  We model the flow of a bi-viscous non-Newtonian fluid in a porous medium by a
square lattice where the links obey a piece-wise linear constitutive equation.
We find numerically that the flow regime where the network transitions from all
links behaving according to the first linear part of the constitutive equation
to all links behaving according to the second linear part of the constitutive
equation, is characterized by a critical point. We measure two critical
exponents associated with this critical point, one of the being the correlation
length exponent. We find that both critical exponents depend on the parameters
of the model.
