Experiments of interfacial roughening in 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 [formula presented] and the gap spacing b. Through the analysis of the rms width as a function of time, we have measured a growth exponent [formula presented] that is almost independent of the experimental parameters. The analysis of the roughness exponent [formula presented] through the power spectrum has shown different behaviors at short [formula presented] and long [formula presented] length scales, separated by a crossover wave number [formula presented] The values of the measured roughness exponents depend on experimental parameters, but at large velocities we obtain [formula presented] independently of the disorder configuration. The dependence of the crossover wave number with the experimental parameters has also been investigated, measuring [formula presented] for the shortest persistence length, in agreement with theoretical predictions. © 2002 The American Physical Society.