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

Jordi Soriano·Jordi Ortin·Aurora Hernandez-Machado
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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.

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Jordi Soriano, Jordi Ortin, Aurora Hernandez-Machado. 2002-07-25. Experiments of Interfacial Roughening in Hele-Shaw Flows with Weak Quenched Disorder. https://doi.org/10.1103/physreve.66.031603

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