An analytic approach to capillary pressure in tree-shaped networks

Abstract: This study analyzes the pressure in capillary tree-shaped networks, based on the thermodynamics and the geometric description of the network. The presence of equilibrium and non-equilibrium effects on pressure is accounted. In particular,the presence of equilibrium effects is shown to be essential for describing the pressure in the network. An approach to the definition of equilibrium capillary pressure is presented in terms of interfacial energies of the phases but also in terms of the geometry characteristics of the tree-shaped network. Among others, the equilibrium capillary pressure is shown to depend on number of branching levels and number of daughter branches. Finally, a criterion is established to evaluate the importance of equilibrium and non-equilibrium effects on the capillary pressure