Compression-driven viscous fingering in a radial Hele-Shaw cell

Abstract

The displacement of a viscous liquid by a gas within a Hele-Shaw cell is a classical problem. The gas-liquid interface is hydrodynamically unstable, forming striking finger-like patterns that have attracted research interest for decades. Generally, both the gas and liquid phases are taken to be incompressible, with the capillary number being the key parameter that determines the severity of the instability. Here, we consider a radially outward displacement driven by the steady compression of a gas reservoir. The associated gas-injection rate is then unsteady due to the compressibility of the gas. We identify a second nondimensional parameter, the compressibility number, that plays a strong role in the development of the fingering pattern. We use an axisymmetric model to study the impact of compressibility number on the unsteady evolution of injection rate and gas pressure. We use linear stability analysis to show that increasing the compressibility number delays the onset of finger development relative to the corresponding incompressible case. Finally, we present and compare a series of experiments and fully nonlinear simulations over a broad range of capillary and compressibility numbers. These results show that increasing the compressibility number systematically decreases the severity of the fingering pattern at high capillary number. Our results provide an unprecedented comparison of experiments with simulations for viscous fingering, a comprehensive understanding of the role of compressibility in unstable gas-liquid displacement flows, and insight into a new mechanism for controlling the development of fingering patterns.

References in corpus (10)

• Numerical investigation of controlling interfacial instabilities in non-standard Hele-Shaw configurations
• Suppression of viscous fluid fingering: a piecewise constant-injection process
• Manipulation of Viscous Fingering in a Radially-Tapered Cell Geometry
• Fjords in viscous fingering: Selection of width and opening angle
• Fluctuations in viscous fingering
• Gas compression systematically delays the onset of viscous fingering
• Extending fields in a level set method by solving a biharmonic equation
• Viscous fingering patterns for Hele--Shaw flow in a doubly connected geometry driven by a pressure differential or rotation
• Growth morphology and symmetry selection of interfacial instabilities in anisotropic environments
• Dynamics of compression-driven gas-liquid displacement in a capillary tube

Cited by in corpus (3)

• Gas compression systematically delays the onset of viscous fingering
• Fingering instability of self-similar radial flow of miscible fluids in a Hele-Shaw cell
• Dynamics of a compressible gas injected into a confined porous layer