Interfaces determined by capillarity and gravity in a two-dimensional porous medium

被引:0
|
作者
Calle, Maria [1 ]
Maria Cuesta, Carlota [2 ]
Velazquez, Juan J. L. [3 ]
机构
[1] Univ Carlos III Madrid UC3M, Dept Econ, Fac Ciencias Sociales & Jurid, Calle Madrid 126, Getafe 28903, Madrid, Spain
[2] Univ Basque Country UPV EHU, Dept Matemat, Aptdo 644, Bilbao 48080, Spain
[3] Univ Bonn, Inst Angew Math, Endenicher Allee 60, D-53115 Bonn, Germany
关键词
Capillarity-gravity interface; two-dimensional porous medium; probabilistic asymptotic analysis; FRONTS; MODEL;
D O I
10.4171/IFB/367
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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.
引用
收藏
页码:355 / 391
页数:37
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