Anomalous Roughening of Hele-Shaw Flows with Quenched Disorder

J. Soriano; J. J. Ramasco; M. A. Rodríguez; A. Hernández-Machado; J. Ortín

doi:10.1103/PhysRevLett.89.026102

Anomalous Roughening of Hele-Shaw Flows with Quenched Disorder

J. Soriano, J. J. Ramasco, M. A. Rodríguez, A. Hernández-Machado, and J. Ortín

Phys. Rev. Lett. 89, 026102 – Published 24 June 2002

Abstract

The kinetic roughening of a stable oil-air interface moving in a Hele-Shaw cell that 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 is introduced.

Received 7 December 2001

DOI:https://doi.org/10.1103/PhysRevLett.89.026102

Authors & Affiliations

J. Soriano¹, J. J. Ramasco^2,3, M. A. Rodríguez², A. Hernández-Machado^1,4, and J. Ortín¹

¹Departament ECM, Facultat de Física, Universitat de Barcelona, Diagonal 647, E-08028 Barcelona, Spain
²Instituto de Física de Cantabria, CSIC, Avenida Los Castros, E-39005 Santander, Spain
³Departamento de Física Moderna, Universidad de Cantabria, E-39005 Santander, Spain
⁴Groupe de Physique des Solides, Université Pierre-et-Marie-Curie, Tour 23, 2 place Jussieu, 75251 Paris Cedex 05, France