Anisotropy of tracer dispersion in rough model fractures with sheared walls

Abstract

Dispersion experiments are compared for two transparent model fractures with identical complementary rough walls but with a relative shear displacement $\vec{\delta }$ parallel ($\vec{\delta }\parallel \vec{U}$) or perpendicular ($\vec{\delta }\perp \vec{U}$) to the flow velocity $\vec{U}$. The structure of the mixing front is characterized by mapping the local normalized local transit time $\bar{t}(x,y)$ and dispersivity $\alpha (x,y)$. For $\vec{\delta }\perp \vec{U}$, displacement fronts display large fingers: their geometry and the distribution of $\bar{t}(x,y)U/x$ are well reproduced by assuming parallel channels of hydraulic conductance deduced from the aperture field. For $\vec{\delta }\parallel \vec{U}$, the front is flatter and $\alpha (x,y)$ displays a narrow distribution and a Taylor-like variation with $Pe$.