On the nonequilibrium statistical mechanics of a binary mixture. I. The distribution functions

In this paper, we obtain the generalization of the BBGKY hierarchy for a binary mixture of chemically neutral particles. Using modified boundary conditions different from the ones proposed by Bogoliubov, we solve the hierarchy, and obtain explicitly the set of two-particle distribution functions for the several species of the mixture, up to first order in the density.     

On the validity of magnetohydrodynamics for ionic mixtures

The collective mode spectrum of the magnetized ionic mixture consisting ofs components is studied by starting from the microscopic balance equations and the fluctuation formulas for the microscopic densities. Apart from a heat mode ands-1 diffusion modes with frequencies of second order in the wavenumber, four modes with complex finite frequencies for vanishing wavenumber are found. If the mixture consist of particles with equal ratios of charge and mass, these four modes become similar to the gyroplasmon modes of the magnetized one-component plasma of which the frequencies are real in lowest order in the wavenumber. Green-Kubo relations are derived for the transport coefficients which appear in the frequencies of the heat mode and the diffusion modes. The long-time behavior of the integrands of the Green-Kubo expressions is evaluated with the help of mode-coupling theory. The static transport coefficients are found to be finite unless the mixture consists of species with equal ratios of charge and mass. It is concluded that the presence of species with different charge-mass ratios is essential for the validity of magnetohydrodynamics for an ionic mixture.     

Perturbation theory for equilibrium properties of a binary mixture of hard discs

The radial distribution function (RDF) and thermodynamic properties of a two-dimensional hard-disc mixture are calculated by using the perturbation theory. Numerical results are given for theRDF, pressure and excess-free energy of the binary mixture of both additive and non-additive hard discs. It is found that the thermodynamic properties of the binary mixture of non-additive hard discs increase with Δ, the non-additive parameter.     

Translational and rotational diffusion of an anisotropic particle in a molecular liquid: Long-time tails and Brownian limit

Formally exact equations are written down, describing the translational and rotational diffusion of an anisotropic tagged particle in a fluid of anisotropic particles. These equations are tractable in the long-time limit, and reduce to the solution of ordinary hydrodynamic equations supplemented by slip boundary conditions in the Brownian limit for a smooth tagged particle. No rotational viscosities or spin-diffusion constants appear in these results. The relation to other work is discussed.     

On the nonequilibrium statistical mechanics of a binary mixture. II. The transport coefficients

This paper is devoted to the study of the hydrodynamic stage of a two-component dense fluid. Starting from the BBGKY hierarchy obtained earlier, we first derive the expressions for the generalized fluxes. We proceed to set up the generalized kinetic equations, using Bogoliubov's functional assumption. Then we solve these equations by means of a Chapman-Enskog method. The generalized expressions for the transport coefficients are thus obtained. All our results are independent of the existence of density expansions of the relevant quantities.     

Angular structure of laser radiation in a Markov binary mixture

Laser-radiation transfer in a Markov binary mixture is compared to transfer in an equivalent homogeneous medium. Within the framework of a small-angle approximation a system of equations that describe the angular moments of the second order (angular dispersion) for a laser beam and the equation for laser-beam intensity is obtained. The results of the calculations show a significant effect of the stochastic nature of the medium on the intensity and the angular structure of the laser beam. Deceased Institute of Applied Optics, National Academy of Sciences of Belarus, 11, Belynitskii-Birulya St., Mogilev, 272793. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 66, No. 1, pp. 36–42, January–February, 1999.     

Connection between thermophoresis and thermodiffusion in a liquid binary mixture

In a liquid suspension, thermophoresis is the motion of a suspended particle under a temperature gradient. In a liquid binary mixture, thermodiffusion is the generation of a composition gradient upon application of a temperature gradient. A quantitative connection is established between the two phenomena without making assumptions about their mechanisms. It is shown that Galilean invariance and the choice of a Galilean reference frame play a key role in that connection. The results are not restricted to very dilute suspensions or mixtures.     

Long-time tails of the velocity autocorrelation functions for the triangular periodic Lorentz gas

We present numrical results on the velocity autocorrelation function (VACF)C(t)=<ν(t)·ν(0)> for the periodic Lorentz gas on a two-dimensional triangular lattice as a function of the radiusR of the hard disk scatterers on the lattice. Our results for the unbounded horizon case confirm 1/t decay of the VACF for long times (out to 100 times the mean free time between collisions) and provide strong support for the conjecture by Friedman and Martin that the 1/t decay is due to long free paths along which a moving particle does not scatter up to timet. Even after new sets of long free paths become available forR<1/4, we continue to find good agreement between numerical results and an analytically estimated 1/t decay. For the bounded horizon case , our numerical VACFs decay exponentially, although it is difficult to discriminate among pure exponential decay, exponential decay with prefactor, and stretched exponential decay.     

Long-time behavior of the nonlocal shear viscosity of a one-component plasma: A microscopic approach

The nonlocal shear viscosity(t) of a classical one-component plasma is shown to have anoscillatory long-time tail. This result is obtained on the basis of amicroscopic theory which does not rely on expansions in a small parameter such as the plasma expansion parameter. Our major approximation is the restriction to the coupling oftwo hydrodynamic propagators in the computation of the long-time behavior of the transport matrix. The Coulomb divergence is correctly accounted for, while the nonanalyticities of both the plasma parameter and gradient expansions are discussed at the level of the kinetic as well as the hydrodynamic equations.     

双组分混合流体中Eckhaus不稳定调谐的行波对流

在双组分混合流体的Rayleigh-Bénard对流系统中，数值模拟获得了周期性时空位错缺陷调谐的扩展行进波对流状态.研究了该状态的时空演化特性.结果表明，Eckhaus不稳定触发的对流涡卷对的产生是调谐的起源，对流涡卷在边界处生成与湮没频率的不同，又使系统返回不稳定区域，系统在稳定与不稳定的波数之间振荡.还探讨了一个周期内传热与混合特性的改变及其控制参数的变化规律. 关键词： 双组分混合流体 行波对流 时空位错缺陷 Eckhaus不稳定调谐     

Phase behaviors in a binary mixture of diblock copolymers confined between two parallel walls

The phase behaviors in a binary mixture of diblock copolymers confined between two parallel walls are investigated by using a cell dynamics simulation of the time-dependent Ginzburg-Landau theory.The morphological dependence of the wall-block interaction and the distance between walls(confinement degree) has been systematically studied,and the effect of repulsive interactions between different monomers is also discussed.It is interesting that multiple novel morphological transitions are observed by changing these factors,and various multilayered sandwich structures are formed in the mixture.Furthermore,the parametric dependence and physical reasons for the microdomain growth and orientational order transitions are discussed.From the simulation,we find that much richer morphologies can form in a binary mixture of diblock copolymers than those in a pure diblock copolymer.Our results provide an insight into the phase behaviors under parallel wall confinement and may provide guidance for experimentalists.This model system can also give a simple way to realize orientational order transition in soft materials through confinement.     

Birefringence study on lyotropic micellar nematic phase in a binary mixture

We report the results of our studies on optical and thermal properties of two non-mesogenic compounds, namely, didodecyl dimethyl ammonium bromide (DDAB) and glacial acetic acid. The mixture exhibits schlieren texture of lyotropic micellar nematic (N_D), SmA, SmB, and SmG phases, respectively, at different concentrations of DDAB sequentially when the specimen is cooled from isotropic phase. The order parameter (S) of lyotropic micellar nematic (N_D) phase is estimated with the help of temperature dependence of optical anisotropy from the measured values of refractive index and density data. The temperature variation of order parameter of the experimental curve is in agreement with the Mayer–Saupe theoretical curve. The formation of the above phases has been confirmed by optical studies.     

Soret效应对具有自由表面的圆柱形浅池内双组分溶液热对流影响的实验研究

为了探究Soret效应对具有自由表面的圆柱形浅液池内双组分溶液热对流过程的影响, 通过实验观察了质量分数为50%的正癸烷/正己烷混合溶液在不同深宽比的液池内流动失稳后的自由表面耗散结构及液池内的温度波动. 结果表明, 双组分溶液流动失稳的临界热毛细Reynolds数小于纯工质的值, 且其随液层深宽比的变化规律与纯工质相同. 当深宽比小于0.0848时, 流动失稳后在自由表面观察到热流体波, 监测点处温度波动主频随热毛细Reynolds数增大而增加; 当深宽比大于0.0848时, 随热毛细Reynolds数的增大, 流动失稳后自由表面依次呈现轮辐状、花苞状、分离-合并-分离交替变化的条纹状结构.     

Phase diagram involving the mesomorphic behavior of binary mixture of sodium oleate and orthophosphoric acid

The present investigation deals with the binary mixture of two non-mesogenic compounds, viz. sodium oleate (Naol) and orthophosphoric acid (H₃PO₄) which exhibits very interesting liquid crystalline smectic phases at large range of concentrations and temperature. The mixtures with concentrations ranging from 10% to 90% Naol in H₃PO₄ exhibit SmA, SmC, SmE and SmB phases, sequentially when the specimen is cooled from its isotropic phase. Physical properties, such as ultrasonic velocity, adiabatic compressibility and molar compressibility, show anomalous behavior at the isotropic to mesosphase transition.     

Hydrodynamics and time correlation functions for cellular automata

Hydrodynamic excitations in lattice gas cellular automata are described in terms of equilibrium time correlation functions for the local conserved variables. For large space and time scales the linearized hydrodynamic equations are obtained to Navier-Stokes order. Exact expressions for the associated susceptibilities and transport coefficients are identified in terms of correlation functions. The general form of the time correlation functions for conserved densities in the hydrodynamic limit is given and illustrated by some examples suitable for comparison with computer simulation. The transport coefficients are related to time correlation functions for the conserved fluxes in a way analogous to the Green-Kubo expressions for continuous fluids. The general results are applied for a one-component fluid and several types of binary diffusion. Also discussed are the effects of unphysical slow modes such as staggered particle or momentum densities.     

Phase behaviors in binary mixture of diblock copolymers confined between two parallel walls

The phase behaviors in binary mixture of diblock copolymers confined between two parallel walls are investigated by using cell dynamics simulation of the time-dependent Ginzburg-Landau theory. The morphological dependence of the wall-block interaction and the distance between walls (confinement degree) has been systematically studied, and the effect of repulsive interactions between different monomers is also discussed. It is interesting that multiple novel morphological transitions are observed by changing these factors, and various multilayered sandwich structures are formed in the mixture. Furthermore, the parametric dependence and physical reasons for the microdomain growth and orientational order transitions are discussed. From the simulation, we find that much richer morphologies can form in binary mixture of diblock copolymers than those in pure diblock copolymer. Our results provide an insight into the phase behaviors under parallel walls confinement and may provide guidance for experimentalists. This model system can also give a simple way to realize orientational order transition in soft materials through confinement.     

分离比对混合流体Rayleigh-Bénard对流解的影响

混合流体Rayleigh-Bénard对流是研究非平衡对流的非线性动力学特性的典型模型之一.基于流体力学方程组的数值模拟,首先探讨了矩形腔体中具有强Soret效应(分离比Ψ=-0.60)的混合流体行波对流的分叉特性及斑图演化,沿着分叉曲线的上部分支,随着相对瑞利数的增加,此系统依次出现了局部行波对流、具有缺陷的行波对流、行波对流、摆动行波对流及定常对流5种行波对流解.然后,研究了分离比Ψ对对流解的影响,与弱Soret效应(Ψ=-0.11)时的对流解相比较,强Soret效应(Ψ=-0.60)时出现的对流解更丰富.由于有强Soret效应的对流的复杂性,Ψ=-0.60时的对流解与Ψ=-0.20,-0.4时的对流解不同.     

椭球与圆球混合胶体体系的玻璃化转变

以椭球与圆球混合的胶体体系为研究对象,通过增加体系的面积分数,从实验上研究了混合体系发生玻璃化转变过程中结构和动力学行为的演变规律.在结构方面,通过计算和分析径向分布函数、泰森多边形以及取向序参量,发现椭球可以有效地抑制圆球结晶,整个体系在结构上始终保持无序.在动力学方面,通过计算体系的均方位移和自散射函数,发现随着面积分数的增加,体系的动力学明显变慢,弛豫时间在接近模耦合理论预测的玻璃化转变点快速增大并发散.通过考察快速粒子参与的协同重排行为,发现协同重排区域形状、大小和位置都与椭球的存在密切关联.     

NaCl structure in a mixture of silica and gold sols

The formation of an NaCl structure in a mixture of a monodisperse silica sol with particle diameter of 5300 A and a gold sol with average particle size of 800 A is described. The mixture was left still for a month, and the particles settled to form a dense layer at the bottom, where phase separation appeared. In the ordered phase only gold particles were observed microscopically as bright spots at their individual lattice points, being arranged in hexagonal or in square pattern. From the distance between the particles in the square pattern and hexagonal pattern, the lattice type for gold particles was concluded to be fcc. Further, it was known that four gold particles forming a square hold one silica particle in its center. On these grounds, the entire lattice was concluded to be of the NaCl-type.