Morphology of air invasion in an immersed granular layer

We report a study of the paths formed by a finite volume of air gently injected at the base of an immersed granular material. A two-dimensional model, based on experimental observations, shows that the typical height and width of the region explored by the branched path depends not only on the injected volume V, but also on a dimensionless parameter chi which accounts for the relative effects of the gravity and capillarity. For a given injected volume V, larger gravity effects lead to taller and narrower structures; for a given chi, the typical height and width of the structure scale like V-1/2 and V-1/4, respectively, while the typical gaseous fraction in the corresponding region increases accordingly like V-1/4. Such results can be of practical importance: For instance, gas can be trapped on purpose in an underground natural container below a granular slurry. Our results can help in predicting if the gas is likely to reach the free surface and escape the system if the container presents a defect (hole or fracture).