Sharif Digital Repository

We present in this paper a simple method of obtaining various equations of state for hard sphere fluid in a simple unifying way. Using the first several virial coefficients of hard sphere fluid, we will guess equations of state by using the asymptotic expansion method. Among the equations of state obtained in this way are Percus-Yevick, Scaled Particle Theory, and Carnahan-Starling equations of state. Also by combining the Monte Carlo results on hard sphere fluid with the asymptotic expansion method many other equations of state for hard sphere fluid can be found where all of them give essentially similar results in the region of isotropic hard sphere liquid, i.e., up to η < 0.5, in which η... 

The Ghotbi-Vera hard sphere equation of state as the reference system, coupled with the mean spherical approximation, (GV-MSA), has been used to accurately correlate the mean ionic activity coefficients of aqueous solutions of single 1:1 electrolytes. The new equation of state considers the ions to be hard spheres in Kelvin tetrakaidekahedron cells. The mean ionic activity coefficients of the electrolytes can be correlated with constant diameter of anions, equal to the crystallographic Pauling diameter and with a concentration dependent relation for the cations. In comparison to their crystallographic Pauling diameters, the new model for the mean ionic activity coefficient produces realistic... 

The predictions of the pair radial distribution function (RDF) at contact value, compressibility factor, and chemical potentials for binary and ternary hard-sphere mixtures obtained with the Barrio-Solana, the Santos et al., and the generalized Lebowitz mixing rules are compared using the Carnahan-Starling, Kolafa, and Khoshkbarchi-Vera one-component hard-sphere EOS. An expression for the pair RDF at contact value for Barrio-Solana mixing rule and the expressions for the chemical potentials in multicomponent hard-sphere fluids are derived. As a general rule, the equations of state obtained based on the generalized Lebowitz mixing rule predict better the pair RDF at contact value simulated... 

The non-primitive mean spherical approximation (NP-MSA) based models were used to correlate the individual and the mean ionic activity coefficients of the symmetric and asymmetric aqueous electrolyte solutions. The results of the models for the mean ionic activity coefficients were directly used to calculate the osmotic coefficient for the electrolyte solutions studied in this work. In the NP-MSA models, the Ghotbi-Vera and the Boublik-Mansoori-Carnahan-Starling- Leland hard sphere equation of state as the reference system coupled with the non-primitive mean spherical approximation model (NP-GV-MSA and NP-BMCSL-MSA models, respectively). In correlating the mean ionic activity coefficients of... 

A new potential function, which can in a simple and reasonable manner represent the molecular interaction of many kinds of hard-core fluids by varying the value of its parameter, is proposed. For prediction of thermodynamic properties of hard-core fluids such as the square-well (SW) and hard core Lennard-Jones (HCLJ), a simple perturbed equation of state (EOS) is derived by using the new potential function along with the Barker-Henderson perturbation theory. This method yields a simple and general analytical expression for each thermodynamic property of such fluids. The most important feature of these expressions is that they have no adjustable parameter and in some regions in which there is... 

Two new hard-sphere EOS are proposed and tested using the same attractive potential terms used by the SAFT EOS. Generalized expressions for the pair RDF at contact value, the compressibility factor, and the excess chemical potentials have been derived. Extension to mixtures is tested using three mixing rules for multicomponent hard-sphere fluids. The proposed EOS combined with the Santos et al. and the Barrio-Solana mixing rules reproduced the compressibility factors and the excess chemical potentials more accurately than the Boublik-Mansoori-Carnahan-Starling-Leland (BMCSL) EOS. However the pair RDF at contact value had larger deviations than those obtained with the BMCSL EOS. The... 

We have derived an analytical equation of state (EOS) based on the soft-core statistical mechanical perturbation theory for fluids, using the Weeks-Chandler-Andersen (WCA) theory recently developed by Ben-Amotz-Stell (BAS) for the choice of the hard-sphere diameter, but with a new algorithm for calculation of the pair and many-body interactions. We have used Carnahan-Starling expression with the Boltzmann factor criterion (BFC) as an effective hard-sphere diameter for the reference system, and also decomposed the perturbed pair potential to symmetric and asymmetric terms. The former term is due to the many-body interactions at high densities as was used in the linear isotherm regularity... 

In this work a modified form of the Ghotbi-Vera Mean Spherical Approximation model (MGV-MSA) has been used to correlate the mean ionic activity coefficients (MIAC) for a number of symmetric and asymmetric aqueous electrolyte solutions at 25 °C. In the proposed model the hard sphere as well as the electrostatic contributions to the MIAC and the osmotic coefficient of the previously GV-MSA model has been modified. The results of the proposed model for the MIAC of the electrolyte solutions studied in this work are used to directly calculate the values of the osmotic coefficients without introducing any new adjustable parameter. In the MGV-MSA model the cation diameter as well as the relative... 

A general regularity was found based on an effective pair potential of Lennard-Jones LJ (12, 6), for both dense, nonmetallic and nonionic fluids and solids according to which (Z-1) v2 linearly varies with respect to ρ2 for each isotherm, and this equation of state (EoS I) is known as LIR. However, despite the fact that Ne is a simple spherical species, unexpectedly, its solid and liquid phases both show a significant deviation from EoS I. In this work, we have investigated the accuracy of the EoS I for other systems, including quantum light molecules, such as D 2, H 2 and He, in both fluid and solid states at different temperatures. Like Ne, we have noticed that these systems do not well... 

In this work, the development of a two-dimensional Direct Simulation Monte Carlo (DSMC) Program for pressure boundaries using unstructured cells and its applications to typical micro-scale gas flows are described. For the molecular collision kinetics, variable hard sphere molecular model and no time counter collision sampling scheme have been used. Applications to micro-scale gas flows include micro-nozzel, nano channel and slider air bearing.The aim is to further test the treatment of pressure boundaries. For slider air bearing gas flows of the computer hard drive, the simulated gas pressures, at different rotating speeds, have a very good agreement with previous studies. The applicability...