Abstract
Tracer dispersion is studied in an open crack where the two rough crack faces have been translated with respect to each other. The different dispersion regimes encountered in rough-wall Hele-Shaw cell are first introduced, and the geometric dispersion regime in the case of self-affine crack surfaces is treated in detail through perturbation analysis. It is shown that a line of tracer is progressively wrinkled into a self-affine curve with an exponent equal to that of the crack surface. This leads to a global dispersion coefficient which depends on the distance from the tracer inlet, but which is still proportional to the mean advection velocity. Besides, the tracer front is subjected to a local dispersion (as could be revealed by point measurements or echo experiments) very different from the global one. The expression of this anomalous local dispersion coefficient is also obtained.
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Roux, S., Plouraboué, F. & Hulin, JP. Tracer Dispersion in Rough Open Cracks. Transport in Porous Media 32, 97–116 (1998). https://doi.org/10.1023/A:1006553902753
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DOI: https://doi.org/10.1023/A:1006553902753