Umberto Marini Bettolo Marconi - Università di Camerino & INFN #
Dynamics of Fluids in Nanospaces #
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, $f(r,v,t)$ rather than on the evolution of the average 
particle density, $\rho(r,t)$, 
which features in dynamic density functional theory 
often employed to describe colloidal systems. </br>
 In order to describe with sufficient accuracy the fluid structure
at length scales comparable with the size of the particles we shall resort
to methods similar to those of density functional theory (DFT)
employed in the study of equilibrium and non equilibrium properties.
In the case of hard-core
fluids,  DFT and its dynamical extension give excellent results and
can be extended to more realistic fluids by using the van der Waals
picture of decomposing the total inter-particle potential into a
short-range repulsive potential and a long-range attractive potential
tail. The first is treated by means of a reference hard-sphere system
whilst the second is considered within the random phase 
approximation (RPA). </br>
A simple analysis of the equations is used to derive explicit
expressions both for equilibrium thermodynamic quantities, such as
pressure, compressibility etc., and for non equilibrium transport
coefficients.
</br>
In the second part of our presentation we shall introduce a
a multicomponent extension of our theory and 
describe miscible and immiscible liquid mixtures
under inhomogeneous, non steady conditions typical of confined
fluid flows.
 We first derive from a microscopic level
the evolution equations of the phase space distribution function of
each component in terms of a set of self consistent fields,
representing both body forces and viscous forces.  Secondly, we solve 
numerically
the resulting governing equations  by means of the
Lattice Boltzmann method whose implementation contains novel
features with respect to existing approaches.  Our model incorporates
hydrodynamic flow, diffusion, surface tension,and the possibility for
global and local viscosity variations.  We validate our model by
studying the bulk viscosity dependence of the mixture on concentration,
packing fraction and size ratio. Finally we consider inhomogeneous systems 
and study the
dynamics of mixtures in slits of molecular thickness and relate structural 
and flow properties. </br>
The resulting equation  for $f(r,v,t)$ is 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 .