Abstract
We study diffusion processes on clusters of non-wetting fluid dispersed in a wetting one flowing in a two-dimensional porous medium under steady-state conditions using a numerical model. At the critical saturation and capillary number of 10−5, where the cluster size distribution follows a power law, we find anomalous diffusion characterized by two critical exponents, drw∥=2.35±0.05 in the average flow direction and drw⊥=3.51±0.05 in the perpendicular direction. We determine the conductivity exponents to be μ∥=1.6±0.2 and μ⊥=1.25±0.1, respectively. The high-frequency scaling exponents of the AC conductivity we find to be η∥=0.37±0.1 and η⊥=0.36±0.1, respectively.