Disorder-mediated wetting transitions in unstable imbibition

An archetypical example of pattern formation is the front instability that emerges when a less viscous fluid displaces a more viscous fluid in a Hele-Shaw cell. This instability, however, has been studied only in drainage—when the invading fluid is nonwetting. Here we show that the interplay between wettability and disorder leads to novel instability regimes. We inject a more wetting liquid into a rough Hele-Shaw cell filled with a less wetting, more viscous liquid. At low injection rates, the displacement is full across the cell gap. Above a critical injection rate, however, a wetting transition occurs and thin films of the invading liquid become entrained on the rough surfaces. This wetting transition is accompanied by a drastic change of the front instability, leading to a dendritic pattern. Our observations point to the crucial role of disorder in pattern formation during fluid-fluid displacement, and its important implications for multiphase flows in porous media.