The Enskog theory for dense multicomponent fluid mixtures is developed. Two versions are considered—the standard and the revised theory. Explicit expressions all transport coefficients (shear bulk viscosity, thermal conductivity, mutual diffusion coefficients) in terms of sizes, masses, concentrations constituents mixture given third approximation. Applications will be discussed subsequent papers.

Using the revised Enskog theory we derive equations for thermal diffusion ratios kTi and factors αij of multicomponent hard-sphere mixtures systems in mechanical equilibrium. The first ten approximations to factor αij[N] (N=1,2,...,10) are evaluated numerically a variety system parameter choices appropriate binary ternary mixtures. We find that approximation does not vanish; sequence converges most rapidly when mass spheres nearly equal. seventh was estimated lie within about 1% exact value...

An equation of state for a fluid hard disks is proposed: Z=[1−2η+(2η0−1)(η/η0)2]−1. The exact fit the second virial coefficient and existence single pole singularity at close-packing fraction η0 are only requirements imposed on its construction. A comparison prediction coefficients values compressibility factor Z with those stemming out other known equations made. overall performance this very simple quite satisfactory.

In order to gain insight into the effects of elasticity on dynamics fluids in porous media, we have analyzed flow a Maxwell fluid tube. The entire problem is transformed frequency domain through time Fourier transform and this allows for derivation dynamic generalization Darcy's law. Analytical results are provided showing dramatic enhancement at certain frequencies. We present parametric analysis dissipative elastic behavior system, obtain an analytic expression maximum value permeability...

In the statistical mechanics approach to liquid-state theory, understanding role of intermolecular potential in determining thermodynamic and structural properties is crucial. The Fisher--Widom (FW) line, which separates regions temperature vs density plane where decay total correlation function monotonic or oscillatory, provides insights into dominance attractive repulsive part interactions. Stopper et al. have recently conjectured [J. Chem. Phys. \textbf{151}, 014501 (2019)] that line...

This paper explores how competing interactions in the intermolecular potential of fluids affect their structural transitions. study employs a versatile model with hard core followed by two constant steps, representing wells or shoulders, analyzed both one-dimensional (1D) and three-dimensional (3D) systems. Comparing these dimensionalities highlights effect confinement on Exact results are derived for 1D systems, while rational function approximation is used unconfined 3D fluids. Both...

A simple recipe to derive the compressibility factor of a multicomponent mixture d-dimensional additive hard spheres in terms that one-component system is proposed. The based (i) on an exact condition has be satisfied special limit where one components corresponds point particles; and (ii) form radial distribution functions at contact as obtained from Percus—Yevick equation three-dimensional system. proposal examined for discs by comparison with well-known equations state these systems...

We present a detailed description of the mutual diffusion coefficients binary and ternary dense fluid mixtures hard spheres, as given by revised Enskog theory (RET) van Beijeren Ernst standard (SET) Tham Gubbins. The formulas for [see part I this series, J. Chem. Phys. 78, 2746 (1983)] involve contact values equilibrium pair distribution functions chemical potentials, which Carnahan–Starling approximation is used. formulas, were obtained making an expansion in Sonine polynomials, are...

The thermodynamic implications of the first deviations with respect to classical hydrodynamic behavior in high-frequency, short-wavelength phenomena are examined. constitutive equations arising from an extended irreversible-thermodynamic formalism taking into account spatial inhomogeneities space state variables compared those used generalized hydrodynamics. so-called exponential model for memory function transverse-velocity correlation is derived under assumptions irreversible...

A recent proposal in which the equation of state a polydisperse hard-sphere mixture is mapped onto that one-component fluid extrapolated beyond freezing point to estimate jamming packing fraction ${\ensuremath{\phi}}_{\mathrm{J}}$ system as simple function ${M}_{1}{M}_{3}/{M}_{2}^{2}$, where ${M}_{k}$ $k$th moment size distribution. An analysis experimental and simulation data for large number different mixtures shows remarkable general agreement with theoretical estimate. To give extra...

This Perspective article provides an overview of some our analytical approaches to the computation structural and thermodynamic properties single-component multicomponent hard-sphere fluids. For properties, they yield a thermodynamically consistent formulation, thus improving extending known results Percus-Yevick theory. Approximate expressions linking equation state fluid one mixtures are also discussed.

A rational-function approximation method to analytically derive the radial distribution function $g(r)$ and structure factor $S(q)$ of a hard-sphere fluid is revisited. The provides thermodynamically consistent with given equation state. Carnahan-Starling recently derived Pad\'e (4,3) equations state are considered. While leads functions even for densities larger than crystalline close-packing density, their physical value questionable already in metastable region. In case much more reliable...

The transport properties of dense binary fluid mixtures with one tracer component are discussed in the context revised Enskog theory (RET). Except for mutual and thermal diffusion coefficients, coefficients those excess alone. kinetic coefficient is given exactly by its low density (Boltzmann) value divided magnitude radial distribution function at contact. values can be estimated to within 1% all mass ratios μ. A comparison earlier work on limiting cases Rayleigh ( μ=∞) Lorentz μ=0) gases made.

Magnetohydrodynamic (MHD) induction devices such as electromagnetic pumps or electric generators are analysed within the approach of entropy generation. The flow an electrically-conducting incompressible fluid in MHD machine is described through well known Hartmann model. Irreversibilities system due to ohmic dissipation, friction and heat included entropy-generation rate. This quantity used define overall efficiency for that considers total loss caused by process irreversibility. For...

A method to obtain (approximate) analytical expressions for the radial distribution functions and structure factors in a multi-component mixture of additive hard spheres is introduced. In this method, only contact values function isothermal compressibility are required thermodynamic consistency achieved. The approach simpler than but yields equivalent results Generalized Mean Spherical Approximation. Calculations presented binary ternary at high density which...

The contact values $g_{ij}(\sigma_{ij})$ of the radial distribution functions a $d$-dimensional mixture (additive) hard spheres are considered. A `universality' assumption is put forward, according to which $g_{ij}(\sigma_{ij})=G(\eta, z_{ij})$, where $G$ common function for all mixtures same dimensionality, regardless number components, $\eta$ packing fraction mixture, and $z_{ij}$ dimensionless parameter that depends on size diameters $i$ $j$. For $d=3$, this universality holds...

A recently derived method [R. D. Rohrmann and A. Santos, Phys. Rev. E 76, 051202 (2007)] to obtain the exact solution of Percus-Yevick equation for a fluid hard spheres in (odd) d dimensions is used investigate convergence properties resulting virial series. This done both compressibility routes, which coefficients B(j) are expressed terms set (d-1)/2 coupled algebraic equations become nonlinear d>/=5. Results have been up d=13. confirmation alternating character series d>/=5, due existence...

An equation of state for a multicomponent mixture nonadditive hard spheres in d dimensions is proposed. It yields rather simple density dependence and constitutes natural extension the additive proposed by us [A. Santos, S. B. Yuste, M. López de Haro, Mol. Phys. 96, 1 (1999)]. The proposal relies on known exact second third virial coefficients requires as input compressibility factor one-component system. A comparison carried out both with another recent theoretical based similar philosophy...