硬球链流体在平板和硬球表面分布的密度泛函理论

采用Yethiraj和Woodward的密度泛函理论方法,结合胡英和刘洪来等发展的硬球链流体状态方程,得到了自由连接硬球链流体在平板狭缝中和球形固体颗粒表面附近的密度分布表达式,并计算了在两平行壁所组成的狭缝中和直径大小不同的球形固体颗粒周围硬球链分子的链节密度分布.理论计算结果与作者采用Dickman 和Hall 的方法进行Monte Carlo计算机模拟结果非常吻合.颗粒直径对链状分子的密度分布有一定的影响,随着固体颗粒直径的增加,靠近颗粒表面附近的链节密度降低.     

共聚高分子体系的分子热力学模型

以共聚硬球链流体的分子热力学模型为基础，通过引入链节间方阱位能相互作用的贡献。建立了实际共聚高分子系统的分子热力学模型，对纯共聚高分子ＰＶＴ的关系结果，平均相对误差为０．２２％－０．８０％。     

软球微扰状态方程的研究

从改进的势能函数出发,由径向分布函数理论和维里方程导出高温下纯流体配位数的计算公式,并与Sandler法结合求得简化的扰动型软球状态方程。用该方程计算的结果与Lennard-Jones模型的计算机模拟PVT数据吻合。     

SIMPLIFIED HARD-SPHERE AND HARD-SPHERE CHAIN EQUATIONS OF STATE FOR ENGINEERING APPLICATIONS

A simple hard-sphere equation of state is proposed. This hard-sphere equation is a ratio of second-order polynomials that meets the ideal gas and close-packed density limits. It predicts the compressibility of hard-sphere fluids at low and medium densities to within a degree of quality similar to the widely used Carnahan-Starling equation. In addition, the proposed equation performs better at high densities, particularly near the close-packed density. An expression is also derived to relate the site-site correlation function at contact for hard dimers with the site-site correlation function at contact for hard spheres. With this relationship, the thermodynamic perturbation-dimer theory (TPT-D) of hard-sphere chains is simplified. The new theory performs comparably with the TPT-D when the compressibility factors of hard-sphere chain fluids containing up to 201-mer are predicted, however, it has the advantages of both simplicity and accuracy. From a practical perspective, this theory can be used to construct equations of state for polymer solutions or fluid systems containing short- and long-chain molecules.     

SIMPLIFIED HARD-SPHERE AND HARD-SPHERE CHAIN EQUATIONS OF STATE FOR ENGINEERING APPLICATIONS

A simple hard-sphere equation of state is proposed. This hard-sphere equation is a ratio of second-order polynomials that meets the ideal gas and close-packed density limits. It predicts the compressibility of hard-sphere fluids at low and medium densities to within a degree of quality similar to the widely used Carnahan-Starling equation. In addition, the proposed equation performs better at high densities, particularly near the close-packed density. An expression is also derived to relate the site-site correlation function at contact for hard dimers with the site-site correlation function at contact for hard spheres. With this relationship, the thermodynamic perturbation-dimer theory (TPT-D) of hard-sphere chains is simplified. The new theory performs comparably with the TPT-D when the compressibility factors of hard-sphere chain fluids containing up to 201-mer are predicted, however, it has the advantages of both simplicity and accuracy. From a practical perspective, this theory can be used to construct equations of state for polymer solutions or fluid systems containing short- and long-chain molecules.     

Development of the semi-empirical equation of state for square-well chain fluid based on the Statistical Associating Fluid Theory (SAFT)

A semi-empirical equation of state for the freely jointed square-well chain fluid is developed. This equation of state is based on Wertheim’s thermodynamic perturbation theory (TPT) and the statistical associating fluid theory (SAFT). The compressibility factor and radial distribution function of square-well monomer are obtained from Monte Carlo simulations. These results are correlated using density expansion. In developing the equation of state the exact analytical expressions are adopted for the second and third virial coefficients for the compressibility factor and the first two terms of the radial distribution function, while the higher order coefficients are determined from regression using the simulation data. In the limit of infinite temperature, the present equation of state and the expression for the radial distribution function are represented by the Carnahan-Starling equation of state. This semi-empirical equation of state gives at least comparable accuracy with other empirical equation of state for the square-well monomer fluid. With the new SAFT equation of state from the accurate expressions for the monomer reference and covalent terms, we compare the prediction of the equation of state to the simulation results for the compressibility factor and radial distribution function of the square-well monomer and chain fluids. The predicted compressibility factors for square well chains are found to be in a good agreement with simulation data. The high accuracy of the present equation of state is ascribed to the fact that rigorous simulation results for the reference fluid are used, especially at low temperatures and low densities. This paper was presented at the 8th APCChE (Asia Pacific Confederation of Chemical Engineering) Congress held at Seoul between August 16 and 19, 1999.     

A cubic simplified perturbed hard-chain equation of state for fluids with chainlike molecules

The simplified version of the perturbed hard-chain theory (SPHCT) developed by Kim et al. (1986) is modified by reformulating the attractive portion of the canonical partition function for mixtures, and replacing the repulsive portion by a simple simulated expression. The final equation of state developed is cubic in volume. The test results on pure fluids, binary/multi-component mixtures and reservoir fluids indicate that the CSPHC EOS retains the advantages of the original PHCT, and significant improvements over the SPHCT in predicting the VLE of heavy hydrocarbon-containing/CO₂-containing mixtures, and liquid phase density are observed.     

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.     

从统计力学推导流体状态方程(Ⅱ)——非球形多方阱势硬粒子微扰理论

本文从考虑真实分子的形状与势能出发,引进一新的用级数表示的径向分布函数形式,导出了任意形状硬粒子流体的级数状态方程.用此方程描述参考体系,用多方阱势来近似真实分子的势能曲线,采用Barker与Henderson的方法近似高级微扰项,导出了非球形多方阱势硬粒子微扰理论的通用表达式,以作为进一步导出实用状态方程的基础.     

用重整化群理论研究硬核Asakura-Oosawa流体的相平衡

An analytical equation of state (EOS) for hard core Asakura-Oosawa (AO) fluid is established by combining the AO potential, the first-order perturbation theory and the radial distribution function (RDF) for the hard sphere fluid.The phase equilibria are studied by using the renormalization-group (RG) theory. The obtained results agree well with the simulation data. Investigation shows that the attractive range parameter plays an important role in the phase equilibria for AO fluid.     

Velocity profiles and circulation in Stefan-diffusion

Recently, a new multicomponent fluid transport theory was presented by Kerkhof and Geboers [2005a. Towards a unified theory of isotropic molecular transport phenomena. A.I.Ch.E. Journal 51, 79-121], in which the transport is described by simultaneous equations of motion for each species. The theory is applied to water vapor and nitrogen in the Stefan tube as an example of two-dimensional fluid transport. Numerical solution results in axial and radial velocity profiles for both species and clearly indicates circulation of nitrogen. Comparison with the classic Stefan-diffusion equation shows that for wide tubes the latter approach is still reasonable, but for narrow tubes shear effects dominate. The nitrogen circulation causes radial concentration profiles. For small diameter tubes, the axial velocity profiles from the present model are close to those from the velocity profile model of Kerkhof et al. [2001. On the isothermal binary transport in a single pore. Chemical Engineering Journal 83, 107-121], in which radial transport was assumed to be infinitely fast.     

用状态方程描述弱电解质NH_3-CO_2-H_2O体系的汽液平衡行为

本文以扰动理论为基础建立了一个新的电解质溶液的状态方程.该方程考虑了分子—分子、分子—离子及离子—离子的二元交互作用,并被用来关联弱电解质体系NH_3-CO_2-H_2O的汽液平衡.该方程只有三个二元交互作用参数,其中两个是可调参数,比其他模型的参数少得多,而关联结果则与其他模型相仿,关联误差在实验误差的范围之内.取得了令人满意的结果.     

RATIONAL CONSTRUCTION OF AN AUGMENTED HARD CORE EQUATION OF STATE FOR PURE COMPOUNDS AND STUDY OF ITS APPLICATION TO MIXTURES

The Carnahan-Starling hard-sphere equation of state perturbed by attractive forces expressed in a virial expansion has been studied in the vicinity of the critical point. The three van der Waals conditions for the critical isotherm at the critical point were used to determine the minimum number of terms required in the perturbation series. P-v-T data at other temperatures were used for the determination of the temperature dependence of the virial terms. The equation has been tested for mixtures using the mixing rules of Arai et at.     

电解质溶液的分子热力学模型

本文以扰动理论为基础建立了含极性组分和电解质的混合物的状态方程.混合物的Helmholtz能由硬球、静电和吸引项三部分组成.对于无电解质的混合物,本状态方程还原成Hu等近期开发的方程.用Bromley、Meissner、pitzer、Chen和本文摸型对25个二元电解质水溶液(最高浓度达20mol/kg)298.15K时的离子平均活度系数进行了关联,本文模型的精度最高.另外,用298.15K回归出的参数对其它温度下的离子平均活度系数进行了预测,结果表明模型参数与温度的关系较小.     

立方扰动硬链方程

本文通过在SPHC方程中引入拟合Carnahan-Starling硬球方程所得的斥力项,建立了立方型扰动硬链状态方程.由拟合正构烷烃的饱和蒸汽压和液相密度所确定的3个纯组分参数与碳原子数呈良好线性关系.对19种纯物质饱和蒸汽压和液相密度数据计算的平均相对误差分别为1.52%和2.97%;对混合物提出了一种新的混合规则,应用于预测含短链和长链烃类及二氧化碳、硫化氢混合物的高压汽液平衡,优于采用SPHC、SRK和PT方程所得的计算结果.     

硬球链流体在狭缝中密度分布的Monte Carlo模拟

Covering a wide range of bulk densities, density profiles for hard-sphere chain fluids (HSCFs) with chain length of 3,4,8,20,32 and 64 confined between two surfaces were obtained by Monte Carlo simulations using extended continuum configurationai-bias (ECCB) method. It is shown that the enrichment of beads near surfaces is happened at high densities due to the bulk packing effect, on the contrary, the depletion is revealed at low densities owing to the configurationai entropic contribution. Comparisons with those calculated by density functional theory presented by Cai et al. indicate that the agreement between simulations and predictions is good. Compressibility factors of bulk HSCFs calculated using volume fractions at surfaces were also used to test the reliability of various eauations of state of HSCFs by different authors.     

用改进的密度泛函理论预测三元硬球混合物的结构

在Ronsenfeld的权重函数的基础上,在计算流体自由能密度时利用硬球混合物流体的Boublik—Mansoori—Canahan-Starling-Leland状态方程来代替硬球的定标粒子理论,从而得到了改进的密度泛函理论。结合测试粒子法,对不同组成的三元硬球混合物流体的径向分布函数进行了计算：与分子模拟数据比较结果表明,使用合适的密度泛函理论,测试粒子法能够成功地计算多元硬球混合物流体的结构性质。本研究为使用统计力学理论计算其它复杂流体的热力学性质提供了一种方法。     

A CUBIC EQUATION OF STATE BASED ON A SIMPLIFIED HARD-CORE MODEL

The Redlich-Kwong (RK) equation of state introduced in 1949 has been considered the most accurate two-constant-parameter cubic equation of state. The other cubic equations which are more accurate than the RK equation contain either three, or more, parameters and/or their parameters are temperature- dependent. A New two-constant-parameter cubic equation of state, $ is introduced using a simplified molecular theory of hard-sphere fluids for its repulsive term. This two-constant-parameter cubic equation of state appreciably increases the accuracy of thermodynamic property predictions and phase equilibria of pure fluids and flluid mixtures over the equations of this category.     

Computational fluid dynamic simulations of chemical looping fuel reactors utilizing gaseous fuels

A computational fluid dynamic (CFD) model for the fuel reactor of chemical looping combustion technology has been developed, with special focus on accurately representing the heterogeneous chemical reactions. A continuum two-fluid model was used to describe both the gas and solid phases. Detailed sub-models to account for fluid–particle and particle–particle interaction forces were also incorporated. Two experimental cases were analyzed in this study (Son and Kim, 2006; Mattison et al., 2001). Simulations were carried out to test the capability of the CFD model to capture changes in outlet gas concentrations with changes in number of parameters such as superficial velocity, metal oxide concentration, reactor temperature, etc. For the experiments of Mattisson et al. (2001), detailed time varying outlet concentration values were compared, and it was found that CFD simulations provided a reasonable match with this data.     

Hydrodynamic force between two hard spheres tangentially translating in a power-law fluid

The hydrodynamic interaction between two hard spheres tangentially translating in a power-law fluid is investigated. By considering the gap between the two spheres being sufficiently small such that the Reynolds’ lubrication theory applies, an analytical equation to the pressure in the gap is obtained using truncated Fourier series. To a good approximation, the pressure equation can be further simplified. The simplified approximate equation over-predicts the pressure for shear thickening fluid (n>1) but under-predicts the pressure for shear-thinning fluid (n<1). However, the errors in the predicted tangential force and moment are relatively small. In particular, for a Newtonian fluid, the accurate solution and the simplified approximate solution degenerate to the asymptotic solution of Goldman et al. [1967. Slow viscous motion of a sphere parallel to a plane wall-motion through a quiescent fluid. Chemical Engineering Science 22, 637-651.] and O’Neill and Stewartson [1967. On the slow motion of a sphere parallel to a nearby plane wall. Journal of Fluid Mechanics 27, 705-724.]. Both solutions predict that for shear thickening fluid (n>1), the hydrodynamic force converged in the inner region of the gap between the two spheres and the contribution from the outer region is sufficiently small. For shear thinning fluid (n<1), the contribution from the outer region is also significant.