Radial fingering in a Hele-Shaw cell: A weakly nonlinear analysis

DOI10.1016/S0167-2789(98)00097-9zbMath0947.76027arXivcond-mat/9708037OpenAlexW2101356411WikidataQ126771488 ScholiaQ126771488MaRDI QIDQ1808333

Michael Widom, J. A. G. Miranda

Publication date: 6 December 1999

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/cond-mat/9708037

zbMATH Keywords

pattern formationHele-Shaw cellsymmetry analysisweakly nonlinear analysisharmonic modesradial flow geometryrectangular flow geometrySaffman-Taylor viscous fingering instabilitysub-harmonic perturbations

Mathematics Subject Classification ID

Nonlinear effects in hydrodynamic stability (76E30) Interfacial stability and instability in hydrodynamic stability (76E17) Other free boundary flows; Hele-Shaw flows (76D27)

Related Items

Classical Solvability of the Two-Phase Radial Viscous Fingering Problem in a Hele-Shaw Cell, Stability results for multi-layer radial Hele-Shaw and porous media flows, Instability of the fluid interface at arbitrary perturbation amplitudes. Displacement in the Hele-Shaw cell, Fingering instability in wildfire fronts, Resonance-like dynamics in radial cyclic injection flows of immiscible fluids in homogeneous porous media, On a two-phase Hele-Shaw problem with a time-dependent gap and distributions of sinks and sources, Radial displacement of a fluid annulus in a rotating Hele–Shaw cell, A boundary element study of the effect of surface dissolution on the evolution of immiscible viscous fingering within a Hele-Shaw cell, Interfacial instabilities of a fluid annulus in a rotating Hele–Shaw cell, Pattern formation in non-Newtonian Hele–Shaw flow, A REVIEW OF ONE-PHASE HELE-SHAW FLOWS AND A LEVEL-SET METHOD FOR NONSTANDARD CONFIGURATIONS, On the selection of viscosity to suppress the Saffman–Taylor instability in a radially spreading annulus, New exact solutions for Hele-Shaw flow in doubly connected regions, Instability of a free boundary in a Hele-Shaw cell with sink/source and its parameter dependence, Modelling the suppression of viscous fingering in elastic-walled Hele-Shaw cells

Cites Work

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• Macroscopic properties of disordered media. Proceedings of a Conference Held at the Courant Institute, New York, June 1-3, 1981
• Laplacian and diffusional growth: A unified theoretical description for symmetrical and parity-broken patterns
• The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid
• Interface conditions for two-phase displacement in Hele-Shaw cells
• Analytic theory for the selection of a symmetric Saffman–Taylor finger in a Hele–Shaw cell
• A numerical study of the effect of surface tension and noise on an expanding Hele–Shaw bubble
• Evolution of Hele-Shaw interface for small surface tension
• Hydrodynamics of quantized shape transitions of lipid domains
• The formation of drops through viscous instability