PACS. 47.55.Mh -Flows through porous media. PACS. 68.35.Ct -Interface structure and roughness. PACS. 05.40.-a -Fluctuation phenomena, random processes, noise, and Brownian motion..Abstract. -We study the forced fluid invasion of an air-filled model porous medium at constant flow rate, in 1+1 dimensions, both experimentally and theoretically. We focus on the non-local character of the interface dynamics, due to liquid conservation, and its effect on the scaling properties of the interface upon roughening. Specifically, we study the limit of large flow rates and weak capillary forces. Our theory predicts a roughening behaviour characterized at short times by a growth exponent β1 = 5/6, a roughness exponent α1 = 5/2, and a dynamic exponent z1 = 3, and by β2 = 1/2, α2 = 1/2, and z2 = 1 at long times, before saturation. This theoretical prediction is in good agreement with the experiments at long times.The ensemble of experiments, theory, and simulations provides evidence for a new universality class of interface roughening in 1 + 1 dimensions.
We study the fingering instability of a circular interface between two immiscible liquids in a radial Hele-Shaw cell. The cell rotates around its vertical symmetry axis, and the instability is driven by the density difference between the two fluids. This kind of driving allows studying the interfacial dynamics in the particularly interesting case of an interface separating two liquids of comparable viscosity. An accurate experimental study of the number of fingers emerging from the instability reveals a slight but systematic dependence of the linear dispersion relation on the gap spacing. We show that this result is related to a modification of the interface boundary condition which incorporates stresses originated from normal velocity gradients. The early nonlinear regime shows nearly no competition between the outgrowing fingers, characteristic of low viscosity contrast flows. We perform experiments in a wide range of experimental parameters, under conditions of mass conservation ͑no injection͒, and characterize the resulting patterns by data collapses of two characteristic lengths: the radius of gyration of the pattern and the interface stretching. Deep in the nonlinear regime, the fingers which grow radially outwards stretch and become gradually thinner, to a point that the fingers pinch and emit drops. We show that the amount of liquid emitted in the first generation of drops is a constant independent of the experimental parameters. Further on there is a sharp reduction of the amount of liquid centrifugated, punctuated by periods of no observable centrifugation.
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.
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