14-17 May 2018
New Orleans
US/Central timezone

Direct experimental measurement of the pair correlation function during the slow drainage of a porous medium

16 May 2018, 15:58
15m
New Orleans

New Orleans

Oral 20 Minutes MS 1.09: front & interface dynamics and  up scaling  transport properties  in porous media Parallel 8-F

Speaker

Dr Marcel Moura (PoreLab, Department of Physics, University of Oslo)

Description

We have given experimental grounding for the remarkable observation made 30 years ago by Furuberg et al. [1] of an unusual dynamic scaling for the pair correlation function $N(r,t)$ during the slow drainage of a porous medium. The authors of that paper have used an invasion percolation algorithm to show numerically that the probability of invasion of a pore at a distance $r$ away and after a time $t$ from the invasion of another pore, scales as $N(r,t)\propto r^{-1}f\left(r^{D}/t\right)$, where $D$ is the fractal dimension of the invading cluster and the function $f(u)\propto u^{1.4}$, for $u \ll 1$ and $f(u)\propto u^{-0.6}$, for $u \gg 1$. Our experimental setup allows us to have full access to the spatiotemporal evolution of the invasion, which was used to directly verify this scaling [2]. Additionally, we have connected two important theoretical contributions from the literature [3,4] to explain the functional dependency of $N(r,t)$ and the scaling exponent for the short-time regime ($t \ll r^{D}$). A new theoretical argument was developed to explain the long-time regime exponent ($t \gg r^{D}$).

References

[1] L. Furuberg, J. Feder, A. Aharony, and T. Jøssang, Dynamics of Invasion Percolation, Phys. Rev. Lett. 61, 2117 (1988).
[2] M. Moura, K.J. Måløy, E.G. Flekkøy and R. Toussaint, Verification of a Dynamic Scaling for the Pair Correlation Function during the Slow Drainage of a Porous Medium, Phys. Rev. Lett. 119, 154503 (2017).
[3] S. Roux and E. Guyon, Temporal development of invasion percolation, J. Phys. A 22, 3693 (1989).
[4] S. Maslov, Time Directed Avalanches in Invasion Models, Phys. Rev. Lett. 74, 562 (1995).

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Primary author

Dr Marcel Moura (PoreLab, Department of Physics, University of Oslo)

Co-authors

Prof. Knut Jørgen Måløy (PoreLab, Department of Physics, University of Oslo) Prof. Eirik Grude Flekkøy (PoreLab, Department of Physics, University of Oslo) Prof. Renaud Toussaint (CNRS, IPGS UMR 7516, University of Strasbourg)

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