Anomalous roughening in experiments of interfaces in Hele-Shaw flows with strong quenched disorder

We report experimental evidence of anomalous kinetic roughening in the stable displacement of an oil-air interface in a Hele-Shaw cell with strong quenched disorder. The disorder consists of a random modulation of the gap spacing that is transverse to the growth direction (tracks). Experiments were performed by varying the average interface velocity and the gap spacing, and measuring the scaling exponents. The following values of the scaling exponents were obtained; $\beta \simeq 0.50,$ ${\beta }^{*}\simeq 0.25,$ $\alpha \simeq 1.0,$ ${\alpha }_{\mathrm{loc}}\simeq 0.5,$ and $z\simeq 2.$ When there is no fluid injection, the interface is driven solely by capillary forces, and a higher value of $\beta$ of approximately $\beta =0.65\mathrm{}$ is measured. The presence of multiscaling and the particular morphology of the interfaces, characterized by large height differences that follow a Lévy distribution, confirms the existence of anomalous scaling. From a detailed study of the motion of the oil-air interface, we show that the anomaly is a consequence of different local velocities on the tracks plus the coupling in the motion between neighboring tracks. The anomaly disappears at high interface velocities, weak capillary forces, or when the disorder is not sufficiently persistent in the growth direction. We have also observed the absence of scaling when the disorder is very strong or when a regular modulation of the gap spacing is introduced.