Anomalous roughening of Hele-Shaw flows with quenched disorder

Jordi Soriano1, José J. Ramasco2,3, Miguel A. Rodríguez2, Aurora Hernández-Machado1,4 and Jordi Ortín1
1Departament ECM, Facultat de Física, Universitat de Barcelona.
2Instituto de Física de Cantabria (CSIC-UC), Av de los Castros s/n 39005 Santander, Spain
3Dpto. de Física Moderna, Universidad de Cantabria.
4Groupe de Physique des Solides, Université Pierre-et-Marie-Curie, Paris.

( July 2002)

The kinetic roughening of a stable oil--air interface, moving in a Hele--Shaw cell which contains a quenched columnar disorder (tracks) has been studied. A capillary effect is responsible for the dynamic evolution of the resulting rough interface, which exhibits anomalous scaling. The three independent exponents needed to characterize the anomalous scaling are determined experimentally. The anomalous scaling is explained in terms of the initial acceleration and subsequent deceleration of the interface tips in the tracks coupled by mass conservation. A phenomenological model that reproduces the measured global and local exponents has been introduced.