Global instability of viscous fingering in a Hele–Shaw cell: formation of oscillatory fingers

DOI10.1017/S0956792500000437zbMath0727.76047OpenAlexW2030252948MaRDI QIDQ3351023

Jian-Jun Xu

Publication date: 1991

Published in: European Journal of Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0956792500000437

zbMATH Keywords

surface tensionHele-Shaw cellviscous fingeringglobal instability mechanismglobal trapped wave instabilitynarrow, oscillatory fingersunique global, neutrally stable state of the system

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Multiphase and multicomponent flows (76T99) Interfacial stability and instability in hydrodynamic stability (76E17) Hydrodynamic stability (76E99)

Related Items (3)

Discrete point spectrum of linear stability operator for Saffman-Taylor bubbles with nonzero surface tension ⋮ Interface closure in the root region of steady deep-cellular growth in directional solidification ⋮ Interfacial pattern formation in nonlinear dynamic systems: Dendrites, fingers and interfacial waves by

Cites Work

• The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid
• Nonlinear unstable viscous fingers in Hele–Shaw flows. II. Numerical simulation
• A boundary-integral method for two-phase displacement in Hele-Shaw cells
• Analytic theory for the selection of a symmetric Saffman–Taylor finger in a Hele–Shaw cell
• The effect of surface tension on the shape of fingers in a Hele Shaw cell
• On Spiral Waves in Galaxies — A Gas Dynamic Approach

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