Carlos Fernández Tejero

APPROXIMATE ANALYTICAL EXPRESSION FOR THE DIRECT CORRELATION FUNCTION OF HARD DISCS WITHIN THE PERCUS-YEVICK EQUATION

A simple approximate analytical expression for the direct correlation function of a hard-sphere fluid in D dimensions within the Percus-Yevick equation is proposed. The approximation exactly reproduces the well-known results for D = 1 and D = 3, while for D = 2 it compares well to the numerical results for densities not very close to the freezing density.

Viscoelastic surface waves and the surface structure of liquids

The dispersion relations for surface waves on a planar liquid surface are obtained from first principles. The high-frequency elastic, low-frequency hydrodynamic and intermediate viscoelastic regimes are investigated separately. It is shown that the structure of the liquid surface modifies the expression for Rayleighs elastic surface waves and Kelvins capillary waves and allows for the existence of new surface waves besides those of the phenomenological theories. For example, an hydrodynamic counterpart to the Rayleigh waves and an elastic counterpart to the capillary waves are found. The experimental observation of these surface waves could in principle yield direct access to the structure of the liquid surface.

Interfacial hydrodynamics: a microscopic approach

Linearized hydrodynamic equations for a nonuniform anisotropic fluid are obtained from the exact Mori–Zwanzig equations for the conserved densities. In the particular case of a two‐phase system with a planar equilibrium interface, these equations can be reduced to the ordinary hydrodynamic equations inside each bulk phase and to surface hydrodynamic equations for the interfacial layer. Surface transport coefficients and surface thermodynamic parameters are hereby obtained as Gibbs surface excess values. All the known phenomenological equations can be recovered by suitable approximations. Various correction terms to the phenomenological results, including Laplace’s formula, are found.

A theoretical estimate of the Wilson-Frenkel kinetics of colloidal crystal growth in charge-stabilized dispersions

The Wilson-Frenkel growth law of colloidal crystals formed in charge-stabilized dispersions of latex spheres is investigated theoretically on the basis of variational free-energy estimates. We find, in agreement with recent experimental results, that the reduced growth velocity is a universal function of some rescaled density variable.

On the relation between the compressibility and the static structure factor of a fluid with a state-dependent pair-potential

The compressibility equation of a fluid with an effective, state-dependent, pair-potential is derived. It is shown that the thermodynamic states for which the infinite wavelength limit of the static structure factor diverges are not consistent with the thermodynamic states for which the compressibility diverges whenever the effective potential is density-dependent. This result is in agreement with some recent numerical simulations.

Virial coefficients and demixing in the Asakura–Oosawa model

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.

Rescaled density expansions and demixing in hard-sphere binary mixtures.

The demixing transition of a binary fluid mixture of additive hard spheres is analyzed for different size asymmetries by starting from the exact low-density expansion of the pressure. Already within the second virial approximation the fluid separates into two phases of different composition with a lower consolute critical point. By successively incorporating the third, fourth, and fifth virial coefficients, the critical consolute point moves to higher values of the pressure and to lower values of the partial number fraction of the large spheres. When the exact low-density expansion of the pressure is rescaled to higher densities as in the Percus-Yevick theory, by adding more exact virial coefficients a different qualitative movement of the critical consolute point in the phase diagram is found. It is argued that the Percus-Yevick factor appearing in many empirical equations of state for the mixture has a deep influence on the location of the critical consolute point, so that the resulting phase diagram for a prescribed equation has to be taken with caution.

A microscopic theory of interfacial hydrodynamics

The exact evolution equations for the conserved densities of a one-component two-phase fluid are reduced, in each bulk phase to the corresponding linearized hydrodynamic equations and at the interface, to boundary conditions, relating the jump in the stress tensor and heat current to surface excess thermodynamic and surface transport properties.

Surface waves: a visco-elastic theory

Abstract The structure of the liquid surface is shown to lead to the appearance of new surface waves which are studied both in the high-frequency elastic domain and in the low-frequency hydrodynamic domain. The experimental observation of these surface waves could yield direct access to the surface structure.

Communication: Virial coefficients and demixing in highly asymmetric binary additive hard-sphere mixtures

The problem of demixing in a binary fluid mixture of highly asymmetric additive hard spheres is revisited. A comparison is presented between the results derived previously using truncated virial expansions for three finite size ratios with those that one obtains with the same approach in the extreme case in which one of the components consists of point particles. Since this latter system is known not to exhibit fluid-fluid segregation, the similarity observed for the behavior of the critical constants arising in the truncated series in all instances, while not being conclusive, may cast serious doubts as to the actual existence of a demixing fluid-fluid transition in disparate-sized binary additive hard-sphere mixtures.