%A Galteland,Olav
%A Bedeaux,Dick
%A Hafskjold,Bjørn
%A Kjelstrup,Signe
%D 2019
%J Frontiers in Physics
%C
%F
%G English
%K thermodynamics of small systems,Representative elementary volume,Nano-porous media,molecular dynamics,Single phase
%Q
%R 10.3389/fphy.2019.00060
%W
%L
%N 60
%M
%P
%7
%8 2019-April-24
%9 Original Research
%#
%! Pressures inside a nano-porous medium. The case of a single phase fluid
%*
%<
%T Pressures Inside a Nano-Porous Medium. The Case of a Single Phase Fluid
%U https://www.frontiersin.org/article/10.3389/fphy.2019.00060
%V 7
%0 JOURNAL ARTICLE
%@ 2296-424X
%X We define the pressure of a porous medium in terms of the grand potential and compute its value in a nano-confined or nano-porous medium, meaning a medium where thermodynamic equations need be adjusted for smallness. On the nano-scale, the pressure depends in a crucial way on the size and shape of the pores. According to Hill [1], two pressures are needed to characterize this situation; the integral pressure and the differential pressure. Using Hill's formalism for a nano-porous medium, we derive an expression for the difference between the integral and the differential pressures in a spherical phase α of radius R, p^α-pα=γ/R. We recover the law of Young-Laplace for the differential pressure difference across the same curved surface. We discuss the definition of a representative volume element for the nano-porous medium and show that the smallest REV is a unit cell in the direction of the pore in the fcc lattice. We also show, for the first time, how the pressure profile through a nano-porous medium can be defined and computed away from equilibrium.