Avalanches, Non-Gaussian Fluctuations and Intermittency in Fluid Imbibition

Abstract

We review our work on the invasion of a model open fracture by a viscous wetting fluid, in the context of research on the spatiotemporal dynamics of fronts in disordered media. The model consists on a Hele-Shaw cell with randomly-distributed dichotomic variations of gap thickness. Distortions of the advancing front produced by fluctuations in capillary pressure and permeability are damped by interfacial tension and fluid viscosity. Competition of forces at different length scales makes that an initially flat front undergoes a kinetic roughening process, leading to a statistically-stationary state characterized by critical interfacial fluctuations and a collective avalanche dynamics. Using fast and high-resolution imaging we are able to track the evolution of the advancing front in space and time with high accuracy. The motion of the front takes place by localized bursts whose lateral sizes, areas and durations are found to be power-law distributed–up to a cutoff scale which diverges as the capillary number of the displacement Ca → 0, a limit corresponding to a critical depinning transition. A scale-dependent statistical analysis of the temporal behavior of the spatially-averaged velocity of the front reveals the presence of non-Gaussian fluctuations, strongly intermittent dynamics and global avalanches.