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

TITLE=Non-isothermal Transport of Multi-phase Fluids in Porous Media. Constitutive Equations

JOURNAL=Frontiers in Physics

VOLUME=Volume 6 - 2018

YEAR=2019

URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2018.00150

DOI=10.3389/fphy.2018.00150

ISSN=2296-424X

ABSTRACT=We develop constitutive equations for multi-component, multi-phase, 
macro-scale flow in a porous medium exposed to temperature-, composition-, and pressure -gradients. The porous medium is non-deformable. We define the pressure and the composition of the representative elementary volume (REV) in terms of contributions from each phase, interface and contact line. Driving forces are formed from these variables. New contributions due to varying porosity or surface tension offer explanations for non-Darcy behavior. The interaction of thermal and mechanical driving forces give thermal osmosis. An experimental program is suggested to verify Onsager symmetry in the transport coefficients.