@incollection{statphys23_0295,
	title = {Fluids confined in random porous media: A hard sponge model},
	address = {Genova, Italy},
	author = {W. Dong and S.L. Zhao},
	booktitle = {Abstract Book of the XXIII IUPAP International Conference on Statistical Physics},
	editor = {Luciano Pietronero and Vittorio Loreto and Stefano Zapperi},
	month = {9-13 July},
	url = {http://st23.statphys23.org/webservices/abstract/preview_pop.php?ID_PAPER=295},
	year = {2007},
	biburl = {http://www.bibsonomy.org/bibtex/2af25cd33537adbbb33026ca4446cdfe2/statphys23},
	abstract = {The morphology of many porous materials is sponge-like. Despite
the abundance of such materials [1,2], simple models which 
allow for a theoretical description of such materials are still
lacking. Here, we propose a hard sponge model which is made by
digging percolated spherical cavities in a solid continuum (see 
Fig.1). The interaction potential of fluid particles with such
a porous medium can be modelled by the following expression,
\begin{equation}
U_{10} = \sum_{i=1}^{N_1}  u_{10}({\mathbf
r}_i; {\mathbf q}^{N_0} ). \label{eq1}
\end{equation}
with
\begin{equation}
u_{10}({\mathbf r}_i; {\mathbf q}^{N_0} ) = - k_B T 
ln [1 - e^{-\beta \sum_{j=1}^{N_0} \phi^{HS}(\left| {\mathbf
r}_i - {\mathbf q}_j \right|)}]. \label{eq2}
\end{equation}
where $k_B$ and $T$ are respectively Boltzmann constant and the
temperature and $\phi^{HS}$ is the hard sphere potential with
a diameter of $\sigma$ which is the diameter of the spherical 
cavity in our model. The interaction potential described by 
eqs.(1) and (2) is clearly not pair additive. Despite of this 
non additive form of
fluid-matrix interaction, we show that the diagrammatic
expansions can be still obtained for various distribution
function. We derived also the Ornstein-Zernike equations for
a fluid confined in such a hard sponge model. We show also
how the replica method [3,4] can be extended to treat this
model.

1) P.M. Adler, {\it Porous Media}, Butterworth-Heinemann, 
Boston, 1992.\\
2) P. Spanne, J.F. Thovert, C.J. Jacquin, W.B. Lindquist, K.W.
Jones and P.M. Adler, Phys. Rev. Lett. 73, 2001, (1994).\\
3) J.A. Given, Phys. Rev. A, 45, 816, (1992).\\
4) J.A. Given and G.R. Stell, Physica A, 209, (1994).},
	keywords = {adsorption equations fluid media ornstein-zernike porous random statphys23 topic-6 }
}