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A new method for calculation of the radial distribution functions (RDFs) at contact from a specified hard-sphere mixture equation of state (EOS) is proposed. The method is applied to two available accurate EOS expressions and new analytical formulas for the RDFs are obtained for binary additive hard-sphere mixtures. The results of the new formulas are compared with available computer simulation data and with those of other RDF expressions from the literature. The evidence to date suggests that the new formula is more accurate than alternative formulas currently available. [ABSTRACT FROM AUTHOR]

We present a new efficient Monte Carlo method for the molecular-based computer simulation of chemical systems undergoing any combination of reaction and phase equilibria. The method requires only a knowledge of the species intermolecular potentials and their ideal-gas properties, in addition to specification of the system stoichiometry and thermodynamic constraints. It avoids the calculation of chemical potentials and fugacities, as is similarly the case for the Gibbs ensemble method for phase equilibrium simulations. The method’s simplicity allows it to be easily used for situations involving any number of simultaneous chemical reactions, reactions that do not conserve the total number of molecules, and reactions occurring within or between phases. The basic theory of the method is presented, its relationship to other approaches is discussed, and applications to several simple example systems are illustrated. [ABSTRACT FROM AUTHOR]

The phase equilibrium behavior of a basic statistical mechanical model of a binary mixture of water and a simple fluid are investigated. For water we use a primitive model which incorporates no attractive forces other than hydrogen bonds within a hard-sphere core, and the simple fluid is modeled by a fluid of hard spheres with an attractive mean-field term. The qualitative behavior of the phase equilibria and P-T critical lines of this model are calculated using an accurate theoretical equation of state for primitive water obtained in analytical form using the Wertheim thermodynamic perturbation theory, for a range of values of the mixture’s two underlying parameters, the hard-sphere size ratio and the mean field strength. The model exhibits type IIId and type IV* phase behavior of three qualitatively different types, characterized by the existence of either one or two three-phase lines. The model exhibits a range of phenomena, including tricritical points and double critical end points. The implications of the model results for corresponding real fluid mixtures are also discussed. [ABSTRACT FROM AUTHOR]

The phase equilibrium properties of a molecular-based model of binary aqueous mixtures are investigated using an extended primitive model (EPW) for water, which incorporates a mean-field attractive term in addition to the interactions given by the primitive model studied in part I of this series of papers. The second component, representing a nonpolar fluid, is modeled by a general hard body with a mean-field attractive term. Analytical expressions for the Helmholtz free energy of this precisely defined molecular model are obtained from statistical mechanical theory, as a function of the molecular size, the mean-field interaction term, and the shape of the second component. The predictions of our model are compared with the behavior of two classes of real aqueous mixtures: Group A={water+inert gases, hydrogen} and Group B={water+n-alkanes}. The phase equilibrium properties are studied as a function of the ratio of the critical temperature τ and critical volume λ with respect to the corresponding quantities for water, and the global phase diagram (i.e., the type of phase behavior and its dependence on the model parameters) is determined. Since τ and λ are obtainable both from our theory and from experiment, our approach thus contains no adjustable parameters. The theory gives qualitatively correct predictions of the phase behavior of these two classes of mixtures, i.e., of the transition between Type IIIc and Type IIId critical line behavior in the Konynenberg and Scott classification scheme, of the presence or absence of pressure minima for Group B mixtures exhibiting Type IIIc behavior, and the dependence of the temperature and pressure of the Type IIIc temperature minimum on the size of the second-component molecule. © 1995 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Homonuclear hard diatomics in the vicinity of a hard wall have been studied using Monte Carlo simulations. During the simulations the cavity distribution functions for parallel and perpendicular orientations with respect to the wall and their Legendre expansion coefficients were calculated. It is demonstrated that the Legendre expansion is rapidly convergent and only several coefficients are required to describe the wall-diatomic correlation function within the simulation error. In addition, two simple methods for theoretical prediction of the cavity distribution function at small distances are compared with the simulation data. These approaches require as input quantities only thermodynamic data for the bulk homogeneous fluid. Both methods yield good accuracy for the cavity correlation function at the specific orientations indicated and for the first two Legendre coefficients, but fail to accurately describe higher Legendre coefficients. [ABSTRACT FROM AUTHOR]

The high Reynolds-number structure of the laminar, chaotic and turbulent attractors is investigated in a two-dimensional Kolmogorov flow. The laminar attractors include the families of multi-phased travelling waves and quasi-periodic standing waves both of which form the backbone of the transition to a turbulent flow. At leading order, each laminar attractor under study is obtained by solving the Euler equations on a manifold subject to the appropriate periodicity and symmetry conditions. The manifold is determined by a finite number of vorticity equations, these being required to suppress the secular terms at the next order. Our results show that, for the multi-phased travelling waves, the first phase velocity can be determined by an integral conservation law for kinetic energy and the subsequent phase velocities can be evaluated by a non-linear eigenvalue problem. The results also reveal that whereas viscosity determines the smallest scales and controls the amplitude of the flow, the inertial terms govern the shape and form of the flow. The comparison of our analytical predictions for evaluating the stable single-phased travelling wave with the direct numerical simulation of the Navier–Stokes equations has been undertaken, the agreement being excellent. For sufficiently high Reynolds number, after the bifurcation to chaotic flow, all of the multi-phased travelling waves and quasi-periodic standing waves become unstable non-wandering sets. Based on the above new findings for these unstable non-wandering sets and other travelling and standing waves of this kind in phase space, necessary conditions for the invariant manifolds of the chaotic and turbulent attractors are obtained, these necessary conditions being conjectured to be also sufficient. [ABSTRACT FROM AUTHOR]