Existence and selection of steady bubbles in a Hele-Shaw cell

DOI10.1016/j.na.2007.07.044zbMath1143.76025OpenAlexW1987986405MaRDI QIDQ944765

Xuming Xie

Publication date: 10 September 2008

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2007.07.044

zbMATH Keywords

integro-differential equationsasymptotic solutionsurface tensionStokes constant

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Asymptotic methods, singular perturbations applied to problems in fluid mechanics (76M45) Capillarity (surface tension) for incompressible viscous fluids (76D45) Liquid-gas two-phase flows, bubbly flows (76T10) Other free boundary flows; Hele-Shaw flows (76D27)

Related Items

Discrete point spectrum of linear stability operator for Saffman-Taylor bubbles with nonzero surface tension ⋮ Local smoothing effect and existence for the one-phase Hele–Shaw problem with zero surface tension

Cites Work

• Analytic theory for the determination of velocity and stability of bubbles in a Hele-Shaw cell. I: Velocity selection
• Rigorous results in selection of steady needle crystals.
• Rigorous results in steady finger selection in viscous fingering
• The penetration of a fluid into a porous medium or Hele-Shaw cell containing a more viscous liquid
• A NOTE ON THE MOTION OF BUBBLES IN A HELE-SHAW CELL AND POROUS MEDIUM
• Asymptotics beyond All Orders in a Model of Crystal Growth
• The effect of surface tension on the shape of a Hele–Shaw cell bubble
• Viscous fingering 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
• Analyticity and nonexistence of classical steady Hele‐Shaw fingers
• On the rôle of Stokes lines in the selection of Saffman–Taylor fingers with small surface tension
• Surprises in viscous fingering
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