Anomalous interface roughening in 3D porous media: experiment and model

We report the first imbibition experiments in 2 + 1 dimensions — using simple materials as the random media and various aqueous suspensions as wetting fluids. We measure the width w(l, t) of the resulting interface and find it to scale with length l as w(l, ∞) ∼lα with α = 0.50±0.05. This value of α is larger than the value of α = 0.40 found for the KPZ universality class in 2 + 1 dimensions. We develop a new imbibition model that describes quantitatively our experiments. For d = 1 + 1, the model can be mapped to directed percolation; for d = 2 + 1, it corresponds to a new anisotropic surface percolation problem. Our model leads to the exponent α = 0.5 ± 0.05 in excellent agreement with the experiment.