LAUSR

We investigate the dynamics, interactions, and decay of immiscible viscous fingers in two and three dimensions over time in a high-aspect ratio (up to 100:1) system. The behavior is related to the viscosity ratio and a macroscopic capillary number. The same four fingering regimes are observed as in miscible displacements (spreading of the interface between wetting and non-wetting fluid but no fingers, the growth of many fingers that can be described by perturbation analysis, non-linear interactions between fingers and decay to a single finger) for low viscosity ratio and high capillary to viscous ratios. At higher viscosity ratios and lower capillary to viscous ratios, periodic tip-splitting and decay results in a fluctuation between one and two fingers at late time. This has not been seen in miscible displacements. We provide a stability plot that can be used to identify when this will occur. Similar behaviors were seen in both two and three dimensions, suggesting that learnings from two-dimensional (2D) linear displacements can be applied to similar three-dimensional (3D) flows. In particular, the square root of the number of fingers seen in the 3D simulations and their decay with time was almost identical to 2D.