We present experiments and simulations of slow drainage in three-dimensional (3D) porous media, either homogeneous and in the presence of gravity or heterogeneous and in its absence. An acoustic technique allows for an accurate study of the 3D fronts and the crossover region. Our results suggest that both cases can be described by invasion percolation in a gradient. For the case of gravity, the front tail width scales with the Bond number as ${\mathrm{\sigma }}_{\mathrm{FT}}$∼${\mathit{B}}^{\mathrm{-}0.47}$, in agreement with the theory. For the case of permeability gradient a different scaling is found, in agreement with a modified theory of gradient percolation developed here.

• Received 18 October 1993

DOI:https://doi.org/10.1103/PhysRevE.49.4133