Influence of granulometry in the Hurst exponent of air liquid interfaces formed during capillary rising in a granular media

Abstract

We report results concerning the fractal dimension of a air/fluid interface formed during the capillary rising of a fluid into a dense granular media. The system consists in a modified Hele-Shaw cell filled with grains at different granulometries and confined in a narrow gap between the glass plates. The system is then placed onto a water reservoir, and the liquid penetrates the medium due to capillary forces. We measure the Hurst exponent of the liquid/air interface with help of image processing, and follow the temporal evolution of the profiles. We observe that the Hurst exponent can be related with the granulometry, but the range of values are odd to the predicted values from models or theory.