Critical behavior of pure confined fluids from an extension of the van der Waals equation of state

The critical behavior of pure fluids confined in porous solids is investigated using an extension of the van der Waals equation of state. The effects of pore size and of the interaction between fluid molecules and pore walls are evaluated. Fluid molecules were assumed spherical, interacting with each other and with the walls of cylindrical pores through distinct square-well potentials. It was found that our model may predict either one or two mechanically stable critical points for the confined fluid, depending on its specifications. When two critical points are predicted, one is attributed to a major contribution of molecule-molecule interactions and the other to a major contribution of molecule-wall interactions. The confined fluid critical point(s) presented a complex dependence on the pore size, due to the interplay of molecule-molecule and molecule-wall interactions. It is shown that the prediction of two critical points for confined fluids is useful to describe adsorption isotherms with two phase transitions.     

EQUATION OF STATE FOR POLAR AND NONPOLAR SUBSTANCES FROM CORRELATIONS OF PURE COMPONENT PROPERTIES

A cubic equation of state of the van der Waals type is presented which is suitable for polar and nonpolar fluids and fluid mixtures. The form is based on the three-parameter equation of lwai, Margerum and Lu. Problems in parameter generalization are avoided by calculating the parameters directly from existing pure component vapor pressure and saturated liquid molar volume correlations. The proposed approach yields excellent representation of pure component saturated and single-phase region properties. Excellent results are also obtained for mixtures.     

Effect of dimethyl carbonate on the behavior of water confined in carbon nanotube

The dehydration of water by dimethyl carbonate (DMC) is of great significance for its application in electrochemistry and oil industry. With the rapid development of nanomaterial, one-dimensional (e.g. carbon nanotube (CNT)) and two-dimensional (e.g. lamellar graphene) materials have been widely used for molecular sieving. In this work, the molecular behavior of dimethyl carbonate/water mixture confined in CNT with varying diameters was studied based on molecular dynamics simulation. Due to different van der Waals interactions for the components in the mixtures with the solid surface, DMC molecules are preferentially adsorbed on the inner surface of the pore wall and formed an adsorption layer. Comparing with the pure water molecules confined in CNT, the adsorption DMC layer shows notable effect on the local compositions and microstructures of water molecules under nanoconfinement, which may result in different water mobility. Our analysis shows that the surface-induced DMC molecules can destroy the hydrogen bonding network of water molecules and result in an uniform and dispersed distribution of water molecules in the tube. These clear molecular understandings can be useful in material design for membrane separation.     

Saturation and metastable properties of the van der waals fluid

Modern applications require accurate thermodynamic equations of state that portray stable and metastable states of fluids. Earlier work has shown that the famous van der Waals equation, contrary to widely held views, finds its natural niche in the rank of real substances ordered according to their values of the acentric factor. In this note, the saturated and metastable state properties of a van der Waals fluid are presented in the form of a temperature table and a pressure table. A comparison of these results with the available data for mercury is made and it is established that mercury is approximated rather well as a van der Waals fluid.     

Prediction of VLE data for alternative refrigerant mixtures

The inevitability of a disaster associated with the depletion of the ozone layer led to the decision to phase out conventional chlorine containing refrigerants and their mixtures. This necessitates the use of non-chlorine substances as refrigerants. In the present work, three different types of mixing rules, namely (i) the classical van der Waals one fluid mixing rule, (ii) the composition dependent mixing rules of the Margules type, and (iii) the conformal solution van der Waals mixing rules are used with the Peng-Robinson (PR) equation of state, to predict the VLE data of 27 alternative refrigerant mixtures, and the results are compared with the experimental data. It is found that the compositiondependent mixing rule coupled with the PR equation of state is quite suitable for predicting the VLE data.     

MOLECULAR PRINCIPLE OF CORRESPONDING STATES FOR VISCOSITY AND THERMAL CONDUCTIVITY OF FLUID MIXTURES

Conformal solution theory is developed for the viscosity and thermal conductivity of fluid mixtures. The procedure involves expanding the transport coefficient for the mixture about the value for an ideal solution, using groupings of the potential parameters and molecular mass as expansion coefficients. The parameters for the ideal solution are chosen so as to annul the first-order term in this expansion, thus encouraging rapid convergence. This yields mixing rules (similar to those of the van der Waals 1 theory for thermodynamic properties) for the potential parameters and molecular mass of the reference fluid. Reference fluid properties are obtained from pure fluid corresponding states correlations

By making calculations for dilute gas mixtures and comparing with Chapman-Enskog theory, it is found that the first-order theory works well for mixtures of quite widely different energy parameters (ε) and molecular masses; it is more sensitive to the size difference of the molecular components, however. For cryogenic liquid mixtures composed of simple liquids good results are obtained using two-parameter corresponding states for the reference fluid. For polyatomic fluids it is necessary to use a three-parameter corresponding states approach for the pure fluids. A method of introducing a third parameter, while retaining the simplicity of having only two independent variables, is used for such fluids. Good results are obtained for a variety of binary mixtures. The method is of particular value for multicomponent fluids. Thus, without fitting any parameters from ternary data the theory predicts viscosities for the system carbon tetrachloride/n-hexane/benzene over the full composition range with a standard deviation of only 1.69%.     

MOLECULAR PRINCIPLE OF CORRESPONDING STATES FOR VISCOSITY AND THERMAL CONDUCTIVITY OF FLUID MIXTURES

Conformal solution theory is developed for the viscosity and thermal conductivity of fluid mixtures. The procedure involves expanding the transport coefficient for the mixture about the value for an ideal solution, using groupings of the potential parameters and molecular mass as expansion coefficients. The parameters for the ideal solution are chosen so as to annul the first-order term in this expansion, thus encouraging rapid convergence. This yields mixing rules (similar to those of the van der Waals 1 theory for thermodynamic properties) for the potential parameters and molecular mass of the reference fluid. Reference fluid properties are obtained from pure fluid corresponding states correlations

By making calculations for dilute gas mixtures and comparing with Chapman-Enskog theory, it is found that the first-order theory works well for mixtures of quite widely different energy parameters (ε) and molecular masses; it is more sensitive to the size difference of the molecular components, however. For cryogenic liquid mixtures composed of simple liquids good results are obtained using two-parameter corresponding states for the reference fluid. For polyatomic fluids it is necessary to use a three-parameter corresponding states approach for the pure fluids. A method of introducing a third parameter, while retaining the simplicity of having only two independent variables, is used for such fluids. Good results are obtained for a variety of binary mixtures. The method is of particular value for multicomponent fluids. Thus, without fitting any parameters from ternary data the theory predicts viscosities for the system carbon tetrachloride/n-hexane/benzene over the full composition range with a standard deviation of only 1.69%.     

链状流体的分子热力学模型(Ⅱ)──混合物汽液平衡

实际链状流体混合物的亥氏函数表示为参考流体（硬球链流体混合物）的贡献和由于链节间的方阱位能相互作用的贡献之和．前者直接用作者先前建立的硬球链流体混合物的分子热力学模型计算,不含混合规则;后者采用Alder等人的结果,用vanderWaals单流体理论计算混合物的能量参数.对于不含氢键作用的二元混合物,有一可调相互作用参数,需由实验数据拟合得到．本模型可以满意地关联小分子混合物和高分子溶液的汽液平衡。     

A new state model of liquid-vapor interfaces—to yield analytical expression for surface tension

Based on the van der Waals fluid model, a simple equation of state, unique for non-uniform fluids, is developed. It is applied to the liquid-vapor interface, to derive the density profile in the interfacial region. The density profile is used in conjunction with the gradient theory, to yield an expression for the surface tension of a saturated fluid as a function of temperature and fluid properties. The non-dimensionalized influence parameter of the gradient theory is assigned best-fit values, which are of a unity order of magnitude, as expected. The predicted surface tension values are in good agreement with experimental data, for a variety of fluids.     

A generalized theorem of corresponding states for the thermodynamic properties of nonpolar and polar fluids

Generalized procedures are discussed for the accurate calculation of thermodynamic properties of nonpolar and polar fluids and mixtures. It is shown that the concepts of van der Waals for simple fluids can be extended to complex substances, and that the properties of a wide range of fluids can be calculated from a sufficient number of macroscopic parameters defined through the vapor pressure.     

On the molecular basis of adsorbed solution behaviour

A theoretical study, based on statistical thermodynamics, of the adsorbed solution behaviour of binary gas monolayers on a homogeneous solid surface is presented. The adsorbate—solid interactions are modelled via the summed 10-4 potential and the adsorbate—adsorbate interactions as those of a two-dimensional fluid mixture in which the molecules interact via Lennard-Jones 12-6 potentials. The thermodynamic properties of the two-dimensional mixture are obtained from the van der Waals one-fluid model. We present results from Monte Carlo computer simulations of two-dimensional fluid mixtures which support the accuracy of this procedure. The model can be used to study the relative importance of adsorbate—solid and adsorbate—adsorbate interactions in determining the adsorbed solution behaviour.Comparisons with experimental adsorption equilibria data for ethane—propane mixtures adsorbed on graphitized carbon black show that the theory gives excellent predictions of the adsorption equilibria, without adjustable parameters. For this system at 298 K and 700 Torr the adsorption selectivity is dominated by the difference in the Henry's law constants. However, it is shown that the adsorbate—adsorbate interactions and nonideal adsorbed solution behaviour become more or less important depending on the conditions in relation to the two-dimensional phase diagram.     

利用正则配分函数计算实际流体的热力学性质及汽液平衡——(Ⅰ)纯流体的热力学性质

通过修改普遍化van der Waals正则配分函数的引力项,发展了一个修正的状态方程式.将表征分子间引力参数α修正为不仅依赖于温度而且与密度有关.用新的状态方程式计算纯气体、饱和蒸汽与饱和液体的压力与逸度系数的结果与实验结果符合较好.     

The generalized van der Waals partition function as a basis for excess free energy models

The important insight of J. D. van der Waals in developing the equation of state that bears his name was the analysis of the separate contributions of the attractive and hard-core repulsive interactions to the equation of state. This insight led him to important advances in understanding fluids and their phase transitions. This same separation of attractive and hard core interactions have been used in statistical mechanics in the form of perturbation theory, and also as here in a form referred to as the Generalized van der Waals partition function. This partition function has been used in the literature to understand the assumptions that underlie equations of state, and to develop equations with a better theoretical basis. Here, we demonstrate how the generalized van der Waals partition function can be used to elucidate the assumptions inherent in all of the commonly used correlative activity coefficient models.     

Interfacial tensions of industrial fluids from a molecular‐based square gradient theory

This work reports a procedure for predicting the interfacial tension (IFT) of pure fluids. It is based on scaling arguments applied to the influence parameter of the van der Waals theory of inhomogeneous fluids. The molecular model stems from the application of the square gradient theory to the SAFT‐VR Mie equation of state. The theory is validated against computer simulation results for homonuclear pearl‐necklace linear chains made up to six Mie (λ ? 6) beads with repulsive exponents spanning from λ = 8 to 44 by combining the theory with a corresponding states correlation to determine the intermolecular potential parameters. We provide a predictive tool to determine IFTs for a wide range of molecules including hydrocarbons, fluorocarbons, polar molecules, among others. The proposed methodology is tested against comparable existing correlations in the literature, proving to be vastly superior, exhibiting an average absolute deviation of 2.2%. © 2016 American Institute of Chemical Engineers AIChE J, 62: 1781–1794, 2016     

从统计力学推导流体状态方程(Ⅲ)——关于马丁-侯状态方程等的统计力学证明与解释

本文从多方阱非球形势硬粒子微扰理论出发,通过适当的近似与化简,导出了马丁-侯状态方程,从而使这个由经验提出的状态方程得到了统计力学的证明与解释.从多方阱非球形势硬粒子微扰理论出发,通过更粗略的近似也能得到范德华状态方程以及Barner与Adler改进的(?)offie状态方程.由理论分析,马丁-侯方程较为全面,不仅有高级微扰项,保留了多级密度展开式,同时取用了较精确的多级参考流体状态方程.     

A calculation for the viscosity of fluids by using van der Waals equation of state

A new equation for the viscosity of fluid is presented by considering that the viscosity is equal to the product of the shear pressure and the shear relaxation time. The shear pressure and the shear relaxation time are calculated thermodynamically by applying the van der Waals model for fluids. The calculated viscosities for various simple substances are in good agreements with those of the observed values through liquid-critical point-gas region.     

平均吸引势模型状态方程用于固体在超临界流体中溶解度的计算

基于膨胀液体概念，把超临界流体看作是被气体膨胀了的液体，并假设体系的分子吸引势为范德华气体和凝聚液体吸引势的体积平均值、导出了一个平均吸引势模型状态方程。该方程较好地关联了纯溶剂蒸汽压及超临界二氧化碳的Ｐ－Ｖ－Ｔ关系；并关联了１４种固体溶质在超临界二氧化碳中的溶解度数据，结果优于ＲＫ、ＳＲＫ及ＰＲ方程。     

推广的van der Waals 压缩因子及其对超临界流体的应用

利用实验测得的液体的热压力系数，修正原始van der Waals模型中的排斥体积，得到了一个适用于高密度流体的推广的van der Waals压缩因子。将它与Redlich和Kwong提出的吸引项相结合，建立了一个流体状态方程。用某些有代表性的超临界流体的pVT数据检验，结果表明，其对体积、压力和逸度系数的计算准确度可与CS-RK方程相媲美。