The numerical solution of the BGYB equation for the liquid-vapour interface

The derivation of the Born-Green-Yvon-Bogolyubov integrodifferential equation is discussed. As the numerical solution of this equation is very sensitive to the approximations it is pointed out that qualitative differences between the density profiles obtained with different approximations can be expected. The connection between the predictions of linear response theory and the behaviour of the resulting density profiles is also indicated.     

Variation of the local field through the liquid-vapour interface

We derive an integral equation for the self-consistent local field E^loc(z) within an inhomogeneous non-polar fluid, with particular application to the liquid-vapour interface. Approximate solutions are given for the cases of induced atomic dipoles oriented perpendicular and parallel to the interface. For the perpendicular case we relate the average field to the local field and thus obtain an equation for the static dielectric constant ?(z) in terms of the density profile n(z). The departures of the local field from Lorentz form $\text{E}{}^{\mathrm{<mtext>ext</mtext>}}\text{/(1 + (}\text{8}\text{3}\text{)παn(z))}$ and of the dielectric constant from the Clausius-Mossotti form ($\text{1 + (}\text{8}\text{3}\text{)πan(z))/(1 ? (}\text{4}\text{3}\text{)παn(z))}$ are shown to be small. For the parallel case we discuss fringing of the external field and show that the dipoles align themselves with the average field, not the external field. The departure of the local field from $\text{E}{}^{\mathrm{<mtext>ave</mtext>}}\text{/(1 ? (}\text{4}\text{3}\text{παn(z))}$ is shown to be small.     

The interface tension atT c in the potts model

Recently there has been a lot of interest in determining the interface tension between the ordered and disordered phases of QCD and other statistical systems with lattice Monte Carlo methods. In this work these methods are further developed with a renormalization transformation to encompass all lattice spin and gauge models. This method is applied to the 2 dimensional 7 state and 3 dimensional 3 state simple cubic lattice Potts models by using the Migdal-Kadanoff scaling approximation. A finite-size analysis for the measured values is performed; the results are /T=(7.4±1.0)×10^–2 for the 2d7s and /T=(4.0±1.2)×10^–3 for the 3d3s model. However, the systematic errors due to the approximation scheme may be of the order of 30%.     

Theory of the liquid-vapour interface of a binary mixture of Lennard-Jones fluids

We present results of calculations of the equilibrium surface tension and density profiles for the liquid-vapour interface of a binary mixture of Lennard-Jones 12-6 fluids. The calculations are based on a density-functional theory for the Helmholtz free energy of the inhomogeneous mixture. This is a ‘microscopic’ generalization of the van der Waals-Cahn-Hilliard theory for the interface of a binary mixture.

Our calculations cover the full range of liquid-vapour coexistence and the whole range of concentration. We find a correlation between the excess surface tension of the mixture and the surface segregation (adsorption) of the species with the lower surface tension. The ways in which segregation and excess surface tension depend on the Lennard-Jones parameters of the pure components are briefly discussed. Our results for the excess surface tension of mixtures of Ar and N₂ and Ar and CH₄ are compared with experiment; the agreement is reasonable.     

The surface tension and density of molten tin with low additions of barium

Data on polytherms of the density and surface tension of tin—barium melts are published for the first time. The data were obtained by means of an automated software complex.     

Capillary waves on the liquid-vapour interface, and propagation near boundaries

The paper will outline the thermally-excited-capillary-wave model for the liquid-vapour interface, and then discuss some factors which are neglected which may well be important when comparing with experiment. To learn about the properties of capillary waves in thin liquid layers we have made a study of the propagation of waves up an inclined beach and preliminary results of this study will be described.     

The quark bag model with surface tension

A membranous closed surface is introduced to confine colored vector gluon fields in a Lorentz invariant manner. Since the colored pointlike quarks are always coupled to the gluon fields, they become confined inside the closed membrane. The Hamiltonian formulation of the model is presented, and the classical string limit is discussed.     

Anisotropy of the interface tension of the three-dimensional Ising model

We determine the interface tension for the 100, 110 and 111 interface of the simple cubic Ising model with nearest-neighbour interaction using novel simulation methods. To overcome the droplet/strip transition and the droplet nucleation barrier we use a newly developed combination of the multimagnetic algorithm with the parallel tempering method. We investigate a large range of inverse temperatures to study the anisotropy of the interface tension in detail.     

Anisotropic surface tension and the liquid drop model

The liquid drop model assumes that the surface tension of all nuclei is isotropic. The consequences of relaxing this assumption are studied. First a macroscopic theory of anisotropic surface tension is presented. Then with a particular choice for the functional form of the surface tension tensor, this theory is applied to a charged liquid drop. A small anisotropy in the surface tension can significantly distort a highly charged drop and lower its fission barrier.     

The nature of the liquid-vapour interface and other topics in the statistical mechanics of non-uniform,classical fluids

Recent theoretical work on the microscopic structure and surface tension of the liquid-vapour interface of simple (argon-like) fluids is critically reviewed. In particular, the form of pairwise intermolecular correlations in the liquid surface and the capillary wave treatment of the interface are examined in some detail. It is argued that conventional capillary wave theory, which leads to divergences in the width of the density profile, is unsatisfactory for describing all the equilibrium aspects of the interface. The density functional formalism which has been developed to study the liquid-vapour interface can also be profitably applied to other problems in the statistical mechanics of non-uniform fluids; here a new generalization of the ‘linear’ theory of spinodal decomposition is formulated and by considering a ‘nearly uniform’ fluid, some useful results for the long-wavelength behaviour of the liquid structure factor of various monatomic liquids are obtained. Some other topics of current interest in this area are briefly discussed.     

Renormalization-group calculation of the dependence on gravity of the surface tension and bending rigidity of a fluid interface

The surface tension and the bending rigidity of a planar liquid-vapor interface in the presence of vanishing gravity are analyzed using the renormalization group. Based on the density functional theory of inhomogeneous fluids, we show that a term, quartic in the density fluctuations, can be added to the classical capillary-wave model so that a renormalization-group calculation can be performed. By comparing the outcome of such a calculation with rigorous results relating the direct correlation function with surface tension and bending rigidity, we find the scaling dependence of the latter on gravity. The results agree with the expected fact that the interface should become unstable as gravity vanishes.     

An all-speed relaxation scheme for interface flows with surface tension

We consider interface flows where compressibility and capillary forces (surface tension) are significant. These flows are described by a non-conservative, unconditionally hyperbolic multiphase model. The numerical approximation is based on finite-volume method for unstructured grids. At the discrete level, the surface tension is approximated by a volume force (CSF formulation). The interface physical properties are recovered by designing an appropriate linearized Riemann solver (Relaxation scheme) that prevents spurious oscillations near material interfaces. For low-speed flows, a preconditioning linearization is proposed and the low Mach asymptotic is formally recovered. Numerical computations, for a bubble equilibrium, converge to the required Laplace law and the dynamic of a drop, falling under gravity, is in agreement with experimental observations.     

The effect of anisotropic surface tension on the morphological stability of planar interface during directional solidification

This paper considers the effect of the anisotropic surface tension on the morphological stability of the planar interface during directional solidification. When the expression exhibiting the four-fold symmetry is included, the modified absolute stability criterion is obtained by employing the multi-variable expansion method. The linear stability analysis reveals that for the given temperature gradient, as the anisotropic surface tension parameter increases, the stability zone tends to decrease.     

The structure of molten germanium

We present a calculation of the structure of molten Ge, based on pseudopotential-derived interatomic forces and the optimized random phase approximation. Good agreement with experiment is achieved. We show that the complex structure of liquid Ge results from the interplay of two characteristic distances: the effective hardcore diameter and the Friedel wavelength of the long range oscillations in the interatomic potential.     

Surface tension,shear viscosity and isothermal compressibility of liquid C60 along the liquid-vapour coexistence

The correlations between the surface tension, shear viscosity, and isothermal compressibility, are investigated for liquid C₆₀ at extended regions of temperature and pressure. An improved equation of state [EOS] is employed, based on hard-core plus three Yukawa potential [HC3YK] which facilitates the analytically accurate series mean spherical approximation [SMSA] formalism for the free energy. The present equation of state is utilized to obtain analytical expressions for the thermodynamic functions of interest and discuss the validity of their mutual relations along the spinodal curve of C₆₀.     

The dependence of the curvature elasticity moduli of a lipid bilayer on the change of the surface tension at a curving oil-water interface

It has been shown that the change of the surface tension γ at an oil-water interface, when this interface is not flat, effects an addition to the sum of the curvature elasticity moduli (2k_c+k?_c) (k_c and k?_c are proposed by Helfrich). The value of this effect is assessed.     

Thermodynamics of molten salt mixtures

The first two terms of the high energy expansion of the relative density of states for two hard spheres (needed for the computation of the second virial coefficient at high temperature) are obtained directly from the analytic expression for the phase shifts. This is enough to give the classical second virial and the first quantum correction.     

Dielectric and transport properties of a supercooled symmetrical molten salt

The liquid-glass transition of the restricted primitive model for a symmetrical molten salt is studied using mode-coupling theory. The transition at high densities is predicted to obey the Lindemann criterion for melting, and the charge-density peak found in neutron-scattering experiments on ionic glass formers is qualitatively reproduced. Frequency-dependent dielectric functions, shear viscosities, and dynamical conductivities of the supercooled liquid are presented. Comparing the latter to the diffusion constant, we find that mode-coupling theory reproduces the Nernst-Einstein relation. The Stokes-Einstein radius is found to be approximately equal to the particle radius only near the high-density glass transition.