117 research outputs found
Percolation, depinning, and avalanches in capillary condensation of gases in disordered porous solids
We propose a comprehensive theoretical description of hysteresis in capillary
condensation of gases in mesoporous disordered materials. Applying mean-field
density functional theory to a coarse-grained lattice-gas model, we show that
the morphology of the hysteresis loops is influenced by out-of-equilibrium
transitions that are different on filling and on draining. In particular,
desorption may be associated to a depinning process and be percolation-like
without explicit pore-blocking effects.Comment: 4 pages, 5 figure
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 may
change the shape of the hysteretic isotherms, leading to a "reentrant" 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.Comment: 16 page
Model fluid in a porous medium: results for a Bethe lattice
We consider a lattice gas with quenched impurities or `quenched-annealed
binary mixture' on the Bethe lattice. The quenched part represents a porous
matrix in which the (annealed) lattice gas resides. This model features the 3
main factors of fluids in random porous media: wetting, randomness and
confinement. The recursive character of the Bethe lattice enables an exact
treatment, whose key ingredient is an integral equation yielding the
one-particle effective field distribution. Our analysis shows that this
distribution consists of two essentially different parts. The first one is a
continuous spectrum and corresponds to the macroscopic volume accessible to the
fluid, the second is discrete and comes from finite closed cavities in the
porous medium. Those closed cavities are in equilibrium with the bulk fluid
within the grand canonical ensemble we use, but are inaccessible in real
experimental situations. Fortunately, we are able to isolate their
contributions. Separation of the discrete spectrum facilitates also the
numerical solution of the main equation. The numerical calculations show that
the continuous spectrum becomes more and more rough as the temperature
decreases, and this limits the accuracy of the solution at low temperatures.Comment: 13 pages, 12 figure
Adsorption of a fluid in an aerogel: integral equation approach
We present a theoretical study of the phase diagram and the structure of a
fluid adsorbed in high-porosity aerogels by means of an integral-equation
approach combined with the replica formalism. To simulate a realistic gel
environment, we use an aerogel structure factor obtained from an off-lattice
diffusion-limited cluster-cluster aggregation process. The predictions of the
theory are in qualitative agreement with the experimental results, showing a
substantial narrowing of the gas-liquid coexistence curve (compared to that of
the bulk fluid), associated with weak changes in the critical density and
temperature. The influence of the aerogel structure (nontrivial short-range
correlations due to connectedness, long-range fractal behavior of the silica
strands) is shown to be important at low fluid densities.Comment: 24 pages, 9 figure
Spontaneous imbibition in a slit pore: a lattice-gas dynamic mean field study
We present a theoretical study of spontaneous imbibition in a slit pore using
a lattice-gas model and a dynamic mean-field theory. Emphasis is put on the
influence of the precursor films on the speed of the imbibition front due to
liquid mass conservation. This work is dedicated to Bob Evans for his 65th
birthday in recognition of his seminal contributions to the theory of fluids in
confining geometries.Comment: 17 pages, 13 figure
Gas adsorption/desorption in silica aerogels: a theoretical study of scattering properties
We present a numerical study of the structural correlations associated to gas
adsorption/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.Comment: 16 pages, 15 figure
A 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 non-zero 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 -line and the wing critical lines, and a tricritical behavior
governed by mean-field exponents.Comment: 11 figures. to appear in Physical Review
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