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In the statistical mechanics approach to liquid-state theory, understanding the role of the intermolecular potential in determining thermodynamic and structural properties is crucial. The Fisher–Widom (FW) line, which separates regions in the temperature vs density plane where the decay of the total correlation function is monotonic or oscillatory, provides insights into the dominance of the attractive or repulsive part of the interactions. Stopper et al. have recently conjectured [J. Chem. Phys. 151, 014501 (2019)] that the line of vanishing excess isothermal compressibility approximates the FW line in simple fluids. Here, we investigate this conjecture using the Jagla potential and also explore the line of vanishing excess pressure. We employ theoretical approximations and Monte Carlo simulations to study one-dimensional and three-dimensional systems. While exact results for the one-dimensional case do not support the conjecture, our Monte Carlo simulations for the three-dimensional fluid validate it. Our findings not only contribute to the understanding of the relationship between the three transition lines but also provide valuable insights into the thermodynamic and structural behaviour of simple fluids. [ABSTRACT FROM AUTHOR]

Values of the fifth virial coefficient, compressibility factors, and fluid-fluid coexistence curves of binary asymmetric nonadditive mixtures of hard disks are reported. The former correspond to a wide range of size ratios and positive nonadditivities and have been obtained through a standard Monte Carlo method for the computation of the corresponding cluster integrals. The compressibility factors as functions of density, derived from canonical Monte Carlo simulations, have been obtained for two values of the size ratio (q = 0.4 and q = 0.5), a value of the nonadditivity parameter (Δ = 0.3), and five values of the mole fraction of the species with the biggest diameter (x1 = 0.1, 0.3, 0.5, 0.7, and 0.9). Some points of the coexistence line relative to the fluid-fluid phase transition for the same values of the size ratios and nonadditivity parameter have been obtained from Gibbs ensemble Monte Carlo simulations. A comparison is made between the numerical results and those that follow from some theoretical equations of state. [ABSTRACT FROM AUTHOR]

The relevance of neglecting three- and four-body interactions in the coarse-grained version of the Asakura-Oosawa model is examined. A mapping between the first few virial coefficients of the binary nonadditive hard-sphere mixture representative of this model and those arising from the coarsegrained (pairwise) depletion potential approximation allows for a quantitative evaluation of the effect of such interactions. This turns out to be especially important for large size ratios and large reservoir polymer packing fractions. [ABSTRACT FROM AUTHOR]

The problem of demixing in the Asakura-Oosawa colloid-polymer model is considered. The critical constants are computed using truncated virial expansions up to fifth order. While the exact analytical results for the second and third virial coefficients are known for any size ratio, analytical results for the fourth virial coefficient are provided here, and fifth virial coefficients are obtained numerically for particular size ratios using standard Monte Carlo techniques. We have computed the critical constants by successively considering the truncated virial series up to the second, third, fourth, and fifth virial coefficients. The results for the critical colloid and (reservoir) polymer packing fractions are compared with those that follow from available Monte Carlo simulations in the grand canonical ensemble. Limitations and perspectives of this approach are pointed out. [ABSTRACT FROM AUTHOR]

A possible approximate route to obtain the equation of state of the monodisperse hard-sphere system in the metastable fluid region from the knowledge of the equation of state of a hard-sphere mixture at high densities is discussed. The proposal is illustrated by using recent Monte Carlo simulation data for the pressure of a binary mixture. It is further shown to exhibit high internal consistency. [ABSTRACT FROM AUTHOR]

The question of whether the known virial coefficients are enough to determine the packing fraction η∞ at which the fluid equation of state of a hard-sphere fluid diverges is addressed. It is found that the information derived from the direct Padé approximants to the compressibility factor constructed with the virial coefficients is inconclusive. An alternative approach is proposed which makes use of the same virial coefficients and of the equation of state in a form where the packing fraction is explicitly given as a function of the pressure. The results of this approach both for hard-disk and hard-sphere fluids, which can straightforwardly accommodate higher virial coefficients when available, lends support to the conjecture that η∞ is equal to the maximum packing fraction corresponding to an ordered crystalline structure. [ABSTRACT FROM AUTHOR]

The depletion force and depletion potential between two in principle unequal “big” hard spheres embedded in a multicomponent mixture of “small” hard spheres are computed using the rational function approximation method for the structural properties of hard-sphere mixtures [S. B. Yuste, A. Santos, and M. López de Haro, J. Chem. Phys. 108, 3683 (1998)]. The cases of equal solute particles and of one big particle and a hard planar wall in a background monodisperse hard-sphere fluid are explicitly analyzed. An improvement over the performance of the Percus–Yevick theory and good agreement with available simulation results are found. [ABSTRACT FROM AUTHOR]

The contact values g(σ,σ′) of the radial distribution functions of a fluid of (additive) hard spheres with a given size distribution f(σ) are considered. A “universality” assumption is introduced, according to which, at a given packing fraction η,g(σ,σ′)=G(z(σ,σ′)), where G is a common function independent of the number of components (either finite or infinite) and z(σ,σ′)=[2σσ′/(σ+σ′)]μ2/μ3 is a dimensionless parameter, μn being the nth moment of the diameter distribution. A cubic form proposal for the z dependence of G is made and known exact consistency conditions for the point particle and equal size limits, as well as between two different routes to compute the pressure of the system in the presence of a hard wall, are used to express G(z) in terms of the radial distribution at contact of the one-component system. For polydisperse systems we compare the contact values of the wall-particle correlation function and the compressibility factor with those obtained from recent Monte Carlo simulations. [ABSTRACT FROM AUTHOR]

Following the work of Leutheusser [Physica A 127, 667 (1984)], the solution to the Percus-Yevick equation for a seven-dimensional hard-sphere fluid is explicitly found. This allows the derivation of the equation of state for the fluid taking both the virial and the compressibility routes. An analysis of the virial coefficients and the determination of the radius of convergence of the virial series are carried out. Molecular-dynamics simulations of the same system are also performed and a comparison between the simulation results for the compressibility factor and theoretical expressions for the same quantity is presented. [ABSTRACT FROM AUTHOR]

A universality ansatz for the contact values of a multicomponent mixture of additive hard spheres is used to propose new formulae for the case of disparate-size binary mixtures. A comparison with simulation data and with a recent proposal by Alawneh and Henderson for binary mixtures shows reasonably good agreement with the predictions for the contact values of the large-large radial distribution functions. A discussion on the usefulness and limitations of the new proposals is also presented. [ABSTRACT FROM AUTHOR]

Recent Monte Carlo simulation results for the contact values of polydisperse hard-sphere mixtures at a hard planar wall are considered in the light of a universality assumption made in approximate theoretical approaches. It is found that the data appear to fulfill the universality ansatz reasonably well, thus opening up the possibility of inferring the properties of complicated systems from the study of simpler ones. [ABSTRACT FROM AUTHOR]

The radial flow between two parallel circular disks is investigated with the aim to determine the optimum convective heat transfer conditions at the external disk surfaces in order to minimize the intrinsic irreversibilities. A general situation is considered where the fluid is electrically conducting and may be under the influence of a transversal magnetic field. The velocity and electric current density fields are obtained analytically and used to solve the heat transfer equation under boundary conditions of the third kind. The analysis is in the absence of fluid inertia, under creeping flow conditions (Reynolds number « 1). A perturbation approach in order to include the convective heat transfer effects in the flow is used. The Péclet number is assumed to be small. The analytic expressions for the velocity,electric current density and temperature fields are used to calculate explicitly the global entropy generation rate. When the convective heat transfer coefficients for each wall are different, this function displays a minimum for specific heat exchange conditions. The results are shown for both the hydrodynamic and the magnetohydrodynamic cases. It is also found that the mean Nusselt number at the upper wall shows a maximum value for a given value of the Hartman number, when the dimensionless heat transfer coefficients for each disk and the P&ecute;clet number are fixed. This mean Nusselt number for maximum heat transfer is near its value for minimum entropy generation conditions. [ABSTRACT FROM AUTHOR]

A simple equation of state for hard disks on the hyperbolic plane is proposed. It yields the exact second virial coefficient and contains a pole at the highest possible packing. A comparison with another very recent theoretical proposal and simulation data is presented. [ABSTRACT FROM AUTHOR]

The structural properties of fluids whose molecules interact via potentials with a hard core plus two piece-wise constant sections of different widths and heights are presented. These follow from the more general development previously introduced for potentials with a hard core plus n piece-wise constant sections [A. Santos, S. B. Yuste, and M. Lopez de Haro, Condens. Matter Phys. 15, 23602 (2012)] in which use was made of a semi-analytic rational-function approximation method. The results of illustrative cases comprising eight different combinations of wells and shoulders are compared both with simulation data and with those that follow from the numerical solution of the Percus-Yevick and hypernetted-chain integral equations. It is found that the rational-function approximation generally predicts a more accurate radial distribution function than the Percus-Yevick theory and is comparable or even superior to the hypernetted-chain theory. This superiority over both integral equation theories is lost, however, at high densities, especially as the widths of the wells and/or the barriers increase. [ABSTRACT FROM AUTHOR]