Influence of wetting on fingering patterns in lifting Hele-Shaw flows

Abstract

We study the pattern formation dynamics related to the displacement of a viscous wetting fluid by a less viscous nonwetting fluid in a lifting Hele-Shaw cell. A perturbative weakly nonlinear analysis of the problem is presented. We focus on examining how wetting effects influence the morphology of the emerging interfacial patterns at the early nonlinear regime. Our analytical results indicate that wettability has a significant impact on the resulting nonlinear patterns. It restrains finger length variability while inducing the development of structures presenting short, blunt penetrating fingers of the nonwetting fluid, alternated by short, sharp fingers of the wetting fluid. The basic mode-coupling mechanisms leading to such behavior are discussed.