AUTHOR=Sinha Santanu , Gjennestad Magnus Aa. , Vassvik Morten , Winkler Mathias , Hansen Alex , Flekkøy Eirik G. TITLE=Rheology of High-Capillary Number Two-Phase Flow in Porous Media JOURNAL=Frontiers in Physics VOLUME=7 YEAR=2019 URL=https://www.frontiersin.org/journals/physics/articles/10.3389/fphy.2019.00065 DOI=10.3389/fphy.2019.00065 ISSN=2296-424X ABSTRACT=

Flow of immiscible fluids in porous media at high capillary numbers may be characterized by an effective viscosity. We demonstrate that the effective viscosity is well-described by the Lichtenecker-Rother equation. Depending on the pore geometry, wettability, and viscosity of the fluids, the exponent α in this equation can have different values. We find α = 1 when fluids are well-mixed with small bubbles, α = 0.6 in two- and 0.5 in three-dimensional systems when there is less mixing with the appearance of big bubbles, and α = −0.5 when lubrication layers are formed along the pore walls. Our arguments are based on analytical and numerical methods.