Non-linear multiphase flow in hydrophobic porous media

Multiphase flow in porous materials is conventionally described by an empirical extension to Darcy’s law which assumes that the pressure gradient is proportional to flow rate. Through a series of two-phase flow experiments, we demonstrate that even when capillary forces are dominant at the pore scale, there is a non-linear intermittent flow regime with a power-law dependence between pressure gradient and flow rate. Energy balance is used to predict accurately the start of the intermittent regime in hydrophobic porous media. The pore-scale explanation of the behaviour based on the periodic filling of critical flow pathways is confirmed through 3D micron-resolution X-ray imaging.