AUTHOR=Galteland Olav , Bedeaux Dick , Hafskjold Bjørn , Kjelstrup Signe 

TITLE=Pressures Inside a Nano-Porous Medium. The Case of a Single Phase Fluid

JOURNAL=Frontiers in Physics

VOLUME=7

YEAR=2019

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2019.00060

DOI=10.3389/fphy.2019.00060

ISSN=2296-424X

ABSTRACT=<p>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 [<xref ref-type="bibr" rid="B1">1</xref>], 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 <italic>R</italic>, <inline-formula><mml:math id="M1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msup><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mo>^</mml:mo></mml:mover></mml:mrow><mml:mrow><mml:mi>α</mml:mi></mml:mrow></mml:msup><mml:mo>-</mml:mo><mml:msup><mml:mrow><mml:mi>p</mml:mi></mml:mrow><mml:mrow><mml:mi>α</mml:mi></mml:mrow></mml:msup><mml:mo>=</mml:mo><mml:mi>γ</mml:mi><mml:mo>/</mml:mo><mml:mi>R</mml:mi></mml:math></inline-formula>. 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.</p>