Development of finite fluctuations in local density, velocity, and temperature for real fluids

Analytical expressions for large-scale finite local fluctuations of temperature and collective velocity valid for all states of real fluids are presented. Models for the probability distribution of finite density and temperature fluctuations are proposed. It is demonstrated that a fluctuating fluid consists of two fractions. The basic properties of the fractions are established, and the role of each faction in the makeup of the physical and chemical properties of the fluid is specified. It is shown that the development of large-scale finite fluctuations is not an inherent feature of the critical state: it is characteristic of a wide range of states of real fluids.     

基于拟沸腾理论的超临界CO2管内传热恶化量纲分析

超临界流体广泛应用于工程技术领域,其流动传热特性对工程设计具有重要意义,但是,由于超临界流体的物理微观和宏观行为的机理尚不清晰,所以其异常的流动传热特性并未得到很好的解决.普遍认为超临界流体在分子尺度上可分为类气和类液两种不同的特性,直到最近通过实验在宏观上监测到超临界水类液和类气之间的转变,且这一过程与拟沸腾理论一致,使得问题逐渐变得清晰.本文基于拟沸腾理论对超临界CO2异常流动传热行为进行了研究,在假设类液和类气转换过程不均匀的情况下,从经典的量纲分析和亚临界过冷沸腾理论模型出发,提出了一个适用于超临界流体拟沸腾换热过程的分析方法.通过引入表征类气膜生长速度与流体主流平均流速之比π=(qw·ρ1)/(G·Δi·ρg)和表征近壁区类气膜温度梯度π13=(qw·βpc·di)/λg两个无量纲数,来表征拟沸腾如何导致传热恶化,解释了超临界CO2竖直向上加热流动过程中的异常换热特性,即较大的类气膜生长速度使近壁区快速聚集了较多的高温流体,而较大的类气膜温度梯度使类气膜覆盖在壁面.当核心的冷类液不能充分润湿热壁面时,传热恶化.新无量纲数较好的诠释了超临界流体拟沸腾诱导传热恶化机制,为超临界拟沸腾传热研究提供了理论依据.     

浮升力和流动加速对超临界CO2管内流动传热影响

基于单相流体的概念,超临界流体的异常传热行为已经被研究很多年了,但是关于其流动传热机理仍没有统一的认识.本文通过理论分析和实验研究了超临界二氧化碳在竖直管内向上流动过程中,浮升力和流动加速效应对其流动结构和传热过程的影响.结果表明,没有确凿的实验证据表明超临界流体的异常传热行为是浮升力和流动加速直接导致的,存在的估计浮升力和流动加速效应准则均是在常物性流体的基础上,做了大量假设得出的,不同的研究者采用浮升力和流动加速准则分析超临界流体的传热恶化得出的结论不一致.最后,基于拟沸腾理论分析超临界流体的传热恶化过程,提出超临界沸腾数区分了超临界流体正常传热与恶化传热的转换边界,为超临界流体流动传热研究提供新思路,超临界沸腾数对建立用于不同技术的超临界流体动力循环的最佳运行条件具有重要意义.     

The singular points and phase diagram of the supercritical region of a substance

This paper suggests using the supercritical point and the maximum fluctuation point on the supercritical isotherm for the analysis of the behavior of various substances in the vicinity of the critical point. These three points lie at the vertices of a triangle that is formed by the supercritical isotherm, the line of the local minima of stability, and the line of maxima of fluctuations. In this triangle, which is called supercritical, the fluctuations and instability behave such that this part of the phase surface is most interesting from the viewpoint of performing various chemical reactions. Here, large fluctuations and the stability of the system rapidly decrease with increasing volume. This region is studied in the approximation of the van der Waals and Van Laar equations.     

Parastatistics and phase transition from a cluster as a fluctuation to a cluster as a distinguishable object

A phase transition of the first kind is a jump of a function, a phase transition of the second kind is a jump of its first derivative, a phase transition of the third kind, a jump of the second derivative. A phase transition from one statistic to another is very gradual, but finally it is as considerable as the phase transition of the first kind. However, we cannot introduce a clearly defined parameter to which this transition corresponds. This is due to the fact that the fluctuations near the critical point are huge, and this violates, in the vicinity of that point, the main law of equilibrium thermodynamics, which asserts that fluctuations are relatively small. The paper describes the transition in the supercritical fluid region of equilibrium thermodynamics from parastatistics to mixed statistics, in which the Boltzmann statistics is realized for long-living clusters. In economics this corresponds to a negative nominal credit rate. Examples of this non-standard situation are presented.     

MR measurement of critical phase transition dynamics and supercritical fluid dynamics in capillary and porous media flow

Supercritical fluids (SCF) are useful solvents in green chemistry and oil recovery and are of great current interest in the context of carbon sequestration. Magnetic resonance techniques were applied to study near critical and supercritical dynamics for pump driven flow through a capillary and a packed bed porous media. Velocity maps and displacement propagators measure the dynamics of C(2)F(6) at pressures below, at, and above the critical pressure and at temperatures below and above the critical temperature. Displacement propagators were measured at various displacement observation times to quantify the time evolution of dynamics. In capillary flow, the critical phase transition fluid C(2)F(6) showed increased compressibility compared to the near critical gas and supercritical fluid. These flows exhibit large variations in buoyancy arising from large changes in density due to very small changes in temperature.     

Physicochemical foundations and specificity of the practical application of supercritical water oxidation to the destruction of persistent organic pollutants

The theoretical and practical aspects of application of one of the most promising methods for the destruction of persistent organic pollutants, supercritical water oxidation, are discussed. The current state of research in the field of analysis and prediction of the critical parameters of systems with an arbitrary number of components, the behavior of the components in supercritical water-organic pollutant binary systems, and the specificity of supercritical fluids are considered. Various types of phase diagrams of binary systems are examined, and theoretical foundations for calculating the critical physicochemical parameters of multicomponent systems are presented. By the example of hexachlorocyclohexane (Lindane), one of the most toxic pesticides, calculations of the material and heat balance of the oxidation of pesticides with oxygen and hydrogen peroxide are performed. The calculations can be used in designing technological installations for the destruction of pollutants by the supercritical water oxidation.     

超临界流体Rayleigh-Bénard对流的数值模拟研究

物质气液临界点附近热物理性质发生剧烈变化,会出现一种对热力学平衡有显著加速作用的热声活塞效应。而在长时间尺度上,因重力作用而产生的Rayleigh-Bénard对流在活塞效应的影响下,其表现出来的物理特性与普通流体相比存在较大的差异。我们通过SIMPLE方法对超临界氮在不同临界距离下的自然对流发生过程进行数值模拟,结果显示当流体热力学状态接近临界点时,对流作用的发生取决于边界层内热羽流的形成,并且具有明显的湍流特征,而随着离开临界点的距离加大,流场的形成逐渐过渡到一般可压缩流体的情形。     

Stability of a thermal boundary layer in the presence of vibration in weightlessness environment

Several weightless experiment with supercritical fluids have shown that thermal boundary layers can be destabilized when submitted to a harmonic vibration. A study of the phenomenon is given here in a regular fluid during a sudden change of wall temperature in the presence of harmonic tangential vibrations and under weightlessness. A semi-infinite space is filled with a fluid and bounded by a flat wall oscillating in its plane. For this configuration, a state with the fluid velocity parallel to the wall is possible but this fluid motion does not influence the heat transfer. Then the propagation of thermal waves can be described by classical relations. The stability of this state is studied under the assumption of a “frozen” temperature profile. The vibration frequency is assumed to be high such that the viscous boundary layer thickness is small in comparison with the thermal boundary layer thickness. The calculations show that the instability develops when the thickness of the thermal boundary layer attains a critical value. The wavelength of the most dangerous perturbations is found to be about twice the critical thermal boundary layer thickness.     

Modelling and simulation of countercurrent fractional extraction with supercritical solvents

Fractionating fluid mixtures by supercritical fluid extraction has received increasing attention within the last few years. In this paper, a simulation model of a countercurrent fractional extraction column operated with supercritical fluids is presented. The model is based on ideal separation stages and incorporates the equation of state due to Redlich-Kwong and Soave for describing phase equilibria.Simulation studies were performed on the separation of a binary feed using supercritical carbon dioxide as extraction solvent. The system is also used when treating a reaction mixture from an enzymatic conversion effected in supercritical carbon dioxide. To achieve a symmetric fractionation with equal purities in both top and bottom product flow of the column, the reflux ratio has to be set to a distinct ‘optimal’ value. All other column parameters remaining unchanged, the optimal reflux ratio increases as the solvent flow is increased. As a consequence, product purities also increase.     

Fokker-Planck equation approach to fluctuations about nonequilibrium steady states

We examine the properties of steady states in systems which interact at the boundary with a nonequilibrium environment. The examination is based on a nonlinear Fokker-Planck equation, the structure of which is determined by the fact that it also governs the time evolution of the equilibrium fluctuations of the system. The nonlinearities in the Fokker-Planck equation may have two origins: thermodynamic nonlinearities which arise if the thermodynamic potential is not a bilinear function of the state variables, and nonlinear mode coupling which arises if the transport coefficients depend on the state. While these nonlinearities have only a small effect on the equilibrium fluctuations of a system away from critical points, they are shown to be important for the determination of fluctuations about nonequilibrium steady states. In particular the state dependence of the transport coefficients may lead to deviations from local equilibrium and to a breakdown of detail balance. An explicit formula for the time correlations of fluctuations about the nonequilibrium steady state is obtained. The formula leads to long-range correlations in fluids in the presence of a temperature gradient. The result is compared with earlier approaches to the same problem. Finally, we study the linear response to external forces and obtain a generalization of the fluctuation-dissipation formula relating the response functions with the nonequilibrium correlation functions.     

Hydrodynamical description of a hadron-quark first-order phase transition

Solutions of hydrodynamical equations are presented for the equation of state of the Van der Waals type allowing for a first-order phase transition. As an example we consider the hadron-quark phase transition in heavy-ion collisions. It is shown that fluctuations dissolve and grow as if the fluid is effectively very viscous. In the vicinity of the critical point even in spinodal region seeds are growing slowly due to viscosity, surface tension and critical slowing down. These non-equilibrium effects prevent enhancement of fluctuations in the near-critical region, which in thermodynamical approach is frequently considered as a signal of the critical endpoint in heavy-ion collisions.     

Probing structural relaxation in complex fluids by critical fluctuations

Complex fluids, such as polymer solutions and blends, colloids, and gels, are of growing interest in fundamental and applied soft-condensed-matter science. A common feature of all such systems is the presence of a mesoscopic structural length scale intermediate between the atomic and macroscopic scales. This mesoscopic structure of complex fluids is often fragile and sensitive to external perturbations. Complex fluids are frequently viscoelastic (showing a combination of viscous and elastic behavior), with their dynamic response depending on the time and length scales. Recently, noninvasive methods to infer the rheological response of complex fluids have gained popularity through the technique of microrheology, where the diffusion of probe spheres in a viscoelastic fluid is monitored with the aid of light scattering or microscopy. Here, we propose an alternative to traditional microrheology that does not require doping of probe particles in the fluid (which can sometimes drastically alter the molecular environment). Instead, our proposed method makes use of the phenomenon of “avoided crossing” between modes associated with the structural relaxation and critical fluctuations that are spontaneously generated in the system.     

Simulation of phase transitions in highly asymmetric fluid mixtures

We present a novel method for the accurate numerical determination of the phase behavior of fluid mixtures having large particle-size asymmetries. By incorporating the recently developed geometric cluster algorithm within a restricted Gibbs ensemble, we are able to probe directly the density and concentration fluctuations that drive phase transitions, but that are inaccessible to conventional simulation algorithms. We develop a finite-size scaling theory that relates these density fluctuations to those of the grand-canonical ensemble, thereby enabling accurate location of critical points and coexistence curves of multicomponent fluids. Several illustrative examples are presented.     

An equation of state contribution for dipolar and quadrupolar square-well fluids

A dipolar–quadrupolar contribution to the residual Helmholtz energy for a polar square well (a square well plus either a point dipole or a point quadrupole) fluid is developed based on the Padé approximation. Taking the square well system as reference, the contribution is formulated using an expansion for radial distribution function of the reference system. In addition to square well potential parameters the contribution depends only on dipole and quadrupole moments. This term is added as perturbation to a generalized equation of state for square well fluids. The results are then compared with the available simulation data in the literature. With the new equation obtained, it was possible to predict liquid–vapour equilibrium properties and critical properties of polar square well fluids more accurately than with available perturbation theories for multipolar square well systems. Application of the equation of state to a real dipolar (water) and a real quadrupolar (carbon dioxide) fluid indicated that the polar contribution greatly improved the predictions of saturation properties. Accurate prediction of critical properties for polar square well fluids remains as a challenge. This work can be useful in the development of better equations of state.     

Effect of local field fluctuations on orientational ordering in random-site dipole systems

Some peculiarities of dipole ordering in systems with uniaxial or cubic anisotropy with an arbitrary degree of dilution are analyzed in terms of random local field theory. The approach takes into account the effect of thermal and spatial fluctuations of the local fields acting on each particle from its neighbors with an accuracy corresponding to that of the Bethe-Paierls pair clusters approach. We show that ferromagnetic (ferroelectric) structure for uniaxial Ising dipoles distributed on a simple cubic lattice is intrinsically unstable against the fluctuations of the local fields for any concentration of the dipoles. This result is quite different from the prediction of the mean-field theory which implies the possibility of ferromagnetic ordering as a metastable state in field-cooled experiments. The local field fluctuations do not exclude, however, antiferromagnetic ordering above a certain critical concentration. Ferromagnetic ordering is possible for other types of lattice geometries and for an amorphous-like dipole distribution above a certain critical concentration. A simple physical explanation of such behavior is given based on the specific angular dependence of the dipole-dipole interaction that results in a relatively high value of the local field second moment for simple cubic lattice.     

Magnetic fluids in an external field

Within mean field approximation we investigate the phase diagrams of magnetic fluids in presence of a magnetic field. In a finite field the magnetic phase transition is absent, but instead a line of first order liquid-liquid transitions ending in a critical point occurs for a magnetic interaction, which is sufficiently strong. Varying the magnetic field these critical points extend from the tricritical point at H=0 to a critical endpoint. For a fluid with Ising spins we calculate the critical lines and several tricritical exponents analytically. For Heisenberg fluids we obtain the phase diagrams from a numerical solution of the mean field equations of state. Received 20 March 1998     

Thermal plumes and convection in highly compressible fluids

We present simple hydrodynamic equations of supercritical fluids close to the gas-liquid critical point. We numerically solve them to examine plume generation and convection under gravity. These results are in good agreement with the experiment [A. B. Kogan and H. Meyer, Phys. Rev. E 63, 056310 (2001)]. This Letter is a first study of transient behavior of convection, which is unique in compressible fluids due to the piston effect.     

Structure of supercritical water: The concept of critical isotherm as a percolation threshold

Computer simulations are used to study the rearrangements of hydrogen-bonded structures of water upon transition to the supercritical state. It is shown that the destruction of the infinite hydrogen-bonded cluster, i.e., crossing the percolation threshold occurs in the subcritical region and that, at the critical temperature, structural variations reach the point where the fluid acquires the properties of a system with two types of ordering. The existence of tetrahedral clusters in supercritical water is confirmed only at high pressure.