Experiments of Interfacial Roughening in Hele-Shaw Flows with Weak Quenched Disorder

TL;DR

This study investigates the kinetic roughening of an oil-air interface in Hele-Shaw flows with quenched disorder, revealing universal growth exponents and scale-dependent roughness behaviors influenced by experimental parameters.

Contribution

It provides experimental evidence on how disorder configuration and flow velocity affect interface roughening, confirming theoretical predictions about crossover scales and roughness exponents.

Findings

Growth exponent beta approximately 0.5, nearly independent of parameters.

Roughness exponent alpha_1 approximately 1.3 at large velocities.

Crossover wavenumber q_c scales as v^{0.47} for short persistence length.

Abstract

We have studied the kinetic roughening of an oil--air interface in a forced imbibition experiment in a horizontal Hele--Shaw cell with quenched disorder. Different disorder configurations, characterized by their persistence length in the direction of growth, have been explored by varying the average interface velocity v and the gap spacing b. Through the analysis of the rms width as a function of time, we have measured a growth exponent beta ~= 0.5 that is almost independent of the experimental parameters. The analysis of the roughness exponent alpha through the power spectrum have shown different behaviors at short (alpha_1) and long (alpha_2) length scales, separated by a crossover wavenumber q_c. The values of the measured roughness exponents depend on experimental parameters, but at large velocities we obtain alpha_1 ~= 1.3 independently of the disorder configuration. The dependence of the crossover wavenumber with the experimental parameters has also been investigated, measuring q_c ~ v^{0.47} for the shortest persistence length, in agreement with theoretical predictions.