Thermodynamics of the Stockmayer fluid in an applied field

The thermodynamic properties of the Stockmayer fluid in an applied field are studied using theory and computer simulation. Theoretical expressions for the second and third virial coefficients are obtained in terms of the dipolar coupling constant (λ, measuring the strength of dipolar interactions as compared to thermal energy) and dipole–field interaction energy (α, being proportional to the applied field strength). These expressions are tested against numerical results obtained by Mayer sampling calculations. The expression for the second virial coefficient contains terms up to λ⁴, and is found to be accurate over realistic ranges of dipole moment and temperature, and over the entire range of the applied field strength (from zero to infinity). The corresponding expression for the third virial coefficient is truncated at λ³, and is not very accurate: higher order terms are very difficult to calculate. The virial coefficients are incorporated in to a thermodynamic theory based on a logarithmic representation of the Helmholtz free energy. This theory is designed to retain the input virial coefficients, and account for some higher order terms in the sense of a resummation. The compressibility factor is obtained from the theory and compared to results from molecular dynamics simulations with a typical value λ = 1. Despite the mathematical approximations of the virial coefficients, the theory captures the effects of the applied field very well. Finally, the vapour–liquid critical parameters are determined from the theory, and compared to published simulation results; the agreement between the theory and simulations is good.     

Thermodynamics of a long-range triangle-well fluid

The long-range triangle-well fluid has been studied using three different approaches: firstly, by an analytical equation of state obtained by a perturbation theory, secondly via a self-consistent integral equation theory, the so-called self-consistent Ornstein–Zernike approach (SCOZA) which is presently one of the most accurate liquid-state theories, and finally by Monte Carlo simulations. We present vapour–liquid phase diagrams and thermodynamic properties such as the internal energy and the pressure as a function of the density at different temperatures and for several values of the potential range. We assess the accuracy of the theoretical approaches by comparison with Monte Carlo simulations: the SCOZA method accurately predicts the thermodynamics of these systems and the first-order perturbation theory reproduces the overall thermodynamic behaviour for ranges greater than two molecular diameters except that it overestimates the critical point. The simplicity of the equation of state and the fact that it is analytical in the potential range makes it a good candidate to be used for calculating other thermodynamic properties and as an ingredient in more complex theoretical approaches.     

The green function of an infinite,fluid loaded membrane

In this paper the response of a fluid loaded plane structure (a membrane) to a concentrated line force excitation is considered in great detail. The normalized velocity response—here called the Green function G—depends upon a dimensionless range x₀=k_m|x|, where k_m is the free wavenumber on the membrane in a vacuum, on the Mach number $\text{M=}\text{k}{}_0\text{k}{}_{\mathrm{m}}$, the ratio of wave phase speed ω/k_m on the unloaded membrane to the sound speed ω/k₀, and on a parameter ? which can be regarded as a measure of fluid loading at the “coincidence” condition M=1. In the analogous problem involving a thin elastic plate, the corresponding parameter is independent of frequency and plate thickness and may be regarded as an intrinsic measure of fluid loading; moreover, in cases of common interest (steel in water, aluminium in air) that parameter is small. In the present paper, the asymptotic structure of G(x₀, M, ?) is therefore sought in the limit ? → 0. Naturally, no single asymptotic expansion can be expected to be valid throughout the (x₀, M) plane, and the programme therefore involves the delineation of regions of that plane in which distinct asymptotic results apply, the construction and discussion of those results, and the asymptotic matching (according to the procedures of the method of matched asymptotic expansions) of results holding in adjoining regions. The Fourier integral for G is broken into surface wave and acoustic components, and the asymptotic structure obtained for each. Previously obtained results for the behaviour at large distances are recovered, with a demonstration that very large distances indeed (x₀ ? ?^?2) may be needed for their validity for some ranges of M; and the drive point behaviour, of G(x₀=0, M, ?) as ? → 0 qua function of M, is shown to correspond to that already discussed in the literature. Elsewhere, in the covering of the whole (x₀, M) plane by different asymptotic expressions, a wide variety of analytical results is found, reflecting the achievement in different regions of different balances among the five competing physical mechanisms represented in the model: namely, structural stiffness, structural inertia, fluid pressures, fluid compressibility and fluid inertia. These different balances give rise to a wide variety of expressions for the phase and amplitude of the surface wave and acoustic components which can now be used to isolate the dominant structural and acoustic mechanisms at any point in the (x₀, M) plane.     

The thermoelectric working fluid: Thermodynamics and transport

Thermoelectric devices are heat engines, which operate as generators or refrigerators using the conduction electrons as a working fluid. The thermoelectric heat-to-work conversion efficiency has always been typically quite low, but much effort continues to be devoted to the design of new materials boasting improved transport properties that would make them of the electron crystal–phonon glass type of systems. On the other hand, there are comparatively few studies where a proper thermodynamic treatment of the electronic working fluid is proposed. The present article aims at contributing to bridge this gap by addressing both the thermodynamic and transport properties of the thermoelectric working fluid covering a variety of models, including interacting systems.     

Thermodynamics of the λ line in binary fluid mixtures

Thermodynamics of the λ line, variations on a theme by Wheeler and Griffiths, have been presented.     

Third-order Stokes wave solutions for interfacial internalwaves in three-layer dendity-stratified fluid

<正>Interfacial internal waves in a three-layer density-stratified fluid are investigated using a singular perturbation method,and third-order asymptotic solutions of the velocity potentials and third-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory.As expected,the third-order solutions describe the third-order nonlinear modification and the third-order nonlinear interactions between the interfacial waves.The wave velocity depends on not only the wave number and the depth of each layer but also on the wave amplitude.     

Thermodynamics predicts how confinement modifies the dynamics of the equilibrium hard-sphere fluid

We study how confining the equilibrium hard-sphere fluid to restrictive one- and two-dimensional channels with smooth interacting walls modifies its structure, dynamics, and entropy using molecular dynamics and transition-matrix Monte Carlo simulations. Although confinement strongly affects local structuring, the relationships between self-diffusivity, excess entropy, and average fluid density are, to an excellent approximation, independent of channel width or particle-wall interactions. Thus, thermodynamics can be used to predict how confinement impacts dynamics.     

A hybrid numerical method for interfacial fluid flow with soluble surfactant

We address a significant difficulty in the numerical computation of fluid interfaces with soluble surfactant that occurs in the physically representative limit of large bulk Peclet number Pe. At the high values of Pe in typical fluid-surfactant systems, there is a transition layer near the interface in which the surfactant concentration varies rapidly, and large gradients at the interface must be resolved accurately to evaluate the exchange of surfactant between the interface and bulk flow. We use the slenderness of the layer to develop a fast and accurate ‘hybrid’ numerical method that incorporates a separate, singular perturbation analysis of the dynamics in the transition layer into a full numerical solution of the interfacial free boundary problem. The accuracy and efficiency of the method is assessed by comparison with a more ‘traditional’ numerical approach that uses finite differences on a curvilinear coordinate system exterior to the bubble, without the separate transition layer reduction. The traditional method implemented here features a novel fast calculation of fluid velocity off the interface.     

Stability of fluid flow past a membrane

The stability of the flow of a fluid past a solid membrane of infinitesimal thickness is investigated using a linear stability analysis. The system consists of two fluids of thicknesses R and H R and bounded by rigid walls moving with velocities and , and separated by a membrane of infinitesimal thickness which is flat in the unperturbed state. The fluids are described by the Navier-Stokes equations, while the constitutive equation for the membrane incorporates the surface tension, and the effect of curvature elasticity is also examined for a membrane with no surface tension. The stability of the system depends on the dimensionless strain rates and in the two fluids, which are defined as and for a membrane with surface tension , and and for a membrane with zero surface tension and curvature elasticity K. In the absence of fluid inertia, the perturbations are always stable. In the limit , the decay rate of the perturbations is O(k ³ ) smaller than the frequency of the fluctuations. The effect of fluid inertia in this limit is incorporated using a small wave number asymptotic analysis, and it is found that there is a correction of smaller than the leading order frequency due to inertial effects. This correction causes long wave fluctuations to be unstable for certain values of the ratio of strain rates and ratio of thicknesses H. The stability of the system at finite Reynolds number was calculated using numerical techniques for the case where the strain rate in one of the fluids is zero. The stability depends on the Reynolds number for the fluid with the non-zero strain rate, and the parameter , where is the surface tension of the membrane. It is found that the Reynolds number for the transition from stable to unstable modes, , first increases with , undergoes a turning point and a further increase in the results in a decrease in . This indicates that there are unstable perturbations only in a finite domain in the plane, and perturbations are always stable outside this domain. Received: 29 May 1997 / Revised: 9 October 1997 / Accepted: 26 November 1997     

Visualization of transient interfacial waves induced by spin-up of two immiscible fluid layers

Abstract  

Interfacial waves of two immiscible layers in a spin-up container were investigated using experimental visualization. While the interface near the central part rose up, instability waves propagated in an azimuthal direction on the interface. These waves were mainly caused by Kelvin–Helmholtz instability for the velocity difference between two layers during spin-up, but had complicated transient characteristics owing to the rotation in a closed system. We visualized the structure of the interfacial waves by the use of three types of optical characteristics of the interface. Image processing provided the detailed factors of the interfacial waves that were classified in four life stages from their generation to disappearance. The initial generation process involved many frequency modes due to a large velocity difference, and then a low mode stood out during the growth, and disappeared with an ellipsoidal sloshing mode to achieve the rigid rotation in both layers.     

Critical fluctuations of tense fluid membrane tubules

We show that, contrary to planar membranes under tension, tense membrane tubules exhibit important critical fluctuations originating from unidimensional Goldstone modes. The latter yield unexpected behavior, such as correlations extending over the whole tube length and the increase of the fluctuating area over the projected area with increasing tension.     

Second-order random wave solutions for interfacial internal waves in N-layer density-stratified fluid

This paper studies the random internal wave equations describing the density interface displacements and the velocity potentials of N-layer stratified fluid contained between two rigid walls at the top and bottom. The density interface displacements and the velocity potentials were solved to the second-order by an expansion approach used by Longuet-Higgins （1963） and Dean （1979） in the study of random surface waves and by Song （2004） in the study of second- order random wave solutions for internal waves in a two-layer fluid. The obtained results indicate that the first-order solutions are a linear superposition of many wave components with different amplitudes, wave numbers and frequencies, and that the amplitudes of first-order wave components with the same wave numbers and frequencies between the adjacent density interfaces are modulated by each other. They also show that the second-order solutions consist of two parts： the first one is the first-order solutions, and the second one is the solutions of the second-order asymptotic equations, which describe the second-order nonlinear modification and the second-order wave-wave interactions not only among the wave components on same density interfaces but also among the wave components between the adjacent density interfaces. Both the first-order and second-order solutions depend on the density and depth of each layer. It is also deduced that the results of the present work include those derived by Song （2004） for second-order random wave solutions for internal waves in a two-layer fluid as a particular case.     

A set of Boussinesq-type equations for interfacial internal waves in two-layer stratified fluid

Many new forms of Boussinesq-type equations have been developed to extend the range of applicability of the classical Boussinesq equations to deeper water in the study of the surface waves. One approach was used by Nwogu (1993. J. Wtrw. Port Coastal and Oc. Eng. 119, 618--638) to improve the linear dispersion characteristics of the classical Boussinesq equations by using the velocity at an arbitrary level as the velocity variable in derived equations and obtain a new form of Boussinesq-type equations, in which the dispersion property can be optimized by choosing the velocity variable at an adequate level. In this paper, a set of Boussinesq-type equations describing the motions of the interfacial waves propagating alone the interface between two homogeneous incompressible and inviscid fluids of different densities with a free surface and a variable water depth were derived using a method similar to that used by Nwogu (1993. J. Wtrw. Port Coastal and Oc. Eng. 119, 618--638) for surface waves. The equations were expressed in terms of the displacements of free surface and density-interface, and the velocity vectors at arbitrary vertical locations in the upper layer and the lower layer (or depth-averaged velocity vector across each layer) of a two-layer fluid. As expected, the equations derived in the present work include as special cases those obtained by Nwogu (1993, J. Wtrw. Port Coastal and Oc. Eng. 119, 618-638) and Peregrine (1967, J. Fluid Mech. 27, 815-827) for surface waves when the density of the upper fluid is taken as zero.     

Thermodynamics and transport in an active Morse ring chain

We investigate the stochastic dynamics of an one-dimensional ring with N self-driven Brownian particles. In this model neighboring particles interact via conservative Morse potentials. The influence of the surrounding heat bath is modeled by Langevin-forces (white noise) and a constant viscous friction coefficient γ. The Brownian particles are provided with internal energy depots which may lead to active motions of the particles. The depots are realized by an additional nonlinearly velocity-dependent friction coefficient γ ₁(v) in the equations of motions. In the first part of the paper we study the partition functions of time averages and thermodynamical quantities (e.g. pressure) characterizing the stationary physical system. Numerically calculated non-equilibrium phase diagrams are represented. The last part is dedicated to transport phenomena by including a homogeneous external force field that breaks the symmetry of the model. Here we find enhanced mobility of the particles at low temperatures. Received 21 July 2001