Yihuai Zhang , Branko Bijeljic, Ying Gao, Qingyang Lin, Martin J Blunt 

We measure the pressure difference during two-phase flow across a sandstone sample for a range of injection rates and fractional flows of water, the wetting phase, during an imbibition experiment. We quantify the onset of a transition from a linear relationship between flow rate and pressure gradient to a non-linear power-law dependence. We show that the transition from linear (Darcy) to non-linear flow and the exponent in the power-law is a function of fractional flow. We use energy balance to accurately predict the onset of intermittency for a range of fractional flows, fluid viscosities and three rock types, reconciling several literature datasets.