Traveling time and traveling length for flow in porous media

Details Traveling time and traveling length for flow in porous media Traveling time and traveling length for flow in porous media

1999-03-03

arxiv.org/abs/cond-mat/9903066v2

Phys. Rev. E 60(3), (1999)

Physics

Condensed Matter

Statistical Mechanics

4 pages including 9 figures, Minor corrections in text

Scientific paper

We study traveling time and traveling length for tracer dispersion in porous media. We model porous media by two-dimensional bond percolation, and we model flow by tracer particles driven by a pressure difference between two points separated by Euclidean distance $r$. We find that the minimal traveling time $t_{min}$ scales as $t_{min} \sim r^{1.40}$, which is different from the scaling of the most probable traveling time, ${\tilde t} \sim r^{1.64}$. We also calculate the length of the path corresponding to the minimal traveling time and find $\ell_{min} \sim r^{1.13}$ and that the most probable traveling length scales as ${\tilde \ell} \sim r^{1.21}$. We present the relevant distribution functions and scaling relations.

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