RT Journal Article
T1 Interfaces determined by capillarity and gravity in a two-dimensional porous medium
A1 Calle García, María
A1 María Cuesta, Carlota
A1 Velázquez, Juan J.L.
AB We consider a two-dimensional model of a porous medium where circular grains are uniformly distributed in a squared container. We assume that such medium is partially filled with water and that the stationary interface separating the water phase from the air phase is described by the balance of capillarity and gravity. Taking the unity as the average distance between grains, we identify four asymptotic regimes that depend on the Bond number and the size of the container. We analyse, in probabilistic terms, the possible global interfaces that can form in each of these regimes. In summary, we show that in the regimes where gravity dominates the probability of configurations of grains allowing solutions close to the horizontal solution is close to one. Moreover, in such regimes where the size of the container is sufficiently large we can describe deviations from the horizontal in probabilistic terms. On the other hand, when capillarity dominates while the size of the container is sufficiently large, we find that the probability of finding interfaces close to the graph of a given smooth curve without self-intersections is close to one.
PB EMS Press
SN 1463-9963
YR 2016
FD 2016-01-01
LK https://hdl.handle.net/10016/38839
UL https://hdl.handle.net/10016/38839
LA eng
NO The authors acknowledge support of the Hausdorff Center for Mathematics of the University of Bonn as well as the project CRC 1060 The Mathematics of Emergent Effects, that is funded through the German Science Foundation (DFG). This work was also partially supported by the Spanish Government projects DGES MTM2011-24109, MTM2011-22612 and MTM2014-53145-P and the Basque Government project IT641-13.
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