Anomalous Roughening of Viscous Fluid Fronts in Spontaneous Imbibition

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 suggests 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 ($\beta =0.64\pm 0.02$, ${\beta }^{*}=0.33\pm 0.03$) and space ($\alpha =1.94\pm 0.20$, ${\alpha }_{\mathrm{loc}}=0.94\pm 0.10$). These values are compatible with an intrinsic anomalous scaling scenario.