Anomalous roughening of Hele-Shaw flows with quenched disorder

TL;DR

This paper investigates the anomalous kinetic roughening of oil-air interfaces in Hele-Shaw cells with quenched disorder, revealing unique scaling behavior explained by interface dynamics and a phenomenological model.

Contribution

It introduces the first experimental study of anomalous roughening in Hele-Shaw flows with quenched disorder and proposes a model reproducing the observed scaling exponents.

Findings

Identification of three independent exponents for anomalous scaling

Explanation of scaling via initial acceleration and deceleration of interface tips

Development of a phenomenological model matching experimental exponents

Abstract

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.