Traveling liquid bridges in unsaturated fractured porous media
Interplay between capillary, gravity and viscous forces in unsaturated fractures gives rise to a range of complex flow phenomena. Evidence of highly intermittent fluxes, preferential and sustainable flow pathways lead to potentially significant flow focusing of concern for regulatory and management of water resources in fractured rock formations. In previous work[Ghezzehei TA,Or D.: Water Resour. Res. In Review(2005)] we developed mechanistic models for formation, growth and detachment of liquid bridges in geometrical irregularities within fractures. Such discrete and intermittent flows present a challenge to standard continuum theories. Our focus here is on predicting travel velocities of detached liquid elements and their interactions with fracture walls. The scaling relationships proposed by Podgorski et al. [Podgorski, T., et al.: Phys. Rev. Lett. 8703(3), 6102-NIL_95 (2001)] provide a general framework for processes affecting travel velocities of discrete liquid elements in fractures, tubes, and in coarse porous media. Comparison of travel velocity and distance by discrete bridges relative to equivalent continuous film flow reveal significantly faster and considerably larger distances traversed by liquid bridges relative to liquid films. Coalescence and interactions between liquid bridges result in complex patterns of travel times and distances. Mass loss on rough fracture surfaces shortens travel distances of an element; however, results show that such retardation provides new opportunities for coalescence of subsequent liquid elements traveling along the same path, resulting in mass accumulation and formation of larger liquid elements traveling larger distances relative to smooth fracture surfaces. Such flow focusing processes may be amplified considering a population of liquid bridges within a fracture plane and mass accumulation in fracture intersections.