Influence of compressibility on gas-driven viscous fingering in a Hele-Shaw cell

One of the most well-studied problems in interfacial fluid dynamics is the gas-driven displacement of a viscous liquid from a Hele-Shaw cell. This problem has received significant attention because of the distinct interfacial patterns that form due to the Saffman-Taylor instability. Generally, mathematical models of Hele-Shaw flow assume that both phases are incompressible and identify the Capillary number as the key parameter for determining the intensity of the instability. Recently, effort has been targeted at controlling the instability by modifying the geometry of the Hele-Shaw cell and/or the properties of the fluids. However, the practicality of such modifications can be limited. By contrast, compression of the invading gas occurs ‘naturally in experiments and is essentially unavoidable (unless the injection pressure is held constant). Here, we use state-of-the-art numerical simulations and laboratory experiments to study the influence of has compression on viscous fingering. We identify a second key control parameter, the ‘compressibility number’, that is comparable in importance to the capillary number. As such, we argue that compressibility offers a novel and powerful new means of controlling viscous fingering.