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 v and the gap spacing b. Through the analysis of the rms width as a function of time, we have measured a growth exponent ␤Ӎ0.5 that is almost independent of the experimental parameters. The analysis of the roughness exponent ␣ through the power spectrum has shown different behaviors at short (␣ 1 ) and long (␣ 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 ␣ 1 Ӎ1.3 independently of the disorder configuration. The dependence of the crossover wave number with the experimental parameters has also been investigated, measuring q c ϳv 0.47 for the shortest persistence length, in agreement with theoretical predictions.

Kinetic Roughening in Two-Phase Fluid Flow through a Random Hele-Shaw Cell

“…[8], and the exponents reported there for large injection rates, α ≃ 0 for small k and α ≃ 1.3 for large k are fully consistent with our results for large V . However, this is not the case for small values of V .…”

“…Experiments on bead packs in Hele-Shaw cells [3] in particular, have stimulated considerable theoretical efforts, but the problem has consistently revealed itself rather elusive [1,2]. More recently a new surge of interest has arisen with the recognition of the inherently non-local character of the problem as a key ingredient [4,5], and the realization of a new series of experiments in Hele-Shaw cells with random gap [6,7,8]. Roughening exponents of the proposed nonlocal equations have been explored by means of Flory-type scaling arguments [4] and phase field simulations [5,6].…”

Fluctuations in Fluid Invasion into Disordered Media

“…Its presence and dependence on v has also been confirmed experimentally [10,13]. The ratio of disorder strengths imposes another length scale…”

Imbibition in disordered media

“…Although it was examined in the early 1990's [7,45] in connection with percolation theory and deviations from KPZ behaviour, recent work [82,99] pointing to the importance of fluid conservation, has led to a flurry of new experimental results [101,122,311,312,313] supported by further theoretical work [178,261]. Even though many details remain obscure, we feel that the general theoretical picture of roughening in imbibition is now well established.…”