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

Callum Cuttle*, Liam C. Morrow*, and Christopher W. MacMinn†

  • Department of Engineering Science, University of Oxford, Oxford, OX1 3PJ, United Kingdom

  • *These authors contributed equally to this work.
  • †christopher.macminn@eng.ox.ac.uk
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Phys. Rev. Fluids 8, 113904 – Published 29 November, 2023

DOI: https://doi.org/10.1103/PhysRevFluids.8.113904

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 fingerlike 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.

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synopsis

Control Knob Found for Viscous Fingers

Published 29 November, 2023

The onset time for “viscous fingering”—an instability that can occur at a gas–liquid boundary—depends on the compressibility of the gas, offering a way to control the behavior.

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See Also

Gas Compression Systematically Delays the Onset of Viscous Fingering

Liam C. Morrow, Callum Cuttle, and Christopher W. MacMinn
Phys. Rev. Lett. 131, 224002 (2023)

Article Text

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Phys. Rev. Fluids 8, 113904– Published 29 November, 2023
  • Received 28 February 2023
  • Revised 15 September 2023
  • Accepted 20 October 2023
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