Spontaneous imbibition in disordered porous solids: a theoretical study of helium in silica aerogels.

We present a theoretical study of spontaneous imbibition of liquid (4)He in silica aerogels focusing on the effect of porosity on the fluid dynamical behavior. We adopt a coarse-grained three-dimensional lattice-gas description like in previous studies of gas adsorption and capillary condensation and use a dynamical mean-field theory, assuming that capillary disorder predominates over permeability disorder as in recent phase-field models of spontaneous imbibition. Our results reveal a remarkable connection between imbibition and adsorption as also suggested by recent experiments. The imbibition front is always preceded by a precursor film, and the classical Lucas-Washburn √t scaling law is generally recovered, although some deviations may exist at large porosity. Moreover, the interface roughening is modified by wetting and confinement effects. Our results suggest that the interpretation of the recent experiments should be revised.

Effect of the reservoir size on gas adsorption in inhomogeneous porous media.

We study the influence of the relative size of the reservoir on the adsorption isotherms of a fluid in disordered or inhomogeneous mesoporous solids. We consider both an atomistic model of a fluid in a simple, yet structured pore, whose adsorption isotherms are computed by molecular simulation, and a coarse-grained model for adsorption in a disordered mesoporous material, studied by a density functional approach in a local mean-field approximation. In both cases, the fluid inside the porous solid exchanges matter with a reservoir of gas that is at the same temperature and chemical potential and whose relative size can be varied, and the control parameter is the total number of molecules present in the porous sample and in the reservoir. Varying the relative sizes of the reservoir and the sample within experimental range may change the shape of the hysteretic isotherms, leading to a 're-entrant' behavior compared to the grand-canonical isotherm when the latter displays a jump in density. We relate these phenomena to the organization of the metastable states that are accessible for the adsorbed fluid at a given chemical potential or density.

Gas adsorption and desorption in silica aerogels: a theoretical study of scattering properties.

We present a numerical study of the structural correlations associated with gas adsorption and desorption in silica aerogels in order to provide a theoretical interpretation of scattering experiments. Following our earlier work, we use a coarse-grained lattice-gas description and determine the nonequilibrium behavior of the adsorbed gas within a local mean-field analysis. We focus on the differences between the adsorption and desorption mechanisms and their signature in the fluid-fluid and gel-fluid structure factors as a function of temperature. At low temperature, but still in the regime where the isotherms are continuous, we find that the adsorbed fluid density, during both filling and draining, is correlated over distances that may be much larger than the gel correlation length. In particular, extended fractal correlations may occur during desorption, indicating the existence of a ramified cluster of vapor filled cavities. This also induces an important increase of the scattering intensity at small wave vectors. The similarity and differences with the scattering of fluids in other porous solids such as Vycor are discussed.

Helium condensation in aerogel: avalanches and disorder-induced phase transition.

We present a detailed numerical study of the elementary condensation events (avalanches) associated to the adsorption of in silica aerogels. We use a coarse-grained lattice-gas description and determine the nonequilibrium behavior of the adsorbed gas within a local mean-field analysis, neglecting thermal fluctuations and activated processes. We investigate the statistical properties of the avalanches, such as their number, size and shape along the adsorption isotherms as a function of gel porosity, temperature, and chemical potential. Our calculations predict the existence of a line of critical points in the temperature-porosity diagram where the avalanche size distribution displays a power-law behavior and the adsorption isotherms have a universal scaling form. The estimated critical exponents seem compatible with those of the field-driven random field Ising model at zero temperature.

Mechanisms for gas adsorption and desorption in silica aerogels: the effect of temperature.

We present a theoretical study of the adsorption and desorption mechanisms of fluids in silica aerogels, focusing on the effect of temperature. We adopt a coarse-grained lattice description in which the gel structure is generated by a diffusion-limited cluster-cluster aggregation algorithm and the fluid configurations are computed using local mean-field (i.e., density functional) theory. Our calculations reproduce qualitatively the changes in the shape of the hysteresis loops observed with (4)He in gels of varying porosity. We study in detail the morphology of the condensation and evaporation events that correspond to the irreversible processes (avalanches) which are at the origin of the hysteresis. Depending on porosity and temperature, these avalanches may be localized, involve regions that extend beyond the gel correlation length, or even span the entire sample. This makes difficult the characterization of aerogels based on analyzing sorption isotherms.

Local mean-field study of capillary condensation in silica aerogels.

We apply local mean-field (i.e., density functional) theory to a lattice model of a fluid in contact with a dilute, disordered gel network. The gel structure is described by a diffusion-limited cluster aggregation model. We focus on the influence of porosity on both the hysteretic and the equilibrium behavior of the fluid as one varies the chemical potential at low temperature. We show that the shape of the hysteresis loop changes from smooth to rectangular as the porosity increases and that this change is associated with disorder-induced out-of-equilibrium phase transitions that differ in adsorption and in desorption. Our results provide insight in the behavior of 4He in silica aerogels.

Capillary condensation in disordered porous materials: hysteresis versus equilibrium behavior.

We study the interplay between hysteresis and equilibrium behavior in capillary condensation of fluids in mesoporous disordered materials via a mean-field density functional theory of a disordered lattice-gas model. The approach reproduces all major features observed experimentally. We show that the simple van der Waals picture of metastability fails due to the appearance of a complex free-energy landscape with a large number of metastable states. In particular, hysteresis can occur both with and without an underlying equilibrium transition, and thermodynamic consistency is not satisfied along the hysteresis loop.

Thermodynamically self-consistent theory for the Blume-Capel model.

We use a self-consistent Ornstein-Zernike approximation to study the Blume-Capel ferromagnet on three-dimensional lattices. The correlation functions and the thermodynamics are obtained from the solution of two coupled partial differential equations. The theory provides a comprehensive and accurate description of the phase diagram in all regions, including the wing boundaries in a nonzero magnetic field. In particular, the coordinates of the tricritical point are in very good agreement with the best estimates from simulation or series expansion. Numerical and analytical analysis strongly suggest that the theory predicts a universal Ising-like critical behavior along the lambda line and the wing critical lines, and a tricritical behavior governed by mean-field exponents.