70 research outputs found
Gravity‐induced density and concentration profiles in binary mixtures near gas–liquid critical lines
We have calculated gravity‐induced density and concentration gradients using scaled equations of state fashioned after that of Leung and Griffiths for binary mixtures near gas–liquid critical lines. The mixtures considered here are those of helium‐3 and helium‐4 and of carbon dioxide and ethane. Our calculations show that the density profiles for both mixtures in any proportion of the components are similar to those of pure fluids. The concentration gradients in the helium mixture have the same appearance as the density gradients. In the carbon dioxide–ethane system, however, the form of the concentration profile varies greatly, depending on the overall composition. Moreover, the temperature at which a mixture separates into two phases is slightly different from that expected for the mixture in the absence of gravity. We have also examined the case where a mixture is subjected to a large gravitational field such as can be generated in a centrifuge and found that, although the density gradient in all the mixtures is like that in pure fluids, the concentration gradients in the mixtures of carbon dioxide and ethane have complex features related to the presence of critical azeotropy
Master crossover functions for the one-component fluid "subclass"
Introducing three well-defined dimensionless numbers, we establish the link
between the scale dilatation method able to estimate master (i.e. unique)
singular behaviors of the one-component fluid "subclass" and the universal
crossover functions recently estimated [Garrabos and Bervillier, Phys. Rev. E
74, 021113 (2006)] from the bounded results of the massive renormalization
scheme applied to the..
Effects of patch size and number within a simple model of patchy colloids
We report on a computer simulation and integral equation study of a simple
model of patchy spheres, each of whose surfaces is decorated with two opposite
attractive caps, as a function of the fraction of covered attractive
surface. The simple model explored --- the two-patch Kern-Frenkel model ---
interpolates between a square-well and a hard-sphere potential on changing the
coverage . We show that integral equation theory provides quantitative
predictions in the entire explored region of temperatures and densities from
the square-well limit down to . For smaller
, good numerical convergence of the equations is achieved only at
temperatures larger than the gas-liquid critical point, where however integral
equation theory provides a complete description of the angular dependence.
These results are contrasted with those for the one-patch case. We investigate
the remaining region of coverage via numerical simulation and show how the
gas-liquid critical point moves to smaller densities and temperatures on
decreasing . Below , crystallization prevents the
possibility of observing the evolution of the line of critical points,
providing the angular analog of the disappearance of the liquid as an
equilibrium phase on decreasing the range for spherical potentials. Finally, we
show that the stable ordered phase evolves on decreasing from a
three-dimensional crystal of interconnected planes to a two-dimensional
independent-planes structure to a one-dimensional fluid of chains when the
one-bond-per-patch limit is eventually reached.Comment: 26 pages, 11 figures, J. Chem. Phys. in pres
Existence of a critical point in the phase diagram of the ideal relativistic neutral Bose gas
We explore the phase transitions of the ideal relativistic neutral Bose gas
confined in a cubic box, without assuming the thermodynamic limit nor
continuous approximation. While the corresponding non-relativistic canonical
partition function is essentially a one-variable function depending on a
particular combination of temperature and volume, the relativistic canonical
partition function is genuinely a two-variable function of them. Based on an
exact expression of the canonical partition function, we performed numerical
computations for up to hundred thousand particles. We report that if the number
of particles is equal to or greater than a critical value, which amounts to
7616, the ideal relativistic neutral Bose gas features a spinodal curve with a
critical point. This enables us to depict the phase diagram of the ideal Bose
gas. The consequent phase transition is first-order below the critical pressure
or second-order at the critical pressure. The exponents corresponding to the
singularities are 1/2 and 2/3 respectively. We also verify the recently
observed `Widom line' in the supercritical region.Comment: 1+25 pages, 6 B/W figures: Comment on the Widom line added. Minor
improvement. Version to appear in `New Journal of Physics
Free Energy Minimizers for a Two--Species Model with Segregation and Liquid-Vapor Transition
We study the coexistence of phases in a two--species model whose free energy
is given by the scaling limit of a system with long range interactions (Kac
potentials) which are attractive between particles of the same species and
repulsive between different species.Comment: 32 pages, 1 fig, plain tex, typeset twic
Master crossover behavior of parachor correlations for one-component fluids
The master asymptotic behavior of the usual parachor correlations, expressing
surface tension as a power law of the density difference
between coexisting liquid and vapor, is analyzed for a
series of pure compounds close to their liquid-vapor critical point, using only
four critical parameters , , and ,
for each fluid.
... The main consequences of these theoretical estimations are discussed in
the light of engineering applications and process simulations where parachor
correlations constitute one of the most practical method for estimating surface
tension from density and capillary rise measurements
Master singular behavior for the Sugden factor of the one-component fluids near their gas-liquid critical point
We present the master (i.e. unique) behavior of the squared capillary length
- so called the Sudgen factor-, as a function of the temperature-like field
along the critical isochore, asymptotically close to the gas-liquid critical
point of twenty (one component) fluids. This master behavior is obtained using
the scale dilatation of the relevant physical fields of the one-component
fluids. The scale dilatation introduces the fluid-dependent scale factors in a
manner analog with the linear relations between physical fields and scaling
fields needed by the renormalization theory applied to the Ising-like
universality class. The master behavior for the Sudgen factor satisfies
hyperscaling and can be asymptotically fitted by the leading terms of the
theoretical crossover functions for the correlation length and the
susceptibility in the homogeneous domain recently obtained from massive
renormalization in field theory. In the absence of corresponding estimation of
the theoretical crossover functions for the interfacial tension, we define the
range of the temperature-like field where the master leading power law can be
practically used to predict the singular behavior of the Sudgen factor in
conformity with the theoretical description provided by the massive
renormalization scheme within the extended asymptotic domain of the
one-component fluid "subclass"
Thermodynamic characteristics of the classical n-vector magnetic model in three dimensions
The method of calculating the free energy and thermodynamic characteristics
of the classical n-vector three-dimensional (3D) magnetic model at the
microscopic level without any adjustable parameters is proposed. Mathematical
description is perfomed using the collective variables (CV) method in the
framework of the model approximation. The exponentially decreasing
function of the distance between the particles situated at the N sites of a
simple cubic lattice is used as the interaction potential. Explicit and
rigorous analytical expressions for entropy,internal energy, specific heat near
the phase transition point as functions of the temperature are obtained. The
dependence of the amplitudes of the thermodynamic characteristics of the system
for and on the microscopic parameters of the interaction
potential are studied for the cases and . The obtained
results provide the basis for accurate analysis of the critical behaviour in
three dimensions including the nonuniversal characteristics of the system.Comment: 25 pages, 5 figure
The liquid-vapor interface of an ionic fluid
We investigate the liquid-vapor interface of the restricted primitive model
(RPM) for an ionic fluid using a density-functional approximation based on
correlation functions of the homogeneous fluid as obtained from the
mean-spherical approximation (MSA). In the limit of a homogeneous fluid our
approach yields the well-known MSA (energy) equation of state. The ionic
interfacial density profiles, which for the RPM are identical for both species,
have a shape similar to those of simple atomic fluids in that the decay towards
the bulk values is more rapid on the vapor side than on the liquid side. This
is the opposite asymmetry of the decay to that found in earlier calculations
for the RPM based on a square-gradient theory. The width of the interface is,
for a wide range of temperatures, approximately four times the second moment
correlation length of the liquid phase. We discuss the magnitude and
temperature dependence of the surface tension, and argue that for temperatures
near the triple point the ratio of the dimensionless surface tension and
critical temperature is much smaller for the RPM than for simple atomic fluids.Comment: 6 postscript figures, submitted to Phys. Rev.
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