Interface roughening in Hele-Shaw flows with quenched disorder: Experimental and theoretical results

¹ Departament ECM, Facultat de Física, Universitat de Barcelona Diagonal 647, E-08028 Barcelona, Spain
² Groupe de Physique des Solides, Université Pierre-et-Marie-Curie Tour 23, 2 place Jussieu, 75251 Paris Cedex 05, France
³ Departament de Física Aplicada, Universitat Politècnica de Catalunya Avda. Dr. Marañon 44, E-08034 Barcelona, Spain
⁴ Instituto de Física de Cantabria, CSIC Avenida Los Castros, E-39005 Santander, Spain

Corresponding author: aurora@ecm.ub.es

Received: 22 November 2000
Accepted: 14 May 2001

Abstract

We study the forced fluid invasion of an air-filled model porous medium at constant flow rate, in 1+1 dimensions, both experimentally and theoretically. We focus on the nonlocal character of the interface dynamics, due to liquid conservation, and its effect on the scaling properties of the interface upon roughening. Specifically, we study the limit of large flow rates and weak capillary forces. Our theory predicts a roughening behaviour characterized at short times by a growth exponent , a roughness exponent , and a dynamic exponent , and by , , and at long times, before saturation. This theoretical prediction is in good agreement with the experiments at long times.The ensemble of experiments, theory, and simulations provides evidence for a new universality class of interface roughening in 1+1 dimensions.