Kyunil Rah

The generic van der Waals equation of state and self-diffusion coefficients of liquids

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 Monte Carlo simulation method, we have calculated the self-diffusion coefficients of liquid argon and liquid methane. The Cohen–Turnbull free volume theory is used to calculate them. With the empirical parameter appearing in the Cohen–Turnbull theory suitably adjusted, the theoretical and experimental values of the self-diffusion coefficients agree very well with regard to the density and temperature dependence for the cases of available data compared. A pair of analytic formulas for density dependence of the self-diffusion coefficient is obtained by using the approximate cavity functions for hard spheres and tested against the experimental data on methane. A com...

Density and temperature dependence of the bulk viscosity of molecular liquids: Carbon dioxide and nitrogen

A statistical mechanical formula is developed for the bulk viscosity of molecular liquids. It is expressed in terms of the self-diffusion coefficient of the liquid, intermolecular forces, and the site–site pair correlation functions. The density and temperature dependence of the bulk viscosity of carbon dioxide and nitrogen are calculated therewith and compared with experimental data wherever possible. In the case of liquid nitrogen for which experimental data are available the theoretical values of the bulk viscosity are well within the experimental error ranges in almost all cases. There are no experimental data to compare with the theoretical results for liquid carbon dioxide, but in the light of the comparison for nitrogen and the excellent shear viscosity results which were obtained in the same line of approach in the previous work the calculated bulk viscosity values of liquid carbon dioxide may be treated as theoretical predictions.

Generic van der Waals equation of state and theory of diffusion coefficients: Binary mixtures of simple liquids

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 potential model. The free volume thus computed is used to investigate the composition and temperature dependence of the binary diffusion coefficient of argon–krypton mixtures as well as the tracer diffusion coefficients of argon in liquid nitrogen and krypton in liquid argon. The present theoretical predictions compare very well with the experimental or simulation results available in the literature. The size and mass dependence of the ratio of the tracer diffusion to the solvent self-diffusion coefficients is also presented. This ratio is found to be almost independent of temperature and density. It therefore can be used to calculate the tracer diffusion coeffic...

Density fluctuations and shear viscosity of molecular liquids: Carbon dioxide and nitrogen

An expression for the shear viscosity of molecular liquids is derived from the statistical expression for the stress tensor by taking into consideration density fluctuations over the intermolecular force range. The viscosity formula consists of a low density term given in terms of the Chapman–Enskog viscosity and a density dependent term reminiscent of the Stokes–Einstein relation between the viscosity and the self-diffusion coefficient. According to this formula, the shear viscosity of molecular liquids can be calculated in terms of intermolecular site–site forces, the corresponding pair correlation functions, and the self-diffusion coefficient as well as the Chapman–Enskog viscosity at low density. By treating the viscosity expression as a semiempirical formula where the experimental and numerically simulated self-diffusion coefficients available in the literature are used, the shear viscosities of nitrogen and carbon dioxide, both of which are treated as a rigid linear rotator with two sites, are calcu...

Theory of thermal conductivity of dense simple fluids

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 the structure of the liquid described by equilibrium pair correlation function and thus strongly depends on the density, and the other that is given in terms of the Chapman–Enskog thermal conductivity and thus independent of the density. The density dependent part of the thermal conductivity is given in terms of the intermolecular force, the equilibrium pair correlation function, and self-diffusion coefficient in a form similar to the shear and bulk viscosities of the liquid, or in terms of the shear viscosity in a form generalizing to liquids the Eucken relation of thermal conductivity and shear viscosity. The theoretical result obtained for thermal conductivity ...

Self-diffusion coefficient of liquid nitrogen

Self-diffusion coefficients of liquids are important transport coefficients which provide a basic time scale of many dynamic phenomena in liquids and in terms of which other transport coefficients can be expressed; an example for such relations is the Stokes-Einstein relation between viscosity and diffusion coefficient. For this reason considerable attention has been paid to them in the past, and efforts have been made to measure them in the literature. For the phenomenological understanding of the self-diffusion coefficients the Arrhenius activation energy theory has been often used since it sometimes provides a qualitatively correct temperature dependence in a limited range of temperature. Some years ago, Krynicki er al. [l] reported in this journal their NMR measurement of the self-diffusion cofficient of liquid nitrogen at temperatures ranging from 64 K to 98 K. They interpreted their data by means of an activation energy theory and also compared with a couple of simulation data by Barojas et al. [2] and by Cheung and Powles [3]. Their interpretation seems to yield a qualitatively reasonable result, but the nature of the activation energy is unclear as is usually the case in such a phenomenological treatment. We have recently reported on a theory of diffusion processes [4], which combines the idea of free volume theory of diffusion in liquids and the generic van der Waals equation of state [5] that provides a statistical mechanical expression for free volume required for the free volume theory of diffusion. In this theory the selfdiffusion and diffusion coefficients are expressible in a form reminiscent of the Arrhenius activation theory, but the activation energy turns out to be the work required to create a characteristic volume into which a particle can move in the process of diffusion. Thanks to the generic van der Waals equation of state that can be given a rigorous statistical mechanical representation, the work in question and therefore the self-diffusion coefficient can be calculated by means of statistical mechanics, given a model for the potential energy. This theory has been tested against experimental data

Theory of the thermal conductivity of molecular liquids: Nitrogen and carbon dioxide

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 density and the density-dependent potential part. The latter is given in terms of the intermolecular forces, pair correlation function, and self-diffusion coefficient, in a form similar to the shear and bulk viscosities of the molecular liquids. A generalized Eucken relation is also derived for molecular liquids that relates thermal conductivity to shear viscosity, and used for the calculation of thermal conductivities. The theoretical result obtained for thermal conductivity is successfully tested against experimental data on nitrogen and carbon dioxide available in the literature.

A closure for the Ornstein–Zernike relation that gives rise to the thermodynamic consistency

A closure is proposed for the direct correlation function in the grand canonical ensemble theory that gives rise to the thermodynamic consistency, by which it is meant that identical results are obtained when the equations of state are calculated via the virial and compressibility routes, respectively, and when the excess chemical potentials are calculated by means of the thermodynamic derivative and the statistical mechanical formula, respectively. The integral equation for the pair correlation function under the closure is analytically solved in the case of hard spheres. The equation of state for hard spheres turns out to have the same form as that in the scaled particle theory or the compressibility equation of state in the Percus–Yevick theory although the present closure is quite different from that of the Percus–Yevick theory. The excess chemical potential is also found in the same form as that in the scaled particle theory. It seems to suggest that the present closure produces an integral equation ...

Theory of nonequilibrium liquid–vapor interface: effects of shear flow

A theory of nonequilibrium interface structure is developed on the basis of the nonequilibrium ensemble method reported previously. A pair of integro-partial differential equations is presented for the nonequilibrium density profile of the Lennard–Jones fluid subjected to a steady shearing. The forms of the equations are mathematically similar to those in the equilibrium theory. A perturbation technique is employed to calculate the dynamic pair correlation function for a uniform fluid at a low shear rate. The underlying equilibrium theory of interface used is tested against the known results in the literature and found to be reliable. The nonequilibrium corrections arising from the shear flow to the density profile and the surface tension are calculated for different shear parameter values, and a “crossover” phenomenon is observed in density profile and surface tension, as the shear rate increases. Analysis of the transverse structure factor (or the susceptibility) is made to account for the changes in the interfacial properties arising from the nonequilibrium force.