Experiments of interfacial roughening of Hele-Shaw flows with weak quenched disorder

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 β ≃ 0.5 that is almost independent of the experimental parameters. The analysis of the roughness exponent α through the power spectrum has shown different behaviors at short ( α 1 ) and long ( α 2 ) length scales, separated by a crossover wave number q c . The values of the measured roughness exponents depend on experimental parameters, but at large velocities we obtain α 1 ≃ 1.3 independently of the disorder configuration. The dependence of the crossover wave number with the experimental parameters has also been investigated, measuring q c ∼ v 0.47 for the shortest persistence length, in agreement with theoretical predictions.