  It is becoming increasingly clear that there is a regime in immiscible
two-phase flow in porous media where the flow rate depends of the pressure drop
as a power law with exponent different than one. This occurs when the capillary
forces and viscous forces both influence the flow. At higher flow rates, where
the viscous forces dominate, the flow rate depends linearly on the pressure
drop. The question we pose here is what happens to the linear regime when the
system size is increased. Based on analytical calculations using the capillary
fiber bundle model and on numerical simulations using a dynamical network
model, we find that the non-linear regime moves towards smaller and smaller
pressure gradients as the system size grows.
