Carmen Varea

Square well orthobaric densities via spinodal decomposition

Orthobaric densities of a square well fluid are obtained by means of a molecular dynamics simulation. Hard wall boundary conditions in one direction and periodic boundary conditions in the other two, added to a mean density close to the critical have two effects: a fast spinodal decomposition that condenses a slab of liquid at the center of the box plus a better sampling of the whole orthobaric curve. Results for the liquid densities compare well with previously obtained data while vapor densities are more sensitive to capillary effects. These finite size effects are analyzed within a lattice gas model, especially those produced by changes in box size and mean density. The method is well suited to predict orthobaric and miscibility curves for binary mixtures once the orthobaric curves of each molecular species have been properly adjusted to experiment.

Flower Development as an Interplay between Dynamical Physical Fields and Genetic Networks

In this paper we propose a model to describe the mechanisms by which undifferentiated cells attain gene configurations underlying cell fate determination during morphogenesis. Despite the complicated mechanisms that surely intervene in this process, it is clear that the fundamental fact is that cells obtain spatial and temporal information that bias their destiny. Our main hypothesis assumes that there is at least one macroscopic field that breaks the symmetry of space at a given time. This field provides the information required for the process of cell differentiation to occur by being dynamically coupled to a signal transduction mechanism that, in turn, acts directly upon the gene regulatory network (GRN) underlying cell-fate decisions within cells. We illustrate and test our proposal with a GRN model grounded on experimental data for cell fate specification during organ formation in early Arabidopsis thaliana flower development. We show that our model is able to recover the multigene configurations characteristic of sepal, petal, stamen and carpel primordial cells arranged in concentric rings, in a similar pattern to that observed during actual floral organ determination. Such pattern is robust to alterations of the model parameters and simulated failures predict altered spatio-temporal patterns that mimic those described for several mutants. Furthermore, simulated alterations in the physical fields predict a pattern equivalent to that found in Lacandonia schismatica, the only flowering species with central stamens surrounded by carpels.

Stress tensor of curved interfaces

We use density functional theory to analyse the structure of the stress tensor σ for fluid interfaces of arbitrary shape, and determine the spatially non-local components of σ that correspond to a description with a semi-orthogonal set of coordinates (ˆn, t 1, t 2). We then study a local, van der Waals-type, density functional with squared-Laplacian term and arrive at closed and general expressions for the surface tension γ, the bending constants κ and κ and the spontaneous curvature c 0. These expressions have the same general form for all interfacial shapes, but their precise values are curvature-dependent. In the case of γ this dependence is that already known and measured by the Tolman length δ. We discuss and compare our results with those of others and resolve existing discrepancies.

Rigorous interface properties for the van der Waals fluid mixture

A statistical mechanical treatment for the van der Waals fluid mixture is developed, based on Widom’s potential‐distribution theory for nonuniform fluids. For the specific choice of Kac pair interactions, in the van der Waals limit, a set of coupled second‐order differential equations determine the density profiles. The solution of these equations and the determination of the interfacial tension are discussed in terms of a mechanical analogy.

Density functional theory beyond the surface tension. Interfacial width, elastic bending constants and line tension

The long wavelength behavior of the Ornstein-Zernike direct correlation function for nonuniform fluids c(r,r′) has provided important results that comprise our current understanding of fluid interfaces. As we know, the surface tension is obtained from the second moment of c(r,r′), and long-ranged correlations parallel to the surface stand among the main predictions. Also, conventional capillary wave theory leads to its notorious divergent results for the interfacial width when the surface tension cost of thermally excited fluctuations is considered. Here we discuss the consequences of the higher moments of c(r,r′) in the density functional theory of fluid interfaces. We find that in an appropriately extended capillary wave model the interfacial width is finite in the absence of external fields. We derive the expression for the elastic curvature energy and find that the bending moduli are given by the fourth moment of c(r,r′). We obtain too in the same fashion the line tension that originates when interfaces meet.

Nucleation, spinodal decomposition, and interface motion in the van der Waals fluid

We discuss the predictions of the phenomenological theory of Metiu, Kitahara, and Ross for the most probable evolution of density fluctuations in the van der Waals fluid model. The knowledge of the exact (nonlocal) form for the grand potential functional Ω permits a precise study of the kinetics of phase change under strongly nonuniform conditions. It is shown that for every subcritical temperature and chemical potential in the spinodal region there exists an infinite family of periodic stationary states in addition to the usual uniform ones. The stability analysis of these states provides a description of spinodal decomposition in its intermediate and later stages. It is also shown that fluctuations separated in space are correlated through the nonlocality of Ω and that they cooperate in the nucleation process with an additional term absent in the classical and gradient theories. The solitary wave motion which describes condensation–evaporation processes is obtained from a perturbation on the thermodynam...

Bending rigidities and spontaneous curvature for a spherical interface

We report on a study of the free energy of a spherical interface described by a van der Waals density functional with a squared-Laplacian term. We examine the bulk, the surface tension and the bending rigidity terms, and find the position for the dividing surface that satisfies the Laplace equation generalized to nonvanishing bending energy. In doing this we have made explicit the connection between two previously derived but dissimilar sets of expressions for the interfacial coefficients that stem from the same free energy model (one by Romero-Rochin et al. (Phys. Rev. A 44 (1991) 8417; Phys. Rev. E 46 (1993) 1600) and the other by Gompper and Zschocke (Europhys. Lett. 18 (1991) 731) and by Blokhuis and Bedeaux (Mol. Phys. 80 (1993) 705).

Possibility of Continuous Wetting Transition at the Liquid-Vapour Interface of the Binary Liquid Mixture Cyclohexane + Acetonitrile

We have measured the contact angle θ for a lens of liquid L2 suspended at the liquid L1-vapour interface in a mixture of cyclohexane and acetonitrile. A power law θ ∝ |T - Tcw|ν with Tcw = (72.2 ± 0.05) °C is obeyed just below the critical bulk temperature Tc = 75.61 °C. We obtain ν = 0.98 ± 0.08, whereas an attempt to conform the data to the 1st-order transition law θ ∝ |T - Tcw|1/2 leads to Tw = (71.99 ± 0.05) °C and leaves data for the smallest angles unaccounted for. The mean-field prediction θ ∝ |T - Tcw|3/2 for critical wetting in 3D systems with long-ranged forces gives a reasonable fit, however the power law is observed only within an asymptotic region.

FLUCTUATIONS AND INSTABILITIES OF CURVED INTERFACES

We study the stability of cylindrical and spherical interfaces with respect to density fluctuations within the square-gradient approximation. That is, we determine the stability matrix (of the second derivatives of the free energy functional with respect to the density) when the stationary state is a cylindrical or spherical droplet of a stable phase embedded in the metastable phase. For these geometries the stationary states are unstable, some of the eigenvalues are negative and their eigenfunctions represent those fluctuations that are amplified in a process where the equilibrium state is reached. At early times, in a simple model A kinetics, the eigenfunctions represent the fluctuations that grow or decay with a simple exponential law and with a characteristic time that is proportional to the inverse of the eigenvalues. Our results agree with the stability criteria obtained from the Laplace equation, that is, the nucleation of critical droplets and in the case of cylinders also the Rayleigh instability. In the limit of infinite radius we recover the known results for the planar interface between two stable phases. The modes with lowest energy correspond to the customary capillary waves, while other modes with higher energy associated to changes in the interfacial width are shown to be related to a novel interfacial coefficient.

Free energy expressions for a spherical interface

The free energy is analysed of a spherical interface generated in a fluid described by a local free energy density functional that features square-gradient and square-Laplacian terms. The bulk, the surface tension and the bending rigidity terms are investigated, and the position is found for the dividing surface that satisfies the generalized Laplace equation that incorporates bending terms. The results agree with those obtained previously from the general expression for the stress tensor of an interface of arbitrary shape (Romero-Rochin, V., Varea, C., and Robledo, A., 1991, Phys. Rev. A, 44, 8417; 1993, Phys. Rev. E, 46, 1600). Also, when a comparison is made between spherical and planar interfaces the expressions obtained are those derived by Gompper, G., and Zschocke, S. (1991, Europhys. Lett., 18, 731) and by Blokhuis, E. M., and Bedeaux, D. (1993, Molec, Phys., 80, 705). These expressions correspond to the length of Tolman and to similar higher-order correction terms.