Driven two-phase fluid displacements through a localized constriction

The manner in which a two-phase interface propagates through a porous medium is of major utilitarian interest and has been the subject of extensive research, specifically in the limit of quasi-static flow rates. However, the effects of a finite driving velocity, pending in any practical application, have not been carefully looked at nor clarified theoretically. Such non-equilibrium phenomena can already be observed in very simple devices that contain isolated defects. Here, as a model system, we study the driven displacement of an oil-air interface through a localized 'mesa' constriction in a Hele-Shaw cell. Using controlled experiments, theory, and finite element simulations, we find—in noteworthy quantitative agreement—that the driving velocity dramatically and nonlinearly modifies the resultant interface deformations. My talk will focus on the mathematical physics of this free boundary problem, demonstrating, without fitting parameters, how increasing levels of analysis progressively draw better comparisons to experiments.