Singular effects of surface tension in evolving Hele-Shaw flows

DOI10.1017/S0022112096000894zbMath0885.76022OpenAlexW2125782398MaRDI QIDQ4354058

Michael Siegel, Saleh Tanveer, Wei-Shen Dai

Publication date: 26 October 1997

Published in: Journal of Fluid Mechanics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0022112096000894

zbMATH Keywords

daughter singularitiesfinger motion in channel

Mathematics Subject Classification ID

Asymptotic methods, singular perturbations applied to problems in fluid mechanics (76M45) Boundary-layer theory, separation and reattachment, higher-order effects (76D10) Capillarity (surface tension) for incompressible viscous fluids (76D45)

Related Items (15)

Unnamed Item ⋮ On the motion of unsteady translating bubbles in an unbounded Hele-Shaw cell ⋮ The vanishing surface tension limit of the Muskat problem ⋮ Computation of a Shrinking Interface in a Hele-Shaw Cell ⋮ Numerical study of Hele-Shaw flow with suction ⋮ Viscous fingering as a paradigm of interfacial pattern formation: Recent results and new challenges ⋮ The zero surface tension limit of two-dimensional interfacial Darcy flow ⋮ Boundary integral methods for multicomponent fluids and multiphase materials. ⋮ Evolution of material voids for highly anisotropic surface energy ⋮ A dynamical mother body in a Hele-Shaw problem ⋮ Squeeze flow of multiply-connected fluid domains in a Hele-Shaw cell ⋮ The zero surface tension limit of three-dimensional interfacial Darcy flow ⋮ Topological reconfiguration in expanding Hele—Shaw flow ⋮ Dynamics and selection of fingering patterns. Recent developments in the Saffman-Taylor problem ⋮ Univalent functions in the dynamics of viscous flows

Cites Work

• Removing the stiffness from interfacial flows with surface tension
• A well-posed numerical method to track isolated conformal map singularities in the Hele-Shaw flow
• Nonlinear unstable viscous fingers in Hele–Shaw flows. II. Numerical simulation
• Cusp Development in Hele–Shaw Flow with a Free Surface
• Bubble growth in porous media and Hele–Shaw cells
• The effect of thin film variations and transverse curvature on the shape of fingers in a Hele–Shaw cell
• Analytic theory for the linear stability of the Saffman–Taylor finger
• A numerical study of the effect of surface tension and noise on an expanding Hele–Shaw bubble
• Global solutions for small data to the Hele-Shaw problem

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