arXiv subjects

C. Rascón

Publications and source records attributed to C. Rascón.

6 recordsLinked to original sources

arXiv2026

The exact solution of the Koga-Widom-Indekeu model and related models of wetting in fluid mixtures

We show how a broad class of two-component square-gradient models of wetting may be solved exactly for the surface tensions and density profile paths, and clarify how the presence or absence of critical point wetting, in binary and ternary mixtures, is related to universality and symmetry principles at critical end points. We begin by solving a model of fluid interfaces, first introduced by Koga and Widom, in ternary mixtures showing three phase coexistence. Numerical studies had revealed interesting wetting transitions, as well as curious geometrical properties of the profile paths in the density plane, and led these authors to conjecture expressions for the surface tensions. These conjectures were extended by Koga and Indekeu and predicted that partial wetting may persist up to the line of critical end points, i.e. critical point wetting was absent. Here, we obtain the exact density profiles and surface tensions for the Koga-Widom-Indekeu (KWI) model using complex analysis and drawing on the theory of algebraic curves. The exact solution determines the location and order of wetting transitions in the surface phase diagram, confirming that critical point wetting is absent. The model also displays the remarkable property that microscopic density profiles are mapped, by a conformal transform, onto the shape of a macroscopic drop near the contact line whose tensions satisfy the Neumann triangle. Two related models, which illustrate the role of the component isotropy, are also discussed. These models suggest that a universality principle governs wetting in fluid mixtures, resolving contradicting results from earlier studies: Critical point wetting is present if the order-parameter components of the mixture describe Ising-like criticality, but is absent if there is a local XY symmetry. Implications for wetting transitions in more microscopic models and in experiments are discussed.

cond-mat.soft↗

arXiv2024

Wetting, Algebraic Curves and Conformal Invariance

Recent studies of wetting in a two-component square-gradient model of interfaces in a fluid mixture, showing three-phase bulk coexistence, have revealed some highly surprising features. Numerical results show that the density profile paths, which form a tricuspid shape in the density plane, have curious geometric properties, while conjectures for the analytical form of the surface tensions imply that nonwetting may persist up to the critical end points, contrary to the usual expectation of critical point wetting. Here, we solve the model exactly and show that the profile paths are conformally invariant quartic algebraic curves that change genus at the wetting transition. Being harmonic, the profile paths can be represented by an analytic function in the complex plane which then conformally maps the paths onto straight lines. Using this, we derive the conjectured form of the surface tensions and explain the geometrical properties of the tricuspid and its relation to the Neumann triangle for the contact angles. The exact solution confirms that critical point wetting is absent in this square-gradient model.

cond-mat.stat-mech↗

arXiv2015

The local structure factor near an interface; Beyond extended Capillary-Wave models

We investigate the local structure factor $S(z;q)$ at a free liquid-gas interface in systems with short-ranged intermolecular forces and determine the corrections to the leading-order, capillary-wave-like, Goldstone mode divergence of $S(z;q)$ known to occur for parallel wavevectors $q\to 0$. We show from explicit solution of the inhomogeneous Ornstein-Zernike equation that for distances $z$ far from the interface, where the profile decays exponentially, $S(z;q)$ splits unambiguously into bulk and interfacial contributions. On each side of the interface, the interfacial contributions can be characterised by distinct liquid and gas wavevector dependent surface tensions, $σ_l(q)$ and $σ_g(q)$, which are determined solely by the $bulk$ two-body and three-body direct correlation functions. At high temperatures, the wavevector dependence simplifies and is determined almost entirely by the appropriate bulk structure factor, leading to positive rigidity coefficients. Our predictions are confirmed by explicit calculation of $S(z;q)$ within square-gradient theory and the Sullivan model. The results for the latter predict a striking temperature dependence for $σ_l(q)$ and $σ_g(q)$, and have implications for fluctuation effects. Our results account quantitatively for the findings of a recent very extensive simulation study by Höfling and Dietrich of the total structure factor in the interfacial region, in a system with a cut-off Lennard-Jones potential, in sharp contrast to extended Capillary-Wave models which failed completely to describe the simulation results.

cond-mat.stat-mech↗

arXiv2015

Liquid-Gas Asymmetry and the Wavevector-Dependent Surface Tension

Attempts to extend the capillary-wave theory of fluid interfacial fluctuations to microscopic wavelengths, by introducing an effective wave-vector ($q$) dependent surface tension $σ_\text{eff}(q)$, have encountered difficulties. There is no consensus as to even the shape of $σ_\text{eff}(q)$. By analysing a simple density functional model of the liquid-gas interface, we identify different schemes for separating microscopic observables into background and interfacial contributions. In order for the backgrounds of the density-density correlation function and local structure factor to have a consistent and physically meaningful interpretation in terms of weighted bulk gas and liquid contributions, the background of the total structure factor must be characterised by a microscopic $q$-dependent length $ζ(q)$ not identified previously. The necessity of including the $q$ dependence of $ζ(q)$ is illustrated explicitly in our model and has wider implications, i.e. in typical experimental and simulation studies, an indeterminacy in $ζ(q)$ will always be present, reminiscent of the cut-off used in capillary-wave theory. This leads inevitably to a large uncertainty in the $q$ dependence of $σ_\text{eff}(q)$.

cond-mat.stat-mech↗

arXiv2014

Capillary Contact Angle in a Completely Wet Groove

We consider the phase equilibria of a fluid confined in a deep capillary groove of width $L$ with identical side walls and a bottom made of a different material. All walls are completely wet by the liquid. Using density functional theory and interfacial models, we show that the meniscus separating liquid and gas phases at two phase capillary-coexistence meets the bottom capped end of the groove at a capillary contact angle $θ^{\rm cap}(L)$ which depends on the difference between the Hamaker constants. If the bottom wall has a weaker wall-fluid attraction than the side walls, then $θ^{\rm cap}>0$ even though all the isolated walls are themselves completely wet. This alters the capillary condensation transition which is now first-order; this would be continuous in a capped capillary made wholly of either type of material. We show that the capillary contact angle $θ^{\rm cap}(L)$ vanishes in two limits, corresponding to different capillary wetting transitions. These occur as the width i) becomes macroscopically large, and ii) is reduced to a microscopic value determined by the difference in Hamaker constants. This second wetting transition is characterised by large scale fluctuations and essential critical singularities arising from marginal interfacial interactions.

cond-mat.soft↗

arXiv2014

Pair correlation functions and the wavevector-dependent surface tension in a simple density functional treatment of the liquid-vapour interface

We study the density-density correlation function $G({\bf r},{\bf r}')$ in the interfacial region of a fluid (or Ising-like magnet) with short-ranged interactions using square gradient density functional theory. Adopting a simple double parabola approximation for the bulk free-energy density, we first show that the parallel Fourier transform $G(z,z';q)$ and local structure factor $S(z;q)$ separate into bulk and excess contributions. We attempt to account for both contributions by deriving an interfacial Hamiltonian, characterised by a wavevector dependent surface tension $σ(q)$, and then reconstructing density correlations from correlations in the interface position. We show that the standard crossing criterion identification of the interface, as a surface of fixed density (or magnetization), does not explain the separation of $G(z,z';q)$ and the form of the excess contribution. We propose an alternative definition of the interface position based on the properties of correlations between points that "float" with the surface and show that this describes the full $q$ and $z$ dependence of the excess contributions to both $G$ and $S$. However, neither the "crossing-criterion" nor the new "floating interface" definition of $σ(q)$ are quantities directly measurable from the total structure factor $S^{tot}(q)$ which contains additional $q$ dependence arising from the non-local relation between fluctuations in the interfacial position and local density. Since it is the total structure factor that is measured experimentally or in simulations, our results have repercussions for earlier attempts to extract and interpret $σ(q)$.

cond-mat.stat-mech↗