Interfaces in disordered media. Scaling growth, avalanche dynamics, and microfluidic fronts

Pradas, Marc (2009). Interfaces in disordered media. Scaling growth, avalanche dynamics, and microfluidic fronts. PhD thesis Universitat de Barcelona.


The long desired possibility to classify the scaling growth of a rough surface in terms of universality classes has become a considerably ambitious task, not to say impossible in some cases.

This is particularly true, for instance, in the problem of a fluid filling a disordered medium –where the expression disordered medium applies both to a macroscopic porous medium and a microfluidic device. The point is that all the physical forces that play a role at the advancing front, such as the random capillarity of the medium, the surface tension of the interface or the viscous pressure, induce the roughness of the front to show a rich variety of scaling regimes, with the unavoidable presence of crossover effects. In addition, the so-called anomalous scaling, which reflects that the global scales of a rough surface behave in a different fashion as the corresponding local scales, makes difficult to find different physical situations that are described by exactly the same set of scaling exponents, which would make them belong to the same universality class. On the other hand, the characteristic intermittent avalanche-like behavior displayed by the front gives rise to an even more complicated dynamics, described in terms of spatio-temporal complex dynamics, as it is observed in many other disordered systems.

This thesis deals with the scaling properties and avalanche dynamics of interfaces moving in disordered media. Our main motivation in this work has been to understand the underlying physics that governs these complex phenomena, and to relate our findings to the large amount of experimental work carried out in fluid systems, ranging from the macroscopic Hele-Shaw cell to a microchannel.

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