  Flow and transport are studied in transparent model fractures with rough
complementary self-affine walls with a relative shear displacement $\vec{u}$.
The aperture field is shown to display long range correlations perpendicular to
$\vec{u}$: for flow in that direction, the width and geometry of the front of a
dyed shear-thinning polymer solution displacing a transparent one have been
studied as a function of the fluid rheology and flow rate. The front width
increases linearly with distance indicating a convection of the fluids with a
low transverse mixing between the flow paths. The width also increases with the
flow-rate as the fluid rheology shifts from Newtonian at low shear rates $\dot
\gamma$ towards a shear thinning behaviour at higher $\dot \gamma$ values. The
width also increases with the polymer concentration at high flow-rates. These
results demonstrate the enhancement of the flow velocity contrasts between
different flow channels for shear thinning fluids. The relative widths at low
and high $\dot \gamma$ values for different polymer concentrations are well
predicted by an analytical model considering the fracture as a set of parallel
ducts of constant hydraulic apertures. The overall geometry of the experimental
front geometry is also predicted by the theoretical model from the aperture
map.
