Summary: Fingering instabilities at the interface between two immiscible fluids can appear during the displacement of a fluid of higher viscosity by another one of lower viscosity. The evolution of the finger structures is determined by the interface kinematic and dynamic matching conditions, which describe mass and momentum conservation across the interface. In the case when the injected fluid is a gas and the resident one is a liquid, dissolution of the injected gas into the displaced liquid can occur at the interface between the two phases. In this case, the transfer velocity of the dissolved gas reduces the interface displacement velocity as described by the kinematic matching condition, delaying the evolution of the fingering. In addition, the momentum flux across the interface, due to the dissolution, modifies the dynamic matching condition with possible changes in the patterns of the fingers structures.
This work studies the effects of gas dissolution on the evolution of fingering instabilities during the displacement of a viscous liquid by an immiscible injected gas in a Hele-Shaw cell. A boundary element numerical simulation of the growth of the injected gas bubble is developed and implemented. This numerical model takes into account the dissolution across a sharp interface between the two phases. Our numerical simulations suggest that the inclusion of gas dissolution can lead to the eventual breaking of the fingers. These “shed fingers” become individual bubbles, which move away from the injection source with the velocity of the surrounding fluid and eventually will dissolve into the ambient fluid. New fingers evolve, with their concurrent breaking, resulting in the possibility of a cascade of travelling and dissolving bubbles, instead of a continuous fingering structure.