Singularity formation in Hele–Shaw bubbles

DOI10.1063/1.869102zbMath1023.76522OpenAlexW2036667275MaRDI QIDQ4425495

Robert Almgren

Publication date: 18 November 2003

Published in: Physics of Fluids (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1063/1.869102

Mathematics Subject Classification ID

Asymptotic methods, singular perturbations applied to problems in fluid mechanics (76M45) Other free boundary flows; Hele-Shaw flows (76D27)

Related Items (25)

Doubly nonlinear thin-film equations in one space dimension ⋮ Symmetries, first integrals and phase planes of a third-order ordinary differential equation from thin film flow ⋮ Qualitative behaviour of solutions in two models of thin liquid films ⋮ The immersed interface method for axis-symmetric problems and application to the Hele-Shaw flow ⋮ Numerical investigation of a third-order ODE from thin film flow ⋮ Computation of a Shrinking Interface in a Hele-Shaw Cell ⋮ Functional inequalities and strong Lyapunov functionals for free surface flows in fluid dynamics ⋮ Signal processing approach to mesh refinement in simulations of axisymmetric droplet dynamics ⋮ On the determination of the steady film profile for a non-Newtonian thin droplet ⋮ An investigation of an Emden-Fowler equation from thin film flow ⋮ Hele-Shaw flows with anisotropic surface tension ⋮ Self-similar asymptotics for a class of Hele-Shaw flows driven solely by surface tension ⋮ Stretch flow of thin layers of Newtonian liquids: Fingering patterns and lifting forces ⋮ Study of a family of higher order nonlocal degenerate parabolic equations: from the porous medium equation to the thin film equation ⋮ Gradient flow structure for domain relaxation in Langmuir films ⋮ Boundary integral methods for multicomponent fluids and multiphase materials. ⋮ The long-time motion of vortex sheets with surface tension ⋮ Instabilities and singularities in Hele–Shaw flow ⋮ High order quadratures for the evaluation of interfacial velocities in axi-symmetric Stokes flows ⋮ Stable and unstable singularities in the unforced Hele-Shaw cell ⋮ A Free Boundary Problem of Fourth Order: Classical Solutions in Weighted Hölder Spaces ⋮ Relaxation to equilibrium in the one-dimensional thin-film equation with partial wetting and linear mobility ⋮ Topological reconfiguration in expanding Hele—Shaw flow ⋮ On the breakdown of Hele-Shaw solutions with nonzero surface tension ⋮ Lubrication approximation with prescribed nonzero contact anggle

Cites Work

• The Hele--Shaw problem and area-preserving curve-shortening motions
• A short note on the evolution of a surface by its mean curvature
• Removing the stiffness from interfacial flows with surface tension
• Linking anisotropic sharp and diffuse surface motion laws via gradient flows
• Numerical experiments on Hele Shaw flow with a sharp interface
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• 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
• A fast algorithm for particle simulations

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