Pattern formation during capillary rising of a fluid front into a granular media

Abstract

Abstract. We report results concerning the pattern formation during the capillary rising of a fluid front into a dense dry granular media. The system consists in a modified Hele-Shaw cell filled with grains of different gradings and confined in a narrow gap between the glass plates. This assembly is vertically installed over a water reservoir to allow an ascending front of liquid to percolate into the granular media. We acquire digital images of the liquid/air front which are treated by means of imaging analysis techniques. Thus, we are able to assess the temporal evolution of the air/liquid boundary profiles. We measure the roughness of the profiles, using a detrended fluctuation analysis technique, to obtain their fractal dimension. We compare our results with similar experiments reported in literature considering fluid displacement into heterogeneous media and directed percolation theory. However, the range of values for the Hurst exponent obtained from our experiments are odd to the measured/predicted values in experiments or theory.

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

“…A key concept to understand this phenomena is pattern formation, particularly fractal geometry and analysis [4], and despite several efforts devoted to understand the fluid flow in granular media, a unified description for this phenomena still lacking [7][8][9][10][11]. Previously, Atman et al have studied the air/liquid interface formed during the capillary rising of water into a granular media [12], but the results did not fit to the expected theoretic models. Here, we present an extension of that work presenting new results for the Hurst exponent of the air/liquid interface now considering granular media with three different granulometries.…”