Theory Of Classical Fluids Research Articles

Mean-field theory of inhomogeneous fluids.

The Barker-Henderson perturbation theory is a bedrock of liquid-state physics, providing quantitative predictions for the bulk thermodynamic properties of realistic model systems. However, this successful method has not been exploited for the study of inhomogeneous systems. We develop and implement a first-principles "Barker-Henderson density functional," thus providing a robust and quantitatively accurate theory for classical fluids in external fields. Numerical results are presented for the hard-core Yukawa model in three dimensions. Our predictions for the density around a fixed test particle and between planar walls are in very good agreement with simulation data. The density profiles for the free liquid vapor interface show the expected oscillatory decay into the bulk liquid as the temperature is reduced toward the triple point, but with an amplitude much smaller than that predicted by the standard mean-field density functional.

Analysis of dynamic characteristics of two-component granular mixture segregation in thin shear cell

Particle separation is important in industrial production. The granular powder exhibits the property that is like both fluid property and solid property, which makes it difficult to establish a mathematical model to reveal the particle motion mechanism. The fluid property of the granular powder can be partly explained by the classical fluid theory, but the solid property cannot be covered. Theories combining the fluid and solid properties are also used to explain the particle separation phenomenon. However, they are not in consensus about the granular theory to explain the particle separation mechanism. Friction dissipation, which represents the particle pairwise damp interactions, greatly influences the particle separation process. In order to understand the particle separation mechanism and the effect of friction coefficient on the particle motion, a three-dimensional discrete element model is used to simulate the separation of three-dimensional spherical binary particles in a cylindrical groove （shear cell）in this paper. Initially, the large particle is placed at the bottom and the other small particles pile into the groove. The shear flow of the particles is established by rotating the bottom plate of the groove. The large particles gradually jump to the top of the groove under the shearing action. The effect of particle friction coefficient on the separation is studied. Focusing on the characteristics of kinematics and dynamics in the jumping process of large particle, the influence of the friction coefficient on the trajectory, velocity and acceleration of particle are quantitatively analyzed. The conclusions are obtained as follows. 1) The process of large particle jumping can be divided into three stages: relaxation stage (the large particle stays at the bottom of the groove), the take-off stage (the large particle rises up), and the equilibrium stage(the large particle moves to the top and stays there). 2) The relaxation time decreases with friction coefficient increasing. 3) The equilibrium height of particles increases with friction coefficient increasing. 4) The amplitude of the force pulsation of the large particle increases with friction coefficient increasing. For the behavior analysis of the ascending motion of the large particle, we propose a neighborhood analysis method and define a floating factor. The ratio of the number of small particles arranged in the upper to that in the lower adjacent space of the large particle is defined as the buoyancy factor. It is found that the buoyancy factor drops sharply at the jumping point of the large particle, forming the opportunity for the large particle jumping. It is revealed that the take-off of the large particle is the result of both the high-frequency characteristics of force fluctuation and the steep drop of buoyancy factor. The rising motion of the big particle is determined by the force and the surrounding space.

General relativity as a unified fluid and field theory

Einstein’s dream for a unified field theory of Nature is attained with a classical fluid theory founded on space, time and spin, rather than on Einstein’s spacetime. An invariant quantum theory for the primordial fluid obeys the homogeneous Klein-Gordon equation, which is the same three-dimensional classical wave equation (CWE) initially tried by Schrödinger to formulate quantum mechanics (QM), but abandoned by linear superposition considerations. Primordial fluid pervades universe, obeys energy and momentum conservation, and is formed by sagions: energy-like, discrete, extended Planck-size objects of finite size, carriers of linear momentum and spin, moving in absolute 3D-curved space with speed C along straightest path. We briefly describe our novel non-harmonic and inherently quantized solutions for CWE in spherical coordinates, discovered in 1995. Solutions include a steady-state background field (possibly related to the CMB, to non-locality, and to action-at-a-distance), quantized helices, and inherently quantized functions exhibiting stable dynamic equilibrium, and isomorphism under many transformations, including the classical Doppler case, and the relativistic Lorentz, Poincaré, and Einstein transformations. Isomorphism pre-empts ab initio a few interpretative issues regarding relativistic and classical transformations. Mathematical fields represent the realistic physical temporal evolution of the primordial fluid in curved 3D-space.

Fluid State of Dirac Quantum Particles

In our previous works, we suggest that quantum particles are composite physical objects endowed with the geometric and topological structures of their corresponding differentiable manifolds that would allow them to imitate and adapt to physical environments. In this work, we show that Dirac equation in fact describes quantum particles as composite structures that are in a fluid state in which the components of the wavefunction can be identified with the stream function and the velocity potential of a potential flow formulated in the theory of classical fluids. We also show that Dirac quantum particles can manifest as standing waves which are the result of the superposition of two fluid flows moving in opposite directions. However, for a steady motion a Dirac quantum particle does not exhibit a wave motion even though it has the potential to establish a wave within its physical structure, therefore, without an external disturbance a Dirac quantum particle may be considered as a classical particle defined in classical physics. And furthermore, from the fact that there are two identical fluid flows in opposite directions within their physical structures, the fluid state model of Dirac quantum particles can be used to explain why fermions are spin-half particles.

Potential of mean force for electrical conductivity of dense plasmas

The electrical conductivity in dense plasmas can be calculated with the relaxation-time approximation provided that the interaction potential between the scattering electron and the ion is known. To date there has been considerable uncertainty as to the best way to define this interaction potential so that it correctly includes the effects of ionic structure, screening by electrons and partial ionization. Current approximations lead to significantly different results with varying levels of agreement when compared to bench-mark calculations and experiments. We present a new way to define this potential, drawing on ideas from classical fluid theory to define a potential of mean force. This new potential results in significantly improved agreement with experiments and bench-mark calculations, and includes all the aforementioned physics self-consistently.

Current and future prospects for the application of systematic theoretical methods to the study of problems in physical oceanography

This essay is a commentary on the pivotal role of systematic theoretical methods in physical oceanography. At some level, there will always be a conflict between theory and experiment/data collection: Which is pre-eminent? Which should come first? This issue appears to be particularly marked in physical oceanography, to the extreme detriment of the development of the subject. It is our contention that the classical theory of fluids, coupled with methods from the theory of differential equations, can play a significant role in carrying the subject, and our understanding, forward. We outline the philosophy behind a systematic theoretical approach, highlighting some aspects of equatorial ocean dynamics where these methods have already been successful, paving the way for much more in the future and leading, we expect, to the better understanding of this and many other types of ocean flow. We believe that the ideas described here promise to reveal a rich and beautiful dynamical structure.

Resonance Analysis of High-Frequency Electrohydraulic Exciter Controlled by 2D Valve

The resonant characteristic of hydraulic system has not been described yet because it is necessarily restricted by linear assumptions in classical fluid theory. A way of the resonance analysis is presented for an electrohydraulic exciter controlled by 2D valve. The block diagram of this excitation system is established by extracting nonlinear parts from the traditional linearization analysis; as a result the resonant frequency is obtained. According to input energy from oil source which is equal to the reverse energy to oil source, load pressure and load flow are solved analytically as the working frequency reaches the natural frequency. The analytical expression of resonant peak is also derived without damping. Finally, the experimental system is built to verify the theoretical analysis. The initial research on resonant characteristic will lay theoretical foundation and make useful complement for resonance phenomena of classical fluid theory in hydraulic system.

MICROPOLAR FLUID MODEL FOR BLOOD FLOW THROUGH A STENOSED ARTERY

Various experimental observations have demonstrated that the classical fluid theory is incapable of explaining many phenomena at micro and nano scales. On the other hand, micropolar fluid dynamics can naturally pick up the physical phenomena at these scales owing to its additional degrees of freedom caused by incorporating the effects of fluid molecules on the continuum. Therefore, one of the aims of this paper is to investigate the applicability of the theory of micropolar fluids to modeling and calculating flows in circular microchannels depending on the geometrical dimension of the flow field. Hence, a finite element formulation for the numerical analysis of micropolar laminar fluid flow is developed. In order to validate the results of the FE formulation, the analytical and exact solution of the micropolar Hagen–Poiseuille flow in a circular microchannel is presented, and an excellent agreement between the results of the analytical solution and those of the FE formulation is observed. It is also shown that the micropolar viscosity and the length scale parameter have significant roles on changing the flow characteristics. Then, the behavior of an incompressible viscous fluid flow such as blood flow in a stenosed artery, having multiple kinds of stenoses, is investigated. The obtained results are compared to the results reported in the literature, and an excellent agreement is observed.

On the trail of the 2-body reduced density matrix

A brief review is made of developments in the theory of reduced density matrix estimation of fermion system properties, to which John Coleman contributed enormously. Emphasis is placed upon those constraints that are peculiar to the system in question, as well as to those of “universal” validity. The former are typically obtained by following the consequences of the insertion or deletion of one of the particles of the system, and, for example, the PY equation of classical fluid theory is identified as the “saturation” of a valid inequality. An analogous process for fermion systems is introduced but not carried out very far.

Density functional theory for the ground state of spherically confined dusty plasma

The spatial structure of dusty plasma confined in a spherical microcavity has been investigated by use of the density functional theory for classical fluids, in which all particles undergo an isotropic harmonic potential and the interparticle interaction is described by the hard-core Yukawa potential. The fundamental measure theory of Rosenfeld and its modified versions have been used in the energy functional to incorporate hard-core interactions between particles. Based on the variational principle, the equilibrium density profile can be obtained by use of an iteration calculation with the average density of particles as an input. In terms of density profiles presented under various conditions, the roles of the trapped parameter, coupling parameter, screening parameter, and the average number density of particles are discussed, and significant influences of these factors on the structure of confined dusty plasma are found.

L. Peliti: Statistical Mechanics in a Nutshell

Drawing from his considerable involvement as a researcher in the field, and from his teaching notes on the subject for over 15 years, Luca Peliti had put together a remarkably selfcontained and comprehensive, introductory textbook, Appunti di Meccanica Statistica (Bollati Boringhieri 2003). The recent English translation, “Statistical Mechanics in a Nutshell” (by Mark Epstein, from the original Italian), fits very nicely in the new In a Nutshell Princeton series, conceived to provide “concise, accessible, and up-to-date textbooks for advanced undergraduate and graduate students on key subjects in the physical sciences.” The book is in fact almost more of a reference book than a traditional textbook. Though limited to the putative syllabus for a course in statistical mechanics, it is exceptionally comprehensive in scope. Following a brief motivational introduction, utilizing the example of an ideal gas, in Chap. 1, classical thermodynamics is broadly reviewed, in Chap. 2, including the more obscure thermodynamic potentials related to particle number, and the useful Koenig-Born diagram trick for quickly deriving all pertinent Maxwell relations. The statistical mechanical approach, the partition function for different probability ensembles, and the basic application of this machinery to interaction-free systems of Bosons and Fermions is expounded upon in Chaps. 3 and 4. Chapter 5 looks at the liquid-gas transition, as described by the Van der Waals equation and the lattice gas (or Ising) model, and uses this example for the introduction of basic concepts such as critical exponents, universality, and scaling, as well as techniques, including mean-field and Landau theory, and culminating with an exact solution of the 2-dimensional Ising model. These first five chapters comprise the standard material found in many other textbooks on the subject, though none equals the present book in its thoroughness and scope. Chapter 6 discusses renormalization group theory, reviewing all the major techniques and approaches. The theory of classical fluids and the virial expansion (sometimes included in other texts) is covered in Chap. 7. Chapter 8 introduces numerical simulations, molecular dynamics and the Monte Carlo method. Brownian and Generalized Brownian motion is discussed in Chap. 9, and is used to introduce

Renormalized Kinetic Theory of Classical Fluids in and out of Equilibrium

We present a theory for the construction of renormalized kinetic equations to describe the dynamics of classical systems of particles in or out of equilibrium. A closed, self-consistent set of evolution equations is derived for the single-particle phase-space distribution function $f$, the correlation function $C=<\delta f\delta f >$, the retarded and advanced density response functions $\chi^{R,A}=\delta f/\delta\phi$ to an external potential $\phi$, and the associated memory functions $\Sigma^{R,A,C}$. The basis of the theory is an effective action functional $\Omega$ of external potentials $\phi$ that contains all information about the dynamical properties of the system. In particular, its functional derivatives generate successively the single-particle phase-space density $f$ and all the correlation and density response functions, which are coupled through an infinite hierarchy of evolution equations. Traditional renormalization techniques are then used to perform the closure of the hierarchy through memory functions. The latter satisfy functional equations that can be used to devise systematic approximations. The present formulation can be equally regarded as (i) a generalization to dynamical problems of the density functional theory of fluids in equilibrium and (ii) as the classical mechanical counterpart of the theory of non-equilibrium Green's functions in quantum field theory. It unifies and encompasses previous results for classical Hamiltonian systems with any initial conditions. For equilibrium states, the theory reduces to the equilibrium memory function approach. For non-equilibrium fluids, popular closures (e.g. Landau, Boltzmann, Lenard-Balescu) are simply recovered and we discuss the correspondence with the seminal approaches of Martin-Siggia-Rose and of Rose.and we discuss the correspondence with the seminal approaches of Martin-Siggia-Rose and of Rose.

Density Functional Theory Approach for Charged Hard Sphere Fluids Confined in Spherical Micro-Cavity

Within the framework of the density functional theory for classical fluids, the equilibrium density profiles of charged hard sphere fluid confined in micro-cavity are studied by means of the modified fundamental measure theory. The dimension of micro-cavity, the charge of hard sphere and the applied electric field are found to have significant effects on the density profiles. In particular, it is shown that Coulomb interaction, excluded volume interaction and applied electric field play the central role in controlling the aggregated structure of the system.

Energy exchange rate for the equatorial electrojet: Test of the model of two-stream processes that includes thermal corrections

[1] The experiment of Balsley and Farley (1971) in Jicamarca, Peru has been the only multi(3)-frequency investigation of the equatorial electrojet. The radar was operated sequentially at frequencies of 16.25, 49.92 and 146.25 MHz and probed the same ionospheric volume. The most prominent feature of these observations was the increase in the phase velocity Vph of Farley-Buneman (FB) waves with increasing radar frequency while the classical fluid theory gives Vph independent on their wavelength and the simple kinetic theory accounts for only a small increase in Vph. Our recent theory predicts a wavenumber dependence of the FB wave phase velocity. The rate of increase depends on the altitude of the electrojet and seems to match the observed wave behavior. The most important byproduct of this case study is our conclusion that the energy exchange rate in inelastic electron-neutral interactions is about two-to-three times higher that it has been assumed in estimates.

Time-Dependent Density Functional Theory of Classical Fluids

We establish a rigorous time-dependent density functional theory of classical fluids for a wide class of microscopic dynamics. We obtain a stationary action principle for the density. We further introduce an exact practical scheme, to obtain hydrodynamical effects in density evolution, that is analogous to the Kohn-Sham theory of quantum systems. Finally, we show how the current theory recovers existing phenomenological theories in an adiabatic limit.

Phase behavior of polypropylene + n-pentane and polypropylene + n-pentane + carbon dioxide: modeling with cubic and non-cubic equations of state

The phase behavior of polypropylene (PP) + n-pentane ( nC 5) binary mixtures was modeled in order to determine the molecular weight influence by finding the cloud point pressures of PP (MW = 50,400 and 95,400) in high-pressure nC 5. Besides, the cloud point pressure of PP (50,400) in nC 5–CO 2 mixtures was also determined. In this work, the non-cubic equation of state (EoS) perturbed chain statistical associating fluid theory (PC-SAFT) [J. Gross, G. Sadowski, Application of perturbation theory to a hard-chain reference fluid: an equation of state for square-well chains, Fluid Phase Equilib. 168 (2000) 183] and Sanchez and Lacombe (SL) [I. Sanchez, R. Lacombe, An elementary molecular theory of classical fluids. Pure fluids, J. Phys. Chem. 80 (1976) 2352] and the traditional Peng–Robinson (PR) [D.Y. Peng, D.B. Robinson, A new two constant equation of state, Ind. Eng. Chem. Fundam. 15 (1976) 59] cubic EoS were used to predict the cloud point pressures from experimental data [T.M. Martin, A.A. Lateef, C.B. Roberts, Measurements and modeling of cloud points behavior for polypropylene/ n-pentane and polypropylene/ n-pentane/carbon dioxide at high pressure, Fluid Phase Equilib. 154 (1999) 241; A. Leu, D.B. Robinson, Equilibrium phase properties of selected carbon dioxide binary systems: n-pentane–carbon dioxide and isopentane–carbon dioxide, J. Chem. Eng. Data 32 (1987) 447], by fitting one temperature-dependent binary interaction parameter ( κ ij ) for each binary system. The pure-component parameters of all models were obtained by fitting pure-component data [P.A. Rodgers, Pressure–volume–temperature relationships for polymeric liquids: a review of equations of state and their characteristic parameters for 56 polymers, J. Appl. Polym. Sci. 48 (1993) 1061; DIPPR, Information and Data Evaluation Manager, Public Version 1.2.0, 2000]. The estimation of pure-component and binary interaction parameters was performed by using the maximum likelihood method. Good results were obtained with the PC-SAFT EoS, while the performance of the SL and PR EoS were less satisfactory.

A new statistical mechanical formalism for gases

An equilibrium theory of classical fluids based on the space distribution among the particles is derived in the framework of the energy minimization method. This study is motivated by current difficulties of evaluation of optical properties in atmospheres of degenerate stars. Present paper focuses on diluted one-component systems, where the interaction energy is calculated as a sum of binary contributions. The spatial configuration of the gas is described in terms of a particle-state variable v which roughly measures the free space surrounding each particle. The formalism offers a unified treatment of both thermodynamics and structure of fluids, since it not only provides the state function (the Helmholtz free energy) of a fluid, but also automatically gives information on the microstructure of the system (e.g. the nearest-neighbor distribution function). Equations of state and nearest-neighbor distribution functions of perfect and hard-body fluids are obtained in straightforward way in one, two and three dimensions. The formalism is applied to describe the atomic population in a partially ionized hydrogen gas. Combined and self-consistent evaluations of atomic populations and internal effects on bound states are performed in a detailed form. The present theory allow us to resolve the atomic density at each internal level into groups of atoms which experiment different perturbation intensities according to the size of their spaces v.

The density functional theory of classical fluids revisited

We reconsider the density functional theory of nonuniform classical fluids from the point of view of convex analysis. From the observation that the logarithm of the grand-partition function $\log \Xi [\phi]$ is a convex functional of the external potential $\phi$ it is shown that the Kohn-Sham free energy ${\cal A}[\rho]$ is a convex functional of the density $\rho$. $\log \Xi [\phi]$ and ${\cal A}[\rho]$ constitute a pair of Legendre transforms and each of these functionals can therefore be obtained as the solution of a variational principle. The convexity ensures the unicity of the solution in both cases. The variational principle which gives $\log \Xi [\phi]$ as the maximum of a functional of $\rho$ is precisely that considered in the density functional theory while the dual principle, which gives ${\cal A}[\rho]$ as the maximum of a functional of $\phi$ seems to be a new result.

Approximate integral equation theory for classical fluids

A new approximate integral equation with no empirical or adjustable parameters which was recently proposed [J. Chem. Phys. 110, 3961 (1999)] is used for the systematic study of Lennard-Jones fluid. The Ornstein–Zernike (OZ) equation designed originally to describe the thermodynamically stable states is substantiated to be valid also for predicting and studying the metastable states. Both stable and metastable solutions of the OZ equation are analyzed. The problem of determining the chemical potential is considered within the framework of the exact series of the bridge functionals. The structure and thermodynamic properties calculated from proposed approaches show excellent agreement with simulations for both stable and metastable states. Displayed and discussed is the gas–liquid phase diagram predicted by the new equation. Also, to build the liquid–crystal phase diagram some one-phase empirical structural criteria are utilized.

Equivalence of two approaches for the inhomogeneous density in the canonical ensemble

In this Brief Report we show that the inhomogeneous density obtained from a density-functional theory of classical fluids in the canonical ensemble (CE), recently presented by White et al. [Phys. Rev. Lett. 84, 1220 (2000)], is equivalent to first order to the result of the series expansion of the CE inhomogeneous density introduced by Gonzalez et al. [Phys. Rev. Lett. 79, 2466 (1997)].