TY - JOUR
AU - Galteland, Olav
AU - Bedeaux, Dick
AU - Hafskjold, Bjørn
AU - Kjelstrup, Signe
PY - 2019
M3 - 10.3389/fphy.2019.00060
SP - 60
TI - Pressures Inside a Nano-Porous Medium. The Case of a Single Phase Fluid
JO - Frontiers in Physics
UR - https://www.frontiersin.org/article/10.3389/fphy.2019.00060
VL - 7
SN - 2296-424X
N2 - 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.
ER -