The special features of heat transfer in a supercritical fluid: Mathematical and physical modeling results

The special features of heat transfer in a supercritical fluid were considered for the example of two problems, those of Rayleigh-Bénard convection in a horizontal layer heated from below and nonstationary heat transfer in a closed volume with heated boundaries. Isentropic equilibrium of a compressible medium that obeyed the van der Waals equation of state was studied. The calculation results were generalized, and the special features of convective heat transfer in a supercritical fluid beyond the stability threshold of hydrostatic equilibrium were discussed. The results of numerical and experimental studies of the relaxation of density and temperature nonuniformities as the temperature of volume walls changed were presented. The calculations were performed using the complete system of Navier-Stokes equations and the equation of state of an ideal or van der Waals gas.     

A self-consistent approach for modelling the interfacial properties and phase diagrams of Yukawa,Lennard-Jones and square-well fluids

A self-consistent density-functional approach is presented for describing the phase behaviour and interfacial tensions of van der Waals fluids represented by the hard-core Yukawa (HCY), Lennard-Jones (LJ) and square-well (SW) potentials. The excess Helmholtz energy functional is formulated in terms of a modified fundamental measure theory (MFMT) for the short-ranged repulsion and a density-gradient expansion for the van der Waals attractions. Analytical expressions for the direct correlation functions of uniform fluids are utilized to take into account the effect of van der Waals’ attraction on intermolecular correlations. For bulk phases, the density functional theory is reduced to an equation of state (EOS) that provides accurate saturation pressures and vapour–liquid phase diagrams. Near the critical region, the long-range fluctuations can be corrected by using the renormalization group (RG) theory. With the same set of molecular parameters, the theory also yields satisfactory surface tensions and interfacial density profiles at all relevant temperatures.     

普遍化范德华配分函数

对纯流体及其混合物的普遍化范德华配分函数的推导作系统阐述。由该配分函数可导出一些重要的状态方程、混合规则及活度系数模型。还分析了与密度有关的局部组成模型的低密度边界条件，从而可为建立新的局部组成模型及其应用于流体相平衡计算提供理论依据     

Structure of interfaces from uniformity of the chemical potential

It is shown that a generalized chemical potential suggested by the potential-distribution theory is uniform even in a nonuniform fluid. Leng, Rowlinson, and Thompson had already observed its uniformity through the liquid-vapor interface in the penetrable-sphere model, in mean-field approximation. Following those authors, we exploit the uniformity of that generalized chemical potential to obtain unified and transparent derivations of the results of Ono and Kondo and of van der Waals on the liquid-vapor interfaces in the lattice-gas model and in the model of attracting hard spheres, respectively, both in mean-field approximation.Work supported by the National Science Foundation and the Cornell University Materials Science Center.     

A new approach to the evaluation of Casimir and van der Waals forces in the transition region

This paper studies the incorporation of Casimir and van der Waals forces applied to a nanostructure with parallel configuration. The focus of this study is in a transition region in which Casimir force gradually transforms into van der Waals force. It is proposed that in the transition region, a proportion of both Casimir and van der Waals forces, as the interacting nanoscale forces, can be considered based on the separation distance between upper structure and substrate during deflection. Moreover, as the separation distance descends during deflection, the nanoscale forces could transform from Casimir to a proportion of both Casimir and van der Waals forces and so as to van der Waals. This is also extended to the entire surface of the nanostructure in such a way that any point of the structure may be subjected to Casimir, van der Waals or a proportion of both of them about its separation distance from the substrate. Therefore, a mathematical model is presented which calculate the incorporation of Casimir and van der Waals forces considering transition region and their own domination area. The mechanical behavior of a circular nano-plate has been investigated as a case study to illustrate how different approaches to nanoscale forces lead to different results. For this purpose, the pull-in phenomena and frequency response in terms of magnitude have been studied based on Eringen nonlocal elasticity theory. The results are presented using different values of the nonlocal parameter and indicated in comparison with those of the classical theory. These results also amplify the idea of studying the mechanical behavior of nanostructures using the nonlocal elasticity theory.     

Van der Waals forces in electrolyte solutions

In this article we study van der Waals forces in electrolyte solutions from a local point of view. It is shown for arbitrary geometry that the classical limit of the force density exerted on the ions, as found in the macroscopic theory of van der Waals forces, is identical with the force density calculated from electrostatics and thermodynamic fluctuation theory. Thus neither retardation, nor the Lorentz force affect the average force density.     

范德瓦耳斯气液状态方程纵横谈

首先强调了范氏方程是气液系统的状态方程,范氏方程可以很好地说明物质气态和液态的相互转变．分析了焦-汤效应,简述了气体的液化与低温的获得．     

Thermodynamic properties of inhomogeneous fluids

A general method, the method of variation under extension, is presented for expressing the thermodynamic properties of an inhomogeneous fluid as functionals of the local number density, when given a density functional for the total thermodynamic grand potential of the fluid. The method is demonstrated in detail for the van der Waals square-gradient density functional and for the nonlocal density functional which arises in the theory of fluids with long-ranged pair potentials or in the mean-field theory of penetrable-sphere models. As specific examples, we consider the planar and spherical interface between two fluid phases, the line of contact of three fluid phases, the contact line between two surface phases and the planar interface between a solid and fluid.     

Coulombic Phase Transitions in Dense Plasmas

We give a survey on the predictions of Coulombic phase transitions in dense plasmas (PPT) and derive several new results on the properties of these transitions. In particular we discuss several types of the critical point and the spinodal curves of quantum Coulombic systems. We construct a simple theoretical model which shows (in dependence on the parameter values) either one alkali-type transition (Coulombic and van der Waals forces determine the critical point) or one Coulombic transition and another van der Waals transition. We investigate the conditions to find separate Van der Waals and Coulomb transitions in one system (typical for hydrogen and noble gas-type plasmas). The separated Coulombic transitions which are strongly influenced by quantum effects are the hypothetical PPT, they are in full analogy to the known Coulombic transitions in classical ionic systems. Finally we give a discussion of several numerical and experimental results referring to the PPT in high pressure plasmas.     

Equation of state of mixtures of simple fluids at high pressures

Recently Lee and Levesque have extended the Weeks-Chandler-Andersen pure fluid perturbation theory to mixtures and have compared the results to the Leonard-Henderson-Barker mixture theory. The results seem to favour the Leonard-Henderson-Barker theory. This and other previous comparisons of mixture theories have been mostly confined to the study of ‘zero pressure’ thermodynamic properties. In this paper we compare the Lee-Levesque, Leonard-Henderson-Barker and the van der Waals one-fluid theories to high pressure equation of state data for helium-xenon mixtures. This system is modelled by a binary mixture of Lennard-Jones fluids and the hard sphere reference system is characterized by the Grundke-Henderson hard sphere mixture radial distribution function. The Lee-Levesque theory compares favourably with experimental equation of state data up to pressures of 2000 atmospheres. The Leonard-Henderson-Barker and van der Waals one theories are satisfactory. Although the van der Waals one theory yields the poorest results, it does offer the advantage of having the greatest ease of computation.

Previous theoretical and Monte Carlo calculations of mixture properties have assumed the geometric mean rule for the mixed interaction energy parameter, ε ₁₂, with consequent disagreement with experimental results. We point out that ε ₁₂ can be determined from mixed second virial coefficient data and use such improved determinations of ε ₁₂. We show that this method yields significantly improved theoretical predictions.     

Free volume and density and temperature dependence of diffusion coefficients of liquid mixtures

A simple formula for the diffusion coefficient of liquid mixtures, expressed in terms of the work necessary to create a characteristic free volume in the liquid, is presented in the spirit of the Arrhenius activation theory and tested in comparison with available experimental data. If use is made of the generic van der Waals equation of state, the free volume appearing in the formula for the diffusion coefficient can be expressed in terms of the equilibrium pair correlation functions. The theoretical values for diffusion coefficients agree excellently with experimental values with regard to the density and temperature dependence of the diffusion coefficients of argon and krypton.     

Distribution corresponding to classical thermodynamics

A distribution corresponding to classical thermodynamics is constructed. The concept of degrees of freedom is generalized and a concept of temperature-dependent number of collective degrees of freedom is introduced. A relationship between the theory of numbers and mesoscopic physics is established. A geometric interpretation of spinodal as a curve of maximum entropy and as a catastrophe in a quasi-static Caratheodory process is given. A concept of local ideal gas is introduced. The phase transition of fluids to a dispersed system is determined. The distribution obtained is numerically compared with the distribution for a van der Waals gas in the Hougen-Watson diagram.     

A Simple Kinetic Model for the Phase Transition of the van der Waals Fluid

A simple kinetic model, which is presumably minimum, for the phase transition of the van der Waals fluid is presented. In the model, intermolecular collisions for a dense gas has not been treated faithfully. Instead, the expected interactions as the non-ideal gas effect are confined in a self-consistent force term. Collision term plays just a role of thermal bath. Accordingly, it conserves neither momentum nor energy, even globally. It is demonstrated that (i) by a natural separation of the mean-field self-consistent potential, the potential for the non-ideal gas effect is determined from the equation of state for the van der Waals fluid, with the aid of the balance equation of momentum, (ii) a functional which monotonically decreases in time is identified by the H theorem and is found to have a close relation to the Helmholtz free energy in thermodynamics, and (iii) the Cahn–Hilliard type equation is obtained in the continuum limit of the present kinetic model. Numerical simulations based on the Cahn–Hilliard type equation are also performed.     

Van der Waals interactions in DFT made easy by Wannier functions

Ubiquitous van der Waals interactions between atoms and molecules are important for many molecular and solid structures. These systems are often studied from first principles using the density functional theory (DFT). However, the commonly used DFT functionals fail to capture the essence of van der Waals effects. Most attempts to correct for this problem have a basic semiempirical character, although computationally more expensive first principles schemes have been recently developed. We here describe a novel approach, based on the use of the maximally localized Wannier functions, that appears to be promising, being simple, efficient, accurate, and transferable (charge polarization effects are naturally included). The results of test applications to small molecules and bulk graphite are presented.     

Letter: Brane Cosmology with a van der Waals Equation of State

The evolution of a Universe confined onto a 3-brane embedded in a five-dimensional space-time is investigated where the cosmological fluid on the brane is modeled by the van der Waals equation of state. It is shown that the Universe on the brane evolves in such a manner that three distinct periods concerning its acceleration field are attained: (a) an initial accelerated epoch where the van der Waals fluid behaves like a scalar field with a negative pressure; (b) a past decelerated period which has two contributions, one of them is related to the van der Waals fluid which behaves like a matter field with a positive pressure, whereas the other contribution comes from a term of the Friedmann equation on the brane which is inversely proportional to the scale factor to the fourth power and can be interpreted as a radiation field, and (c) a present accelerated phase due to a cosmological constant on the brane.     

The boundary element approach to Van der Waals interactions

We develop a boundary element method to calculate Van der Waals interactions for systems composed of domains of spatially constant dielectric response of a general boundary shape. We achieve this by rewriting the interaction energy expression presented in Phys. Rev. B, 62 (2000) 6997 exclusively in terms of surface integrals of surface operators. We validate this approach in the Lifshitz case and give numerical results for the interaction of two spheres as well as the van der Waals self-interaction of a uniaxial ellipsoid. Our method is simple to implement and is particularly suitable for a full, non-perturbative numerical evaluation of non-retarded van der Waals interactions between objects of a completely general shape.