331 research outputs found
Thermodynamics of non-local materials: extra fluxes and internal powers
The most usual formulation of the Laws of Thermodynamics turns out to be
suitable for local or simple materials, while for non-local systems there are
two different ways: either modify this usual formulation by introducing
suitable extra fluxes or express the Laws of Thermodynamics in terms of
internal powers directly, as we propose in this paper. The first choice is
subject to the criticism that the vector fluxes must be introduced a posteriori
in order to obtain the compatibility with the Laws of Thermodynamics. On the
contrary, the formulation in terms of internal powers is more general, because
it is a priori defined on the basis of the constitutive equations. Besides it
allows to highlight, without ambiguity, the contribution of the internal powers
in the variation of the thermodynamic potentials. Finally, in this paper, we
consider some examples of non-local materials and derive the proper expressions
of their internal powers from the power balance laws.Comment: 16 pages, in press on Continuum Mechanics and Thermodynamic
Eutectic colony formation: A phase field study
Eutectic two-phase cells, also known as eutectic colonies, are commonly
observed during the solidification of ternary alloys when the composition is
close to a binary eutectic valley. In analogy with the solidification cells
formed in dilute binary alloys, colony formation is triggered by a
morphological instability of a macroscopically planar eutectic solidification
front due to the rejection by both solid phases of a ternary impurity that
diffuses in the liquid. Here we develop a phase-field model of a binary
eutectic with a dilute ternary impurity and we investigate by dynamical
simulations both the initial linear regime of this instability, and the
subsequent highly nonlinear evolution of the interface that leads to fully
developed two-phase cells with a spacing much larger than the lamellar spacing.
We find a good overall agreement with our recent linear stability analysis [M.
Plapp and A. Karma, Phys. Rev. E 60, 6865 (1999)], which predicts a
destabilization of the front by long-wavelength modes that may be stationary or
oscillatory. A fine comparison, however, reveals that the assumption commonly
attributed to Cahn that lamella grow perpendicular to the envelope of the
solidification front is weakly violated in the phase-field simulations. We show
that, even though weak, this violation has an important quantitative effect on
the stability properties of the eutectic front. We also investigate the
dynamics of fully developed colonies and find that the large-scale envelope of
the composite eutectic front does not converge to a steady state, but exhibits
cell elimination and tip-splitting events up to the largest times simulated.Comment: 18 pages, 18 EPS figures, RevTeX twocolumn, submitted to Phys. Rev.
A variational formulation of anisotropic geometric evolution equations in higher dimensions
Accepted versio
Threshold criterion for wetting at the triple point
Grand canonical simulations are used to calculate adsorption isotherms of
various classical gases on alkali metal and Mg surfaces. Ab initio adsorption
potentials and Lennard-Jones gas-gas interactions are used. Depending on the
system, the resulting behavior can be nonwetting for all temperatures studied,
complete wetting, or (in the intermediate case) exhibit a wetting transition.
An unusual variety of wetting transitions at the triple point is found in the
case of a specific adsorption potential of intermediate strength. The general
threshold for wetting near the triple point is found to be close to that
predicted with a heuristic model of Cheng et al. This same conclusion was drawn
in a recent experimental and simulation study of Ar on CO_2 by Mistura et al.
These results imply that a dimensionless wetting parameter w is useful for
predicting whether wetting behavior is present at and above the triple
temperature. The nonwetting/wetting crossover value found here is w circa 3.3.Comment: 15 pages, 8 figure
Spinodal Decomposition in a Binary Polymer Mixture: Dynamic Self Consistent Field Theory and Monte Carlo Simulations
We investigate how the dynamics of a single chain influences the kinetics of
early stage phase separation in a symmetric binary polymer mixture. We consider
quenches from the disordered phase into the region of spinodal instability. On
a mean field level we approach this problem with two methods: a dynamical
extension of the self consistent field theory for Gaussian chains, with the
density variables evolving in time, and the method of the external potential
dynamics where the effective external fields are propagated in time. Different
wave vector dependencies of the kinetic coefficient are taken into account.
These early stages of spinodal decomposition are also studied through Monte
Carlo simulations employing the bond fluctuation model that maps the chains --
in our case with 64 effective segments -- on a coarse grained lattice. The
results obtained through self consistent field calculations and Monte Carlo
simulations can be compared because the time, length, and temperature scales
are mapped onto each other through the diffusion constant, the chain extension,
and the energy of mixing. The quantitative comparison of the relaxation rate of
the global structure factor shows that a kinetic coefficient according to the
Rouse model gives a much better agreement than a local, i.e. wave vector
independent, kinetic factor. Including fluctuations in the self consistent
field calculations leads to a shorter time span of spinodal behaviour and a
reduction of the relaxation rate for smaller wave vectors and prevents the
relaxation rate from becoming negative for larger values of the wave vector.
This is also in agreement with the simulation results.Comment: Phys.Rev.E in prin
From nonwetting to prewetting: the asymptotic behavior of 4He drops on alkali substrates
We investigate the spreading of 4He droplets on alkali surfaces at zero
temperature, within the frame of Finite Range Density Functional theory. The
equilibrium configurations of several 4He_N clusters and their asymptotic trend
with increasing particle number N, which can be traced to the wetting behavior
of the quantum fluid, are examined for nanoscopic droplets. We discuss the size
effects, inferring that the asymptotic properties of large droplets correspond
to those of the prewetting film
To wet or not to wet: that is the question
Wetting transitions have been predicted and observed to occur for various
combinations of fluids and surfaces. This paper describes the origin of such
transitions, for liquid films on solid surfaces, in terms of the gas-surface
interaction potentials V(r), which depend on the specific adsorption system.
The transitions of light inert gases and H2 molecules on alkali metal surfaces
have been explored extensively and are relatively well understood in terms of
the least attractive adsorption interactions in nature. Much less thoroughly
investigated are wetting transitions of Hg, water, heavy inert gases and other
molecular films. The basic idea is that nonwetting occurs, for energetic
reasons, if the adsorption potential's well-depth D is smaller than, or
comparable to, the well-depth of the adsorbate-adsorbate mutual interaction. At
the wetting temperature, Tw, the transition to wetting occurs, for entropic
reasons, when the liquid's surface tension is sufficiently small that the free
energy cost in forming a thick film is sufficiently compensated by the fluid-
surface interaction energy. Guidelines useful for exploring wetting transitions
of other systems are analyzed, in terms of generic criteria involving the
"simple model", which yields results in terms of gas-surface interaction
parameters and thermodynamic properties of the bulk adsorbate.Comment: Article accepted for publication in J. Low Temp. Phy
Three-dimensional lattice-Boltzmann simulations of critical spinodal decomposition in binary immiscible fluids
We use a modified Shan-Chen, noiseless lattice-BGK model for binary
immiscible, incompressible, athermal fluids in three dimensions to simulate the
coarsening of domains following a deep quench below the spinodal point from a
symmetric and homogeneous mixture into a two-phase configuration. We find the
average domain size growing with time as , where increases
in the range , consistent with a crossover between
diffusive and hydrodynamic viscous, , behaviour. We find
good collapse onto a single scaling function, yet the domain growth exponents
differ from others' works' for similar values of the unique characteristic
length and time that can be constructed out of the fluid's parameters. This
rebuts claims of universality for the dynamical scaling hypothesis. At early
times, we also find a crossover from to in the scaled structure
function, which disappears when the dynamical scaling reasonably improves at
later times. This excludes noise as the cause for a behaviour, as
proposed by others. We also observe exponential temporal growth of the
structure function during the initial stages of the dynamics and for
wavenumbers less than a threshold value.Comment: 45 pages, 18 figures. Accepted for publication in Physical Review
Monte Carlo Methods for Estimating Interfacial Free Energies and Line Tensions
Excess contributions to the free energy due to interfaces occur for many
problems encountered in the statistical physics of condensed matter when
coexistence between different phases is possible (e.g. wetting phenomena,
nucleation, crystal growth, etc.). This article reviews two methods to estimate
both interfacial free energies and line tensions by Monte Carlo simulations of
simple models, (e.g. the Ising model, a symmetrical binary Lennard-Jones fluid
exhibiting a miscibility gap, and a simple Lennard-Jones fluid). One method is
based on thermodynamic integration. This method is useful to study flat and
inclined interfaces for Ising lattices, allowing also the estimation of line
tensions of three-phase contact lines, when the interfaces meet walls (where
"surface fields" may act). A generalization to off-lattice systems is described
as well.
The second method is based on the sampling of the order parameter
distribution of the system throughout the two-phase coexistence region of the
model. Both the interface free energies of flat interfaces and of (spherical or
cylindrical) droplets (or bubbles) can be estimated, including also systems
with walls, where sphere-cap shaped wall-attached droplets occur. The
curvature-dependence of the interfacial free energy is discussed, and estimates
for the line tensions are compared to results from the thermodynamic
integration method. Basic limitations of all these methods are critically
discussed, and an outlook on other approaches is given
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