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Pressure Model for Capillary Tree-Shaped Fractal Networks

Capillary tree networks can be efficiently used for several applications. These trees display the same patterns at different levels of scale, which is a property found in fractal objects. This paper combines a thermodynamic formulation with the geometric characteristics of the tree fractal network, to describe the equilibrium capillary pressure. The model proposed here accounts for, in addition to physical properties of the fluids, the fractal dimension, the scale factor between the size of parent and daughter tubes, and the branching level. The effect of each of these properties on the capillary pressure is also investigated.