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Transport in Porous Media

, Volume 32, Issue 1, pp 97–116 | Cite as

Tracer Dispersion in Rough Open Cracks

  • Stéphane Roux
  • Franck Plouraboué
  • Jean-Pierre Hulin
Article

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.

dispersion anomalous diffusion Taylor dispersion roughness self-affine 

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Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Stéphane Roux
    • 1
  • Franck Plouraboué
    • 2
  • Jean-Pierre Hulin
    • 3
  1. 1.Surface du Verre et Interfaces,UMR CNRS/St-Gobain n° 125Aubervilliers CedexFrance
  2. 2.Institut de Mécanique des FluidesToulouseFrance
  3. 3.Laboratoire Fluide, Automatique et Systèmes ThermiquesUniv. Paris-SudOrsay CedexFrance

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