Anomalous Roughening of Viscous Fluid Fronts in Spontaneous Imbibition

TL;DR

This study investigates the anomalous roughening behavior of viscous fluid fronts during spontaneous imbibition in a porous medium, revealing non-self-affine interface scaling and capillary-driven dynamics.

Contribution

It provides experimental evidence of anomalous scaling and non-self-affine interfaces in spontaneous imbibition, expanding understanding of fluid interface dynamics.

Findings

Interface fluctuations follow Washburn's law for average position.

Dynamic exponent z ≈ 3 indicates capillary-driven global dynamics.

Interfaces exhibit intrinsic anomalous scaling with distinct local and global exponents.

Abstract

We report experiments on spontaneous imbibition of a viscous fluid by a model porous medium in the absence of gravity. The average position of the interface satisfies Washburn's law. Scaling of the interface fluctuations provides a dynamic exponent z \simeq 3, indicative of global dynamics driven by capillary forces. The complete set of exponents clearly shows that interfaces are not self-affine, exhibiting distinct local and global scaling, both for time (b=0.64\pm 0.02, b* =0.33 \pm 0.03) and space (a=1.94 \pm 0.20, a_loc=0.94 \pm 0.10). These values are compatible with an intrinsic anomalous scaling scenario.