189 research outputs found
Dynamic density functional theory versus Kinetic theory of simple fluids
By combining methods of kinetic and density functional theory, we present a
description of molecular fluids which accounts for their microscopic structure
and thermodynamic properties as well as for the hydrodynamic behavior. We focus
on the evolution of the one particle phase space distribution, rather than on
the evolution of the average particle density, which features in dynamic
density functional theory. The resulting equation can be studied in two
different physical limits: diffusive dynamics, typical of colloidal fluids
without hydrodynamic interaction, where particles are subject to overdamped
motion resulting from the coupling with a solvent at rest, and inertial
dynamics, typical of molecular fluids. Finally, we propose an algorithm to
solve numerically and efficiently the resulting kinetic equation by employing a
discretization procedure analogous to the one used in the Lattice Boltzmann
method.Comment: 15 page
Tracer diffusion of hard-sphere binary mixtures under nano-confinement
The physics of diffusion phenomena in nano- and microchannels has attracted a lot of attention in recent years, due to its close connection with many technological, medical, and industrial appli- cations. In the present paper, we employ a kinetic approach to investigate how the confinement in nanostructured geometries affects the diffusive properties of fluid mixtures and leads to the appearance of properties different from those of bulk systems. In particular, we derive an expression for the friction tensor in the case of a bulk fluid mixture confined to a narrow slit having undulated walls. The boundary roughness leads to a new mechanism for transverse diffusion and can even lead to an effective diffusion along the channel larger than the one corresponding to a planar channel of equivalent section. Finally, we discuss a reduction of the previous equation to a one dimensional effective diffusion equation in which an entropic term encapsulates the geometrical information on the channel shape
Kinetic Density Functional Theory: A microscopic approach to fluid mechanics
In the present paper we give a brief summary of some recent theoretical
advances in the treatment of inhomogeneous fluids and methods which have
applications in the study of dynamical properties of liquids in situations of
extreme confinement, such as nanopores, nanodevices, etc. The approach obtained
by combining kinetic and density functional methods is microscopic, fully
self-consistent and allows to determine both configurational and flow
properties of dense fluids.
The theory predicts the correct hydrodynamic behavior and provides a
practical and numerical tool to determine how the transport properties are
modified when the length scales of the confining channels are comparable with
the size of the molecules. The applications range from the dynamics of simple
fluids under confinement, to that of neutral binary mixtures and electrolytes
where the theory in the limit of slow gradients reproduces the known
phenomenological equations such as the Planck-Nernst-Poisson and the
Smoluchowski equations. The approach here illustrated allows for fast numerical
solution of the evolution equations for the one-particle phase-space
distributions by means of the weighted density lattice Boltzmann method and is
particularly useful when one considers flows in complex geometries.Comment: 14 page
Charge transport in nanochannels: a molecular theory
We introduce a theoretical and numerical method to investigate the flow of
charged fluid mixtures under extreme confinement. We model the electrolyte
solution as a ternary mixture, comprising two ionic species of opposite charge
and a third uncharged component. The microscopic approach is based on kinetic
theory and is fully self-consistent. It allows to determine configurational
prop- erties, such as layering near the confining walls, and the flow
properties. We show that, under appropriate assumptions, the approach
reproduces the phenomenological equations used to describe electrokinetic
phenomena, without requiring the introduction of constitutive equations to
determine the fluxes. Moreover, we model channels of arbitrary shape and
nanometric roughness, features that have important repercussions on the
transport properties of these systems. Numerical simulations are obtained by
solving the evolution dynamics of the one-particle phase- space distributions
of each species by means of a Lattice Boltzmann method for flows in straight
and wedged channels. Results are presented for the microscopic density, the
velocity profiles and for the volumetric and charge flow-rates. Strong
departures from electroneutrality are shown to appear at molecular level
Clausius relation for active particles: what can we learn from fluctuations?
Many kinds of active particles, such as bacteria or active colloids, move in
a thermostatted fluid by means of self-propulsion. Energy injected by such a
non-equilibrium force is eventually dissipated as heat in the thermostat. Since
thermal fluctuations are much faster and weaker than self-propulsion forces,
they are often neglected, blurring the identification of dissipated heat in
theoretical models. For the same reason, some freedom - or arbitrariness -
appears when defining entropy production. Recently three different recipes to
define heat and entropy production have been proposed for the same model where
the role of self-propulsion is played by a Gaussian coloured noise. Here we
compare and discuss the relation between such proposals and their physical
meaning. One of these proposals takes into account the heat exchanged with a
non-equilibrium active bath: such an "active heat" satisfies the original
Clausius relation and can be experimentally verified.Comment: 10 pages, submitted to Entropy journal for the special issue
"Thermodynamics and Statistical Mechanics of Small Systems" (see
http://www.mdpi.com/journal/entropy/special_issues/small_systems
Multicomponent Diffusion in Nanosystems
We present the detailed analysis of the diffusive transport of spatially
inhomogeneous fluid mixtures and the interplay between structural and dynamical
properties varying on the atomic scale. The present treatment is based on
different areas of liquid state theory, namely kinetic and density functional
theory and their implementation as an effective numerical method via the
Lattice Boltzmann approach. By combining the first two methods it is possible
to obtain a closed set of kinetic equations for the singlet phase space
distribution functions of each species. The interactions among particles are
considered within a self-consistent approximation and the resulting effective
molecular fields are analyzed. We focus on multispecies diffusion in systems
with short-range hard-core repulsion between particles of unequal sizes and
weak attractive long-range interactions. As a result, the attractive part of
the potential does not contribute explicitly to viscosity but to diffusivity
and the thermodynamic properties. Finally, we obtain a practical scheme to
solve the kinetic equations by employing a discretization procedure derived
from the Lattice Boltzmann approach. Within this framework, we present
numerical data concerning the mutual diffusion properties both in the case of a
quiescent bulk fluid and shear flow inducing Taylor dispersion.Comment: 19 pages + 5 figure
Time dependent Ginzburg-Landau equation for an N-component model of self-assembled fluids
We study the time evolution of an N-component model of bicontinuous
microemulsions based on a time dependent Ginzburg-Landau equation quenched from
an high temperature uncorrelated state to the low temperature phases. The
behavior of the dynamical structure factor is obtained, in each
phase, in the framework of the large- limit with both conserved (COP) and
non conserved (NCOP) order parameter dynamics. At zero temperature the system
shows multiscaling in the unstructured region up to the tricritical point for
the COP whereas ordinary scaling is obeyed for NCOP. In the structured phase,
instead, the conservation law is found to be irrelevant and the form , with and , is
obtained in every case. Simple scaling relations are also derived for the
structure factor as a function of the final temperature of the thermal bath.Comment: 9 pages,Apste
Controlling electroosmotic flows by polymer coatings: A joint experimental-theoretical investigation
We analyze the electroosmotic flow (EOF) of an electrolytic solution in a polymer coated capillary electrophoresis tube. The polymeric density, charge, thickness, and the capillary tube charge vary as a function of pH and produce a non-trivial modulation of the EOF, including a flow reversal at acid pH conditions. By means of a theoretical argument and numerical simulations, we recover the experimental curve for the EOF, providing a firm approach for predictive analysis of electroosmosis under different polymeric coating conditions. A proposed application of the approach is to determine the near-wall charge of the coating to be used for further quantitative analysis of the electroosmotic flow and mobility
Active chiral particles under confinement: surface currents and bulk accumulation phenomena
In this work, we study the stationary behavior of an assembly of independent
chiral active particles under confinement by employing an extension of the
active Ornstein-Uhlenbeck model. The chirality modeled by means of an effective
torque term leads to a drastic reduction of the accumulation near the walls
with respect to the case without handedness and to the appearance of currents
parallel to the container walls accompanied by a large accumulation of
particles in the inner region. In the case of two-dimensional chiral particles
confined by harmonic walls, we determine the analytic form of the distribution
of positions and velocities in two different situations: a rotationally
invariant confining potential and an infinite channel with parabolic walls.
Both these models display currents and chirality induced inner accumulation.
These phenomena are further investigated by means of a more realistic
description of a channel, where the wall and bulk regions are clearly
separated. The corresponding current and density profiles are obtained by
numerical simulations. At variance with the harmonic models, the third model
shows a progressive emptying of the wall regions and the simultaneous
enhancement of the bulk population. We explain such a phenomenology in terms of
the combined effect of wall repulsive forces and chiral motion and provide a
semiquantitative description of the current profile in terms of an effective
viscosity of the chiral gas.Comment: 5 figure
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