78 research outputs found
Systematically extending classical nucleation theory
The foundation for any discussion of first-order phse transitions is
Classical Nucleation Theory(CNT). CNT, developed in the first half of the
twentieth century, is based on a number of heuristically plausible assumtptions
and the majority of theoretical work on nucleation is devoted to refining or
extending these ideas. Ideally, one would like to derive CNT from a more
fundamental description of nucleation so that its extension, development and
refinement could be developed systematically. In this paper, such a development
is described based on a previously established (Lutsko, JCP 136:034509, 2012 )
connection between Classical Nucleation Theory and fluctuating hydrodynamics.
Here, this connection is described without the need for artificial assumtions
such as spherical symmetry. The results are illustrated by application to CNT
with moving clusters (a long-standing problem in the literature) and the
constructrion of CNT for ellipsoidal clusters
The low-density/high-density liquid phase transition for model globular proteins
The effect of molecule size (excluded volume) and the range of interaction on
the surface tension, phase diagram and nucleation properties of a model
globular protein is investigated using a combinations of Monte Carlo
simulations and finite temperature classical Density Functional Theory
calculations. We use a parametrized potential that can vary smoothly from the
standard Lennard-Jones interaction characteristic of simple fluids, to the ten
Wolde-Frenkel model for the effective interaction of globular proteins in
solution. We find that the large excluded volume characteristic of large
macromolecules such as proteins is the dominant effect in determining the
liquid-vapor surface tension and nucleation properties. The variation of the
range of the potential only appears important in the case of small excluded
volumes such as for simple fluids. The DFT calculations are then used to study
homogeneous nucleation of the high-density phase from the low-density phase
including the nucleation barriers, nucleation pathways and the rate. It is
found that the nucleation barriers are typically only a few and that
the nucleation rates substantially higher than would be predicted by Classical
Nucleation Theory.Comment: To appear in Langmui
Nonlinear viscosity and velocity distribution function in a simple longitudinal flow
A compressible flow characterized by a velocity field is
analyzed by means of the Boltzmann equation and the Bhatnagar-Gross-Krook
kinetic model. The sign of the control parameter (the longitudinal deformation
rate ) distinguishes between an expansion () and a condensation ()
phenomenon. The temperature is a decreasing function of time in the former
case, while it is an increasing function in the latter. The non-Newtonian
behavior of the gas is described by a dimensionless nonlinear viscosity
, that depends on the dimensionless longitudinal rate . The
Chapman-Enskog expansion of in powers of is seen to be only
asymptotic (except in the case of Maxwell molecules). The velocity distribution
function is also studied. At any value of , it exhibits an algebraic
high-velocity tail that is responsible for the divergence of velocity moments.
For sufficiently negative , moments of degree four and higher may diverge,
while for positive the divergence occurs in moments of degree equal to or
larger than eight.Comment: 18 pages (Revtex), including 5 figures (eps). Analysis of the heat
flux plus other minor changes added. Revised version accepted for publication
in PR
Structure and Instability of High-Density Equations for Traffic Flow
Similar to the treatment of dense gases, fluid-dynamic equations for the
dynamics of congested vehicular traffic are derived from Enskog-like kinetic
equations. These contain additional terms due to the anisotropic vehicle
interactions. The calculations are carried out up to Navier-Stokes order. A
linear instability analysis indicates an additional kind of instability
compared to previous macroscopic traffic models. The relevance for describing
granular flows is outlined.Comment: For related work see
http://www.theo2.physik.uni-stuttgart.de/helbing.htm
Segregation by thermal diffusion of an intruder in a moderately dense granular fluid
A solution of the inelastic Enskog equation that goes beyond the weak
dissipation limit and applies for moderate densities is used to determine the
thermal diffusion factor of an intruder immersed in a dense granular gas under
gravity. This factor provides a segregation criterion that shows the transition
between the Brazil-nut effect (BNE) and the reverse Brazil-nut effect (RBNE) by
varying the parameters of the system (masses, sizes, density and coefficients
of restitution). The form of the phase-diagrams for the BNE/RBNE transition
depends sensitively on the value of gravity relative to the thermal gradient,
so that it is possible to switch between both states for given values of the
parameters of the system. Two specific limits are considered with detail: (i)
absence of gravity, and (ii) homogeneous temperature. In the latter case, after
some approximations, our results are consistent with previous theoretical
results derived from the Enskog equation. Our results also indicate that the
influence of dissipation on thermal diffusion is more important in the absence
of gravity than in the opposite limit. The present analysis extends previous
theoretical results derived in the dilute limit case [V. Garz\'o, Europhys.
Lett. {\bf 75}, 521 (2006)] and is consistent with the findings of some recent
experimental results.Comment: 10 figure
Tracer diffusion in granular shear flows
Tracer diffusion in a granular gas in simple shear flow is analyzed. The
analysis is made from a perturbation solution of the Boltzmann kinetic equation
through first order in the gradient of the mole fraction of tracer particles.
The reference state (zeroth-order approximation) corresponds to a Sonine
solution of the Boltzmann equation, which holds for arbitrary values of the
restitution coefficients. Due to the anisotropy induced in the system by the
shear flow, the mass flux defines a diffusion tensor instead of a
scalar diffusion coefficient. The elements of this tensor are given in terms of
the restitution coefficients and mass and size ratios. The dependence of the
diffusion tensor on the parameters of the problem is illustrated in the
three-dimensional case. The results show that the influence of dissipation on
the elements is in general quite important, even for moderate values
of the restitution coefficients. In the case of self-diffusion (mechanically
equivalent particles), the trends observed in recent molecular dynamics
simulations are similar to those obtained here from the Boltzmann kinetic
theory.Comment: 5 figure
Hydrodynamic fluctuations in the Kolmogorov flow: Linear regime
The Landau-Lifshitz fluctuating hydrodynamics is used to study the
statistical properties of the linearized Kolmogorov flow. The relative
simplicity of this flow allows a detailed analysis of the fluctuation spectrum
from near equilibrium regime up to the vicinity of the first convective
instability threshold. It is shown that in the long time limit the flow behaves
as an incompressible fluid, regardless of the value of the Reynolds number.
This is not the case for the short time behavior where the incompressibility
assumption leads in general to a wrong form of the static correlation
functions, except near the instability threshold. The theoretical predictions
are confirmed by numerical simulations of the full nonlinear fluctuating
hydrodynamic equations.Comment: 20 pages, 4 figure
A new approach for the limit to tree height using a liquid nanolayer model
Liquids in contact with solids are submitted to intermolecular forces
inferring density gradients at the walls. The van der Waals forces make liquid
heterogeneous, the stress tensor is not any more spherical as in homogeneous
bulks and it is possible to obtain stable thin liquid films wetting vertical
walls up to altitudes that incompressible fluid models are not forecasting.
Application to micro tubes of xylem enables to understand why the ascent of sap
is possible for very high trees like sequoias or giant eucalyptus.Comment: In the conclusion is a complementary comment to the Continuum
Mechanics and Thermodynamics paper. 21 pages, 4 figures. Continuum Mechanics
and Thermodynamics 20, 5 (2008) to appea
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