title: Macroscopic phase-field model of partial wetting: bubbles in a capillary tube.
abstract: Drops and bubbles are nonspreading, local, compactly supported features. They are also equilibrium configurations in partial wetting phenomena. Yet, current macroscopic theories of capillary-dominated flow are unable to describe these systems. We propose a framework to model multiphase flow in porous media with nonspreading equilibrium configurations. We illustrate our approach with a one-dimensional model of two-phase flow in a capillary tube. Our model allows for the presence of compactons: nonspreading steady-state solutions in the absence of external forces. We show that local rate dependency is not needed to explain globally rate-dependent displacement patterns, and we interpret dynamic wetting transitions as the route from equilibrium, capillary-dominated configurations, towards viscous-dominated flow. Mathematically, these transitions are possible due to nonclassical shock solutions and the role of bistability and higher-order terms in our model.
authors.affiliation: Massachusetts Institute of Technology, 77 Massachusetts Avenue, Building 48, Cambridge, Massachusetts 02139, USA.
authors.forename: Luis
authors.initials: L
authors.lastname: Cueto-Felgueroso
authors.forename: Ruben
authors.initials: R
authors.lastname: Juanes