Plouraboué, Franck and Hulin, Jean-Pierre and Roux, Stéphane and Koplik, Joel Numerical study of geometrical dispersion in self-affine rough fractures. (1998) Physical Review E, vol. 58 (n° 3). pp. 3334-3346. ISSN 1063-651X
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Official URL: http://dx.doi.org/10.1103/PhysRevE.58.3334
We report a numerical study of passive tracer dispersion in fractures with rough walls modeled as the space between two complementary self-afﬁne surfaces rigidly translated with respect to each other. Geometrical dispersion due to the disorder of the velocity distribution is computed using the lubrication approximation. Using a spectral perturbative scheme to solve the ﬂow problem and a mapping coordinate method to compute dispersion, we perform extensive ensemble averaged simulations to test theoretical predictions on the dispersion dependence on simple geometrical parameters. We observe the expected quadratic dispersion coefﬁcient dependence on both the mean aperture and the relative shift of the crack as of well as the anomalous dispersion dependence on tracer traveling distance. We also characterize the anisotropy of the dispersion front, which progressively wrinkles into a self-afﬁne curve whose exponent is equal to that of the fracture surface.
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