Avalanche dynamics of imbibition fronts

Jordi Ortin

Universitat de Barcelona, Facultat de Fisica, Barcelona, Spain

The dynamics of immiscible fluid-fluid displacements in porous media has been a subject of much interest in last years, both from a fundamental point of view, as a dynamical nonequilibrium process, and from a technological point of view. In forced-flow imbibition an invading fluid that wets preferentially the medium displaces a resident fluid at a constant injection rate. As a result of the comeptition between stabilizing viscous and surface tension forces at long length scales, and destabilizing capillary forces at short length scales, the fluid-fluid interface gets rough. While the scaling properties of the rough interface have been studied exten- sively, the spatiotemporal dynamics of the roughening process has not received the same attention.

In this work we use a model porous medium that consists on a Hele-Shaw cell with two diŽerent values of gap spacing, randomly distributed in space. By means of a measurement system with high spatial and temporal resolution we track the spatiotemporal dynamics of imbibition in this medium.

The interface dynamics is governed by local and irregular avalanches, with very large size and velocity fluctuations. Our results show that the avalanche size distribution follows a power law(with an exponential cut-off at large sizes). The analysis allows studying also the anisotropic shape of the avalanches and the statistical distribution of their durations.

We study also the statistical fluctuations of the average velocity of the interface in windows of lateral size l. Our results show that for windows narrower than the lateral correlation length of the interface the fluctuations of the average velocity follow a generalized Gumbel distribution characteristic of the statistics of extreme events.