Critical behavior in porous media flow

TL;DR

This paper experimentally investigates critical phenomena in porous media flow, revealing intermittent burst dynamics, self-similar structures, and $1/f^eta$ spectra, including a transition from $1/f$ to $1/f^2$ scaling under certain conditions.

Contribution

It provides the first experimental evidence of $1/f^eta$ spectra in porous media flow and verifies a theoretical burst size distribution scaling.

Findings

Observation of $1/f^eta$ power spectra in porous media flow

Verification of theoretically predicted burst size distribution scaling

Identification of a transition from $1/f$ to $1/f^2$ scaling under specific boundary conditions

Abstract

The intermittent burst dynamics during the slow drainage of a porous medium is studied experimentally. We have shown that this system satisfies a set of conditions known to be true for critical systems, such as intermittent activity with bursts extending over several time and length scales, self-similar macroscopic fractal structure and $1/f^\alpha$ power spectrum. Additionally, we have verified a theoretically predicted scaling for the burst size distribution, previously assessed via numerical simulations. The observation of $1/f^\alpha$ power spectra is new for porous media flows and, for specific boundary conditions, we notice the occurrence of a transition from $1/f$ to $1/f^2$ scaling. An analytically integrable mathematical framework was employed to explain this behavior.