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

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 approximately 0.5 that is almost independent of the experimental parameters. The analysis of the roughness exponent alpha through the power spectrum has shown different behaviors at short (alpha(1)) and long (alpha(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 alpha(1) approximately 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) approximately v(0.47) for the shortest persistence length, in agreement with theoretical predictions.