼乌斯方程、吸附热力学、范特霍夫方程和克拉佩龙方程中的运用;介绍了利用导数推导开尔文微小液滴饱和蒸气压公式,并介绍了导数在物理化学中的一些证明题和计算题中的巧妙运用。从而把物理化学抽象的内容通过数学知识具体化,使深奥的物理化学理论变成简单的数学知识。     

基于超声振动的微液滴生成装置设计与实验研究

设计了一种基于V型直线超声电机驱动的微液滴生成装置用于制备具有微米级尺寸的微液滴.此装置由基于V型直线超声电机驱动的微液滴生成部件、基于V型直线超声电机的三维位移控制平台和基于压电振子的微液滴分离部件组成.其中,生成部件包含超声电机、医用注射器、硅胶软管和自制的玻璃基微喷嘴.利用控制器驱动直线超声电机高精度地移动,由滑台推动注射器,在玻璃基喷嘴尖端产生附着的微小液滴;再利用压电振子激发杆状喷嘴的固有振型,使得附着的液滴克服粘性力从微喷嘴尖端分离,落在一定的范围内, 并计算生成的球形微液滴的半径.以蒸馏水作为初始液体,探究此装置生成的微液滴的特性.研究结果表明,蒸馏水在直线电机的精密驱动下,在微喷嘴尖端形成附着的球冠状液滴.通过分离部件的振动,附着的液滴克服自身的粘性力从喷嘴尖端分离, 形成球形液滴,通过测量得出此装置生成的球形液滴的半径小于40 μm.     

Effect of water droplet in solvent sublation

Aqueous phase layer around bubble and water droplet are two additional processes in solvent sublation. In the dynamic process of mass transfer, they are always neglected, but they are very important in the investigation of thermodynamic equilibrium. In this paper, the effect of water droplet in solvent sublation was discussed in detail, and the previous mathematical model of solvent subaltion was improved. Matlab 6.5 was used to simulate the process of water droplets, and the comparison between the previous hypothesis and the improvement in this paper showed the superiority, especially in the investigation of thermodynamic equilibrium. Moreover, the separation and concentration of the complex compound dithizone-Co（Ⅱ） from aqueous phase to n-octanol by solvent sublation also proved the improved mathematical model was reasonable.     

Experimental study of the relative effect of pressure drop and flow rate on the droplet size downstream of a pipe restriction

An experimental setup consisting of a 100?mm inner diameter pipeline, a butterfly valve with inner diameter of 100?mm, and oil and water pumping capacities of up to 20?m³/h were used to study droplet breakup in two-phase oil–water flow. The tests were performed at atmospheric pressure and under ambient temperatures. A particle-sizing camera was used to quantify droplet sizes. Combinations of different flow rates, water cuts, and pressure drops were tested to determine the relative effects of flow rate and pressure drop over a valve on the droplet breakup process. The test matrix was designed so that it should be possible to determine if the droplet sizes produced were independent of the flow rate. The fluid system consisted of a water phase and a mineral oil with viscosity of 4?mPa?·?s. Two different droplet breakup models were compared against the measured droplet sizes. The two models considered turbulence and droplet acceleration through the restriction respectively as the main contributor for droplet breakup.     

An Image-Based Technique for Measuring Droplet Size Distribution: The Use of CNN Algorithm

A challenging task in measuring droplet size is the ability to perform in-situ droplet size distribution analysis on multiphase fluids in their native states in the undisturbed environment. In this study, an inline two-dimensional low cost–high accuracy technique is presented for continuous measurement of spherical or non-spherical droplets in emulsions using image processing. The characteristic of the droplets is evaluated and the describe drop size distributions in different ranges is determined. This droplet size determination algorithm is based on both cellular neural networks and linear matrix inequality. Our main work focuses on the performance of the proposed methodology for exploring the dynamical evolution of such droplet size distributions by in-situ measurement. Moreover, the results were compared with those obtained using laser diffraction analyzer technique. It was proved that this method can efficiently characterize the quality of dispersed phase by determining droplet size distribution.     

共聚焦拉曼测量中激光焦点在球形液滴中的穿透深度

针对在共聚焦拉曼测量中激光在球形液滴中的聚焦问题建立理论模型, 推导出激光焦点在球形液滴中的穿透深度公式, 将激光焦点在球形液滴中的实际穿透深度和拉曼平台的垂直移动距离关联起来. 研究表明, 平台移动距离和激光焦点移动距离是非线性的, 激光焦点分别聚焦于液滴上表面和球心处时, 激光焦点的移动距离等于平台移动距离, 而当激光焦点在液滴上表面和液滴球心之间时, 激光焦点的移动距离大于平台移动距离. 并利用此结论初步获得MgSO₄球形液滴胶态结构的空间分布信息. 发现MgSO₄液滴在低湿度下形成的胶态结构是具有一定厚度的壳状结构, 且其厚度与液滴所处环境的相对湿度有关.     

Self‐Powered Multimodal Temperature and Force Sensor Based‐On a Liquid Droplet

Herein we report a self‐powered multimodal temperature and force sensor based on the reverse electrowetting effect and the thermogalvanic effect in a liquid droplet. The deformation of the droplet and the temperature difference across the droplet can induce an alternating pulse voltage and a direct voltage, respectively, which is easy to separate/analyze and can be utilized to sense the external force and temperature simultaneously. In addition, an integral display system that can derive information from external temperature/force concurrently is constructed. Combined with advantages of excellent sensing properties and a simple structure, the droplet sensor has promising applications in a wide range of intelligent electronics.     

Molecular dynamics simulation of polymer dispersed liquid crystal droplets under competing boundary conditions

This paper is devoted to the molecular dynamics simulation of structural organization inside a polydispersed liquid crystal (LC) droplet under competing boundary conditions. The droplet is assumed to be placed at the liquid crystal interface between two different regions of the solid polymer matrix, which accordingly separates the droplet into two hemispheres: the first of these is under radial boundary conditions; the second hemisphere is under bipolar boundary conditions. The droplet is considered as a jagged sphere filled with LC molecules, modelled as classical spins (unit vectors), whose centres of mass are associated with sites of a cubic lattice inside the cavity. The orienting action of the polymer matrix, and hence the resulting boundary conditions, are modelled by the interaction between the internal LC molecules (possessing only orientational degrees of freedom), and those of a delimiting surface layer (a jagged spherical shell), whose orientations are fixed, radial or bipolar, respectively. All interactions are modelled by the short range McMillan pair potential. The molecular orientation inside the LC droplet has been determined for various anchoring strengths of the interaction between internal spins and boundary layers. We have investigated the structure of the spherical defect resulting in the central region of the droplet, as well as of the boojum ‐ like defects existing near the poles of the droplet. It has been found that a change of relative radial and bipolar anchoring strengths can affect both central and boojum ‐ like defects. The effect of an external field on the molecular orientation inside the droplet has also been investigated. It has been found that a sufficiently strong external field increases the radius of the spherical defect placed in the central region of the droplet.     

Analytical and Numerical Study of Equilibrium Characteristics of a Droplet with Charged Condensation Nucleus in the External Electric Field

The equilibrium parameters of small dielectric droplet with charged condensation nucleus in the external uniform electric field are studied. Two typical cases are considered: (i) the droplet with charged nucleus suspended by external uniform electric field in the gravitational field and (ii) the droplet moves steadily under the action of external electric field with allowance for the resistance of surrounding vapor–gas medium. It is taken into account that the charged condensation nucleus can be displaced from the mass center of the droplet to new equilibrium position inside the droplet under the action of external electric field and response field. The scheme of the numerical solution of a nonlinear system of differential equations for the droplet equilibrium profile and electric potentials inside the droplet and in the vapor–gas medium at the arbitrary values of droplet size, strength of external field, and the charge of condensation nucleus is formulated and realized. Dependences of an equilibrium profile and the thermodynamic characteristics of a droplet such as the chemical potential of condensate and formation work on the droplet size, mass, and charge of condensation nucleus, the strength of external field and ratio of permittivities of droplet and the vapor–gas medium are plotted. Results of numerical calculations are supplemented by the analytical relations for equilibrium droplet characteristics in the first orders of the perturbation theory for a weak external field.     

Molecular dynamics simulation of polymer dispersed liquid crystal droplets under competing boundary conditions

This paper is devoted to the molecular dynamics simulation of structural organization inside a polydispersed liquid crystal (LC) droplet under competing boundary conditions. The droplet is assumed to be placed at the liquid crystal interface between two different regions of the solid polymer matrix, which accordingly separates the droplet into two hemispheres: the first of these is under radial boundary conditions; the second hemisphere is under bipolar boundary conditions. The droplet is considered as a jagged sphere filled with LC molecules, modelled as classical spins (unit vectors), whose centres of mass are associated with sites of a cubic lattice inside the cavity. The orienting action of the polymer matrix, and hence the resulting boundary conditions, are modelled by the interaction between the internal LC molecules (possessing only orientational degrees of freedom), and those of a delimiting surface layer (a jagged spherical shell), whose orientations are fixed, radial or bipolar, respectively. All interactions are modelled by the short range McMillan pair potential. The molecular orientation inside the LC droplet has been determined for various anchoring strengths of the interaction between internal spins and boundary layers. We have investigated the structure of the spherical defect resulting in the central region of the droplet, as well as of the boojum - like defects existing near the poles of the droplet. It has been found that a change of relative radial and bipolar anchoring strengths can affect both central and boojum - like defects. The effect of an external field on the molecular orientation inside the droplet has also been investigated. It has been found that a sufficiently strong external field increases the radius of the spherical defect placed in the central region of the droplet.