  The flow of non-Newtonian fluids is ubiquitous in many applications in the
geological and industrial context. We focus here on yield stress fluids (YSF),
i.e. a material that requires minimal stress to flow. We study numerically the
flow of yield stress fluids in 2D porous media on a macroscopic scale in the
presence of local heterogeneities. As with the microscopic problem,
heterogeneities are of crucial importance because some regions will flow more
easily than others. As a result, the flow is characterized by preferential flow
paths with fractal features. These fractal properties are characterized by
different scale exponents that will be determined and analyzed. One of the
salient features of these results is that these exponents seem to be
independent of the amplitude of heterogeneities for a log-normal distribution.
In addition, these exponents appear to differ from those at the microscopic
level, illustrating the fact that, although similar, the two scales are
governed by different sets of equations.
