368 research outputs found
Mesoscopic modeling of a two-phase flow in the presence of boundaries: the Contact Angle
We present a mesoscopic model, based on the Boltzmann Equation, for the
interaction between a solid wall and a non-ideal fluid. We present an analytic
derivation of the contact angle in terms of the surface tension between the
liquid-gas, the liquid-solid and the gas-solid phases. We study the dependency
of the contact angle on the two free parameters of the model, which determine
the interaction between the fluid and the boundaries, i.e. the equivalent of
the wall density and of the wall-fluid potential in Molecular Dynamics studies.
We compare the analytical results obtained in the hydrodynamical limit for
the density profile and for the surface tension expression with the numerical
simulations. We compare also our two-phase approach with some exact results for
a pure hydrodynamical incompressible fluid based on Navier-Stokes equations
with boundary conditions made up of alternating slip and no-slip strips.
Finally, we show how to overcome some theoretical limitations connected with a
discretized Boltzmann scheme and we discuss the equivalence between the surface
tension defined in terms of the mechanical equilibrium and in terms of the
Maxwell construction.Comment: 29 pages, 12 figure
Phase transition and percolation in Gibbsian particle models
We discuss the interrelation between phase transitions in interacting lattice
or continuum models, and the existence of infinite clusters in suitable
random-graph models. In particular, we describe a random-geometric approach to
the phase transition in the continuum Ising model of two species of particles
with soft or hard interspecies repulsion. We comment also on the related
area-interaction process and on perfect simulation.Comment: Survey article, 25 page
Profile and width of rough interfaces
In the context of Landau theory and its field theoretical refinements,
interfaces between coexisting phases are described by intrinsic profiles. These
intrinsic interface profiles, however, are neither directly accessible by
experiment nor by computer simulation as they are broadened by long-wavelength
capillary waves. In this paper we study the separation of the small scale
intrinsic structure from the large scale capillary wave fluctuations in the
Monte Carlo simulated three-dimensional Ising model. To this purpose, a
blocking procedure is applied, using the block size as a variable cutoff, and a
translationally invariant method to determine the interface position of
strongly fluctuating profiles on small length scales is introduced. While the
capillary wave picture is confirmed on large length scales and its limit of
validity is estimated, an intrinsic regime is, contrary to expectations, not
observed.Comment: 18 pages, 4 Postscript figures, LaTeX2e, formulation of sec.3.2
improved, 1 reference adde
Histogram analysis as a method for determining the line tension by Monte-Carlo simulations
A method is proposed for determining the line tension, which is the main
physical characteristic of a three-phase contact region, by Monte-Carlo (MC)
simulations. The key idea of the proposed method is that if a three-phase
equilibrium involves a three-phase contact region, the probability distribution
of states of a system as a function of two order parameters depends not only on
the surface tension, but also on the line tension. This probability
distribution can be obtained as a normalized histogram by appropriate MC
simulations, so one can use the combination of histogram analysis and
finite-size scaling to study the properties of a three phase contact region.
Every histogram and results extracted therefrom will depend on the size of the
simulated system. Carrying out MC simulations for a series of system sizes and
extrapolating the results, obtained from the corresponding series of
histograms, to infinite size, one can determine the line tension of the three
phase contact region and the interfacial tensions of all three interfaces (and
hence the contact angles) in an infinite system. To illustrate the proposed
method, it is applied to the three-dimensional ternary fluid mixture, in which
molecular pairs of like species do not interact whereas those of unlike species
interact as hard spheres. The simulated results are in agreement with
expectations
The random geometry of equilibrium phases
This is a (long) survey about applications of percolation theory in
equilibrium statistical mechanics. The chapters are as follows:
1. Introduction
2. Equilibrium phases
3. Some models
4. Coupling and stochastic domination
5. Percolation
6. Random-cluster representations
7. Uniqueness and exponential mixing from non-percolation
8. Phase transition and percolation
9. Random interactions
10. Continuum modelsComment: 118 pages. Addresses: [email protected]
http://www.mathematik.uni-muenchen.de/~georgii.html [email protected]
http://www.math.chalmers.se/~olleh [email protected]
Ordering and Demixing Transitions in Multicomponent Widom-Rowlinson Models
We use Monte Carlo techniques and analytical methods to study the phase
diagram of multicomponent Widom-Rowlinson models on a square lattice: there are
M species all with the same fugacity z and a nearest neighbor hard core
exclusion between unlike particles. Simulations show that for M between two and
six there is a direct transition from the gas phase at z < z_d (M) to a demixed
phase consisting mostly of one species at z > z_d (M) while for M \geq 7 there
is an intermediate ``crystal phase'' for z lying between z_c(M) and z_d(M). In
this phase, which is driven by entropy, particles, independent of species,
preferentially occupy one of the sublattices, i.e. spatial symmetry but not
particle symmetry is broken. The transition at z_d(M) appears to be first order
for M \geq 5 putting it in the Potts model universality class. For large M the
transition between the crystalline and demixed phase at z_d(M) can be proven to
be first order with z_d(M) \sim M-2 + 1/M + ..., while z_c(M) is argued to
behave as \mu_{cr}/M, with \mu_{cr} the value of the fugacity at which the one
component hard square lattice gas has a transition, and to be always of the
Ising type. Explicit calculations for the Bethe lattice with the coordination
number q=4 give results similar to those for the square lattice except that the
transition at z_d(M) becomes first order at M>2. This happens for all q,
consistent with the model being in the Potts universality class.Comment: 26 pages, 15 postscript figure
Surface tension of the Widom-Rowlinson model
11 pags., 5 figs., 3 tabs.We consider the computation of the surface tension of the fluid-fluid interface for the Widom-Rowlinson [J. Chem. Phys. 52, 1670 (1970)] binary mixture from direct simulation of the inhomogeneous system. We make use of the standard mechanical route, in which the surface tension follows from the computation of the normal and tangential components of the pressure tensor of the system. In addition to the usual approach, which involves simulations of the inhomogeneous system in the canonical ensemble, we also consider the computation of the surface tension in an ensemble where the pressure perpendicular (normal) to the planar interface is kept fixed. Both approaches are seen to provide consistent values of the interfacial tension. The issue of the system-size dependence of the surface tension is addressed. In addition, simulations of the fluid-fluid coexistence properties of the mixture are performed in the semigrand canonical ensemble. Our results are compared with existing data of the Widom-Rowlinson mixture and are also examined in the light of the vapor-liquid equilibrium of the thermodynamically equivalent one-component penetrable sphere model. © 2007 American Institute of Physics.Financial support is due to the Spanish Dirección General de Investigación Project Nos. FIS2004-06627-C02-01
E.d.M. and FIS2004-02954-C03-01 N.G.A. and from
Universidad de Huelva and Junta de Andalucía. Additional
funding from the Dirección General de Universidades e Investigación Comunidad de Madrid, Spain under the
MOSSNOHO-CM program Grant No. S0505/ESP/0299
and from the Engineering and Physical Sciences EPSRC of
the UK Grant Nos. GR/N20317, GR/N03358, GR/N35991,
GR/R09497, and EP/E016340, the Joint Research Equipment Initiative JREI GR/M94427, and the Royal Society Wolfson Foundation refurbishment grant is also acknowledged. Finally we are grateful to the Royal Society for the
award of a International Short Visit grant which has facilitated the collaborative work
- …