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

Cuttle, Callum; Morrow, Liam C.; MacMinn, Christopher W.

doi:10.1103/physrevfluids.8.113904

Phys. Rev. Fluids

2023

DOI: 10.1103/physrevfluids.8.113904

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

Callum Cuttle,

Liam C. Morrow,

Christopher W. MacMinn

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Cited by 4 publications

(1 citation statement)

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“…But that surface can destabilize, with gas pushing slender protrusions, or "fingers," into the liquid. Now researchers have uncovered a potentially new way to control the time it takes for this instability to appear [1,2].…”

mentioning

confidence: 99%

Control Knob Found for Viscous Fingers

Schirber

2023

Physics

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mentioning

confidence: 99%

Control Knob Found for Viscous Fingers

Schirber

2023

Physics

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Pore-scale viscous fingering as a mechanism for pattern formation – a historical overview, application, and the ways of controlling it

Cvetkovic,

Milicev

2024

Advances in Physics: X

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Exact and numerical solutions of a free boundary problem with a reciprocal growth law

McDonald,

Harris

2024

IMA Journal of Applied Mathematics

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A two-dimensional free boundary problem is formulated in which the normal velocity of the boundary is proportional to the inverse of the gradient of a harmonic function $T$. The field $T$ is defined in a simply connected region which includes the point at infinity where it has a logarithmic singularity. The growth problem in which the boundary expands outward is formulated both in terms of the Schwarz function of the boundary and a Polubarinova-Galin equation for the conformal map of the region from the exterior of the unit disk. An expanding free boundary is shown to be stable and explicit solutions for growing ellipses and a class of polynomial lemniscates are derived. Numerical solution of the Polubarinova-Galin equation is used to compute the evolution of the boundary having other initial shapes.

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

Cited by 4 publications

References 59 publications

Control Knob Found for Viscous Fingers

Control Knob Found for Viscous Fingers

Pore-scale viscous fingering as a mechanism for pattern formation – a historical overview, application, and the ways of controlling it

Exact and numerical solutions of a free boundary problem with a reciprocal growth law

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