We consider a simplified model for two-phase flows in one-dimensional heterogeneous porous media made of two different rocks. We focus on the effects induced by the discontinuity of the capillarity field at interface. We first consider a model with capillarity forces within the rocks, stating an existence/uniqueness result. Then we look for the asymptotic problem for vanishing capillarity withi...

To overcome a world-wide water shortage problem, numerous desalination methods have been developed with state-of-the-art power efficiency. Here we propose a spontaneous desalting mechanism referred to as the capillarity ion concentration polarization. An ion-depletion zone is spontaneously formed near a nanoporous material by the permselective ion transportation driven by the capillarity of the...

We consider the stability problem for shock layers in Slemrod’s model of an isentropic gas with capillarity. We show that these traveling waves are monotone in the weak capillarity case, and become highly oscillatory as the capillarity strength increases. Using a spectral energy estimate we prove that small-amplitude monotone shocks are spectrally stable. We also show, through the use of a nove...

The systems of conservation laws have been used to model dynamical phase transitions in, for example, the propagating phase boundaries in solids and the van der Waals uid. When integrating such mixed hyperbolic-elliptic systems the Lax-Friedrichs scheme is known to give the correct solutions selected by a viscosity-capillarity criterion except a spike at the phase boundary which does not go awa...

We discuss the convergence of the upstream phase-by-phase scheme (or upstream mobility scheme) towards the vanishing capillarity solution for immiscible incompressible two-phase flows in porous media made of several rock types. Troubles in the convergence where recently pointed out in [S. Mishra & J. Jaffré, Comput. Geosci., 2010] and [S. Tveit & I. Aavatsmark, Comput. Geosci, 2012]. In this pa...

We prove uniform convexity of solutions to the capillarity boundary value problem for fixed boundary angle in (0, π/2) and strictly positive capillarity constant provided that the base domain Ω ⊂ R is sufficiently close to a disk in a suitable C-sense.

Selective breeding for high voluntary wheel running in untrained mice has resulted in a 'mini muscle' (MM) phenotype, which has increased skeletal muscle capillarity compared with muscles from non-selected control lines. Vascular endothelial growth factor (VEGF) and thrombospondin-1 (TSP-1) are essential mediators of skeletal muscle angiogenesis; thus, we hypothesized that untrained MM mice wit...