Byung Chan Eu

McGill University | McGill · Department of Chemistry

We have reviewed thermodynamically consistent evolution equations of fluids in an invited review article in the McGill University bicentennial memorial issue [B. C. Eu, Can. J. Chem. (in press) (2021)]. In this article, we apply the generalized hydrodynamic evolution equations of heat fluxes to derive integral equations for thermal conductivity coe...

In this article, a review is presented of the thermodynamic theory of irreversible processes, based on the Clausius inequality representative of the literal forms of the second law of thermodynamics as stated by Kelvin and Clausius. Generalized hydrodynamic equations in conformation to the law are presented for transport processes in fluids removed...

This book enables the reader to learn, in a single volume, equilibrium and nonequilibrium thermodynamics as well as generalized forms of hydrodynamics for linear and nonlinear processes applied to various hydrodynamic flow processes - including chemical oscillation phenomena and pattern formations, shock wave phenomena, sound wave propagations, and...

Normal stress effects are investigated on tube flow of a single-component non-Newtonian fluid under a constant pressure gradient in a constant temperature field. The generalized hydrodynamic equations are employed, which are consistent with the laws of thermodynamics. In the cylindrical tube flow configuration, the solutions of generalized hydrodyn...

In this work, we are interested in a molecular theory (i.e., statistical mechanics) of time- and space-dependent nonequilibrium (irreversible) processes in matter regarded as composed of many discrete particles.

We have shown in Chap. 3 that, if the concept of calortropy is made use of in place of the Boltzmann entropy, the Boltzmann equation [1] is capable of providing a satisfactory formalism for a theory of irreversible processes in dilute monatomic fluids and the attendant generalized hydrodynamics in a manner consistent with the laws of thermodynamics...

Although controversial initially because of its irreversibility that contradicts the time reversal invariance of mechanical equations from which it was perceived to have descended, Boltzmann’s kinetic equation [1] has drawn enduring attractions from kinetic theorists owing to its alluring features for studying nonequilibrium phenomena in gases and...

The generalized hydrodynamic equations derived from various kinetic equations for nonequilibrium ensembles in the previous chapters are capable of describing transport processes and hydrodynamic phenomena in fluids.

The nonequilibrium thermophysical properties, typical examples being transport coefficients, of liquid mixtures are not only important as molecular properties of liquids but also essential for understanding nonequilibrium phenomena in physical, chemical, and biological systems in condensed phase.

In Chap. 6 we have confined the formulation of the kinetic theory to a pure dense fluid for simplicity of formulation. To develop a theory of irreversible thermodynamics in a general form covering liquid mixtures it is now necessary to generalize the theories formulated in the previous chapters. It is possible to achieve this goal if we first formu...

The statistical mechanical theories of transport processes and attendant irreversible thermodynamics presented in the previous chapters are formal and their computational implementation to make them compared with experiments would require knowledge of dynamics of many particles in the phase space.

Once we accept the particulate concept of matter it is inevitable to try to understand thermodynamics and thermodynamic processes in continuum systems in terms of atoms and molecules constituting matter, and formulate molecular theories of macroscopic processes and thermodynamics. To this aim, statistical mechanics or, rather, kinetic theory of mat...

In Chap. 5, we have glimpsed into the possibility that the Boltzmann equation may be an archetype, but only in a special form, of irreversible kinetic equation for fluids, after which the kinetic equation for dense fluids of correlated particles may be fashioned and therewith the Gibbs ensemble theory can be formulated for time-dependent irreversib...

This chapter consists of two separate sections: (1) Integral Equation Method for Pair Correlation Functions and (2) Pair Correlation Function in the Subcritical Regimes. The two sections discuss pair correlation functions on quite different aspects.

In this chapter we make an important departure from the approach taken in Chaps. 3, 5, 6 and 7 of Volume 1 in which nonrelativistic kinetic equations have been discussed for gases and liquids. Now we consider relativistic kinetic equations for dilute uncorrelated particle systems.

In this chapter we apply the covariant kinetic theory of quantum dilute relativistic gases developed in Chap. 2 of this Volume and, in particular, the theory of transport processes to explicitly calculate transport coefficients of photons interacting with matter. A model will be taken for collision processes so as to facilitate explicit computation...

The relativistic kinetic theory of irreversible processes in a system of matter presented in Chap. 1 of this volume is generalized to include radiation in this chapter.

This book presents the fundamentals of irreversible thermodynamics for nonlinear transport processes in gases and liquids, as well as for generalized hydrodynamics extending the classical hydrodynamics of Navier, Stokes, Fourier, and Fick. Together with its companion volume on nonrelativistic contexts, it provides a comprehensive picture of the rel...

This book presents the fundamentals of irreversible thermodynamics for nonlinear transport processes in gases and liquids, as well as for generalized hydrodynamics extending the classical hydrodynamics of Navier, Stokes, Fourier, and Fick. Together with its companion volume on relativistic theories, it provides a comprehensive picture of the kineti...

In this paper, on the basis of the Onsager--Wilson theory of strong binary electrolyte solutions we completely work out the solutions of the governing equations (Onsager-Fuoss equations and Poisson equations) for nonequilibrium pair correlation functions and ionic potentials and the solutions for the Stokes equation for the velocity and pressure in...

In the preceding paper, the exact solution of Stokes equation was obtained for a binary strong electrolyte solution in an external electric field. In the present paper, the solution is applied to calculate the Wien effect on deviation from the Coulombic law of conduction in high fields. One of the important aims of the present line of work was in r...

We present an improved version of the recently introduced formulas for the self-diffusion coefficient in the modified free volume theory of diffusion in simple fluids of particles interacting with Lennard-Jones potential. A suitable modification of the soft sphere levitation diameter and the replacement of the hard sphere radius with the Chapman–En...

A method of improving the uniform WKB solution for single turning point problems is discussed and the correction formulas for the WKB phase shifts are obtained. The method involves the equation of motion which is in a form similar to that used by Fröman and Fröman to obtain the connection formulas in the WKB approximation. A sequence of solutions t...

We present tables for self-diffusion coefficients of the Lennard-Jones liquids and gases for various model formulas in the modified free volume theory of diffusion in the case of reduced temperatures $T^{\ast}=6.0$, 4.0, 1.3, 1.0, 0.8, 0.7 with reduced density ranging from $\rho^{\ast}=0.025$ to 1. Their accuracies are compared with the molecular d...

By using the example of plane Couette flow between two plates maintained at different temperatures, we present a method of calculating flow profiles for rarefied gases. In the method, generalized hydrodynamic equations are derived from the Boltzmann equation. They are then solved with boundary conditions calculated by taking into consideration the...

Linear stability analysis is carried out for cylindrical Couette flow of a Lennard–Jones fluid in the density range from the dense liquid to the dilute gas regime. Generalized hydrodynamic equations are used to calculate marginal stability curves and compare them with those obtained by using the Navier–Stokes–Fourier equations for compressible flui...

Approximate analytic expressions of eigenvalues for Lennard–Jones (10,6) and (12,6) potentials are obtained. The eigenvalues obtained from such expressions are compared with the WKB or numerical eigenvalues for the estimation of accuracy.

Reaction cross sections and internal energy distributions are calculated quantum mechanically for the K + Br2 system. The formulation is based on some essential ideas in the Butler theory of the nuclear stripping reactions and results provide a qualitative agreement with experiment on the system.

A complete set of irreducible isotropic tensors of rank six is presented which is obtained by the parentage scheme. The set is more compact in form than the available set in the literature and the symmetry properties of elements are transparent.

A simple heuristic method of constructing tensor operator bases for spins larger than 1/2 is presented which yields the same matrix representations as reported in the literature. By using the basis sets, we discuss the evolution of density matrices which can be put in Sylvester's form for an exponential operator. Use of quaternions is discussed for...

In this paper, we make use of the exact hydrodynamic solution for the Stokes equation for the velocity of a binary ionic solution that we have recently obtained, and show that the nonequilibrium pressure in an electrolyte solution subjected to an external electric field can be not only compressive, but also divergent in the region containing the co...

In this paper, we follow the general idea of the Onsager--Wilson theory of strong binary electrolyte solutions and completely calculate the velocity profile of ionic flow by first formally solving the hydrodynamic (Stokes) equation for the ionic solutions subjected to an external electric field by a Fourier transform method and then explicitly eval...

Thermodynamics is an ever evolving subject. This book aims to introduce to advanced undergraduate students and graduate students the fundamental ideas and notions of the first and second laws of thermodynamics in a manner unavailable in the usual textbooks on the subject of thermodynamics. For example, it treats the notions of unavailable work, com...

In this paper, a molecular theory of self-diffusion coefficient is developed for polymeric liquids (melts) on the basis of the integral equation theory for site–site pair correlation functions, the generic van der Waals equation of state, and the modified free volume theory of diffusion. The integral equations supply the pair correlation functions...

In the kinetic theory of dense fluids the many-particle collision bracket integral is given in terms of a classical collision operator defined in the phase space. To find an algorithm to compute the collision bracket integrals, we revisit the eigenvalue problem of the Liouville operator and re-examine the method previously reported[Chem. Phys. 20,...

In this review paper, we present and critically re-examine the formal expressions for the electrophoretic effect and the ionic field appearing in the unpublished Yale University PhD dissertation of W. S. Wilson which form the basis of the Onsager--Wilson theory of the Wien effect in the binary strong electrolyte solutions. It is pointed out that so...

The Voronoi volume of simple fluids was previously made use of in connection with volume transport phenomena in nonequilibrium simple fluids. To investigate volume transport phenomena, it is important to develop a method to compute the Voronoi volume of fluids in nonequilibrium. In this work, as a first step to this goal, we investigate the equilib...

An exact analytic form for the second virial coefficient, valid for the entire range of temperature, is presented for the Lennard-Jones fluid in this paper. It is derived by making variable transformation that gives rise to the Hamiltonian mimicking a harmonic oscillator-like dynamics for negative energy. It is given in terms of parabolic cylinder...

In this paper, we further examine the modified free volume (MFV) theory of diffusion in an effort to improve the accuracy of self-diffusion coefficients calculated with the help of the generic van der Waals equation of state. It is shown that the self-diffusion coefficient of the Lennard-Jones (LJ) fluid can be improved significantly over the resul...

In this paper, the effects of volume transport on the generalized hydrodynamic equations for a pure simple fluid are examined from the standpoint of statistical mechanics and, in particular, kinetic theory of fluids. First, we derive the generalized hydrodynamic equations, namely, the constitutive equations for the stress tensor and heat flux for a...

In the traditional theories of irreversible thermodynamics and fluid mechanics, the specific volume and molar volume have been interchangeably used for pure fluids, but in this work we show that they should be distinguished from each other and given distinctive statistical mechanical representations. In this paper, we present a general formula for...

The notion of barycentric velocity appears in irreversible thermodynamics and fluid mechanics, in which it is a field variable obeying the hydrodynamic equations or, more specifically, the momentum balance equation, which is coupled to the rest of hydrodynamic equations. Therefore, its behavior is not known until the hydrodynamic equations are solv...

In this Perspective, we discuss the role of voids in transport processes in liquids and the manner in which the concept of voids enters the generic van der Waals equation of state and the modified free volume theory. The density fluctuation theory is then discussed and we show how the density fluctuation theory can be made a molecular theory with t...

We calculate the generic van der Waals parameters A and B for a square well model by means of a perturbation theory. To calculate the pair distribution function or the cavity function necessary for the calculation of A and B, we have used the Percus-Yevick integral equation, which is put into an equivalent form by means of the Wiener-Hopf method. T...

Generalized thermodynamics or extended irreversible thermodynamics presumes the existence of thermodynamic intensive variables (e.g., temperature, pressure, chemical potentials, generalized potentials) even if the system is removed from equilibrium. It is necessary to properly understand the nature of such intensive variables and, in particular, of...

In the previous papers applying the generic van der Waals equation of state the mean excluded volume was defined with the contact diameter of particles at which the potential energy is equal to zero-the size parameter in the case of the Lennard-Jones potential. This parameter appears as the upper limit of the integral for the generic van der Waals...

In this paper the thermal conductivity of the Lennard-Jones fluid is calculated by applying the combination of the density-fluctuation theory, the modified free volume theory of diffusion, and the generic van der Waals equation of state. A Monte Carlo simulation method is used to compute the equilibrium pair-correlation function necessary for compu...

Nonequilibrium statistical mechanics via density fluctuation theory predicts relations between the bulk and shear viscosity, thermal conductivity, and self-diffusion coefficient of a fluid. In this Feature Article, we discuss such relations holding for fluids over wide ranges of density and temperature experimentally studied in the laboratory. It i...

The generalized Boltzmann equation for simple dense fluids gives rise to the stress tensor evolution equation as a constitutive equation of generalized hydrodynamics for fluids far removed from equilibrium. It is possible to derive a formula for the non-Newtonian shear viscosity of the simple fluid from the stress tensor evolution equation in a sui...

In this paper, we apply the Matteoli-Mansoori empirical formula for the pair correlation function of simple fluids obeying the Lennard-Jones potential to calculate reduced self-diffusion coefficients on the basis of the modified free volume theory. The self-diffusion coefficient thus computed as functions of temperature and density is compared with...

In previous work on the density fluctuation theory of transport coefficients of liquids, it was necessary to use empirical self-diffusion coefficients to calculate the transport coefficients (e.g., shear viscosity of carbon dioxide). In this work, the necessity of empirical input of the self-diffusion coefficients in the calculation of shear viscos...

The shear viscosity formula derived by the density fluctuation theory in previous papers is computed for argon, krypton, and methane by using the self-diffusion coefficients derived in the modified free volume theory with the help of the generic van der Waals equation of state. In the temperature regime near or above the critical temperature, the d...

In this article the thermodynamically consistent formulation of generalized hydrodynamics is reviewed and applications to shock-wave structures, ultrasonic wave absorption and dispersion and microchannel flows of the generalized hydrodynamics so formulated are discussed. The kinematic terms of the constitutive equations in the generalized hydrodyna...

In this paper, a mathematical model within the framework of generalized hydrodynamics is developed for the description of flows in microsystems where the Knudsen number is large and the aspect ratio [(width)/(length)] is not so small. The model is based on a set of empirical generalized hydrodynamic equations, which are fashioned from the steady-st...

This monograph presents, from the viewpoint of continuum mechanics, a newly emerging field of irreversible thermodynamics, in which linear irreversible thermodynamics are extended to the nonlinear regime and macroscopic phenomena far removed from equilibrium are studied in a manner consistent with the laws of thermodynamics. The tool to develop thi...

The classical hydrodynamics described by the Navier-Stokes and Fourier equations works impressively if the Mach and Knudsen numbers are low. However, as the gas density becomes sufficiently low as to make the Knudsen number high or as the Mach number becomes large, the classical hydrodynamic theory based on the Navier-Stokes and Fourier equations i...

A statistical mechanical theory is presented for viscosity of relatively low molecular weight organic liquids which are supercooled down to the glass transition temperature. In this theory a relation resembling the Stokes-Einstein relation between the viscosity and self-diffusion coefficient of supercooled liquids and an expression for the self-dif...

The Comments by Santos [Phys. Rev. E 67, 053201 (2003)] are addressed in this paper. It is shown that his comments are based on an assumption that is not made in the paper [Phys. Rev. E 65, 031202 (2002)] commented upon by him. It is also shown that the hydrodynamic equations used by him are not the same as those implied by the constitutive equatio...

The Comments by Santos [Phys. Rev. E 67, 053201 (2003)] are addressed in this paper. It is shown that his comments are based on an assumption that is not made in the paper [Phys. Rev. E 65, 031202 (2002)] commented upon by him. It is also shown that the hydrodynamic equations used by him are not the same as those implied by the constitutive equatio...

In this paper, phenomenological models for the generic van der Waals equation of state are proposed for the subcritical regime of a simple fluid by assuming empirical forms for the generic van der Waals parameters A and B. The models that are assumed are tested against the critical parameters. It is shown that quadratic and cubic models for A and B...

The Wiener–Hopf technique has been been applied to solve the Ornstein–Zernike equation for hard sphere fluids and to calculate thereby a thermodynamically consistent equation of state. An analytic form of a thermodynamically consistent equation of state for hard sphere fluids is obtained in which the correlation range is treated as an adjustable pa...

It is shown that the tracer diffusion and self-diffusion coefficients of liquids are in a simple linear relation with a constant coefficient, which depends on only the molecular size ratio and the mass ratio of the solute and the solvent molecule. With experimentally determined tracer diffusion and self-diffusion coefficients, the relation can be u...

The self-diffusion coefficient of liquid nitrogen was presented. The self-diffusion and diffusion coefficients were expressed in a form reminiscent of the Arrhenius activation theory. In this work, nitrogen was treated as a spherical molecule. The proposed self-diffusion coefficient can be used for calculating shear viscosity, bulk viscosity and th...

A statistical mechanical formula of the thermal conductivity of molecular liquids is developed as a generalization to molecular fluids of the theory of thermal conductivity of simple liquids reported recently. The theoretical expression presented for the thermal conductivity of molecular liquids consists of the kinetic part independent of the densi...

A free volume theory of diffusion coefficients is formulated for binary mixtures of simple liquids. The free volume is defined by means of the generic van der Waals equation of state for mixtures, which is developed in this work, and computed in terms of the pair correlation function obtained by means of Monte Carlo simulations with a square-well p...

The present work attempts to theoretically characterize irreversible processes requiring a generalization of the linear theory to regimes far removed from equilibrium. Attention is given to balance equations and the first law of thermodynamics, the second law of thermodynamics, the local theory of irreversible processes, the irreversible thermodyna...

In this paper we examine the stress tensor component evolution equations recently derived by Uribe and Garcia-Colin [Phys. Rev. E 60, 4052 (1999)] for unidirectional flow at uniform temperature under the assumption/approximation of vanishing transversal velocity gradients. By removing this assumption/approximation we derive the stress tensor evolut...

A simple formula for the diffusion coefficient of liquid mixtures, expressed in terms of the work necessary to create a characteristic free volume in the liquid, is presented in the spirit of the Arrhenius activation theory and tested in comparison with available experimental data. If use is made of the generic van der Waals equation of state, the...

A theory of thermal conductivity of simple liquids is developed in a way parallel with the theory of shear and bulk viscosities reported in previous papers. A molecular theoretic expression for the thermal conductivity of simple liquids is presented, which consists of two distinctive parts: one that is given in terms of intermolecular forces and th...

In the literature on extended thermodynamics the nonequilibrium partition function in the presence of a heat flux appears in a divergent form, which has been usually evaluated by expanding the divergence causing exponential factor involving the heat flux and by arbitrarily truncating the resulting divergent series of the integrals. In this paper we...

Generalized hydrodynamic theory of shock waves is phenomenologically developed for rigid diatomic molecules. The generalized hydrodynamic equations developed are thermodynamically consistent, obeying the laws of thermodynamics. They reduce to the Navier-Stokes-Fourier theory of the classical hydrodynamics in the limit of low Mach number. The theory...

In this paper we use the generic van der Waals equation of state to define the free volume of liquids along the liquid-vapor coexistence line (liquids curve) in the case of liquid argon and along three isotherms in the high-pressure regime in the case of liquid methane. With the free volume computed from the cavity function obtained by means of a M...