Pattern formation in non-Newtonian Hele–Shaw flow

DOI10.1063/1.1359417zbMath1184.76156OpenAlexW2080534764MaRDI QIDQ3555453

Michael J. Shelley, Lou Kondic, Petri Fast, Peter Palffy-Muhoray

Publication date: 22 April 2010

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

Full work available at URL: https://doi.org/10.1063/1.1359417

zbMATH Keywords

two-phase flowsolidificationnon-Newtonian fluidsboundary-value problemsbubblesflow simulationliquid crystalsnon-Newtonian flowflow instabilityairdendritic structure

Mathematics Subject Classification ID

Fluid mechanics (76-XX)

Related Items

Miscible viscous fingering involving viscosity changes of the displacing fluid by chemical reactions ⋮ Viscoelastic Hele-Shaw flow in a cross-slot geometry ⋮ Selection Mechanism in Non-Newtonian Saffman–Taylor Fingers ⋮ Lemniscate growth ⋮ Buoyant displacement flows in slightly non-uniform channels ⋮ Stability of lubricated viscous gravity currents. Part 1. Internal and frontal analyses and stabilisation by horizontal shear ⋮ Stability of lubricated viscous gravity currents. Part 2. Global analysis and stabilisation by buoyancy forces ⋮ A moving overset grid method for interface dynamics applied to non-Newtonian Hele--Shaw flow. ⋮ Solving Nonlinear Parabolic Equations by a Strongly Implicit Finite Difference Scheme ⋮ Viscous fingering instabilities in an oil in water emulsion ⋮ A REVIEW OF ONE-PHASE HELE-SHAW FLOWS AND A LEVEL-SET METHOD FOR NONSTANDARD CONFIGURATIONS ⋮ Boundary integral methods for multicomponent fluids and multiphase materials. ⋮ Flow regime analysis of non-Newtonian duct flows ⋮ A hybrid variational front tracking-level set mesh generator for problems exhibiting large deformations and topological changes ⋮ Converging gravity currents of power-law fluid ⋮ Fingering instabilities in adhesive failure ⋮ Modelling the suppression of viscous fingering in elastic-walled Hele-Shaw cells

Cites Work

• A model for viscoelastic fluid behavior which allows non-affine deformation
• Gas-assisted displacement of viscoelastic fluids: Flow dynamics at the bubble front
• Removing the stiffness from interfacial flows with surface tension
• Radial fingering in a Hele-Shaw cell: A weakly nonlinear analysis
• Numerical solution of the nonlinear magnetostatic-field equation in two dimensions
• Deposition of a viscous fluid on the wall of a tube
• The motion of long bubbles in tubes
• The Taylor–Saffman problem for a non-Newtonian liquid
• Nonlinear unstable viscous fingers in Hele–Shaw flows. II. Numerical simulation
• Pushing a non-Newtonian fluid in a Hele-Shaw cell: From fingers to needles
• Viscous fingering in a shear-thinning fluid
• Two-phase displacement in Hele Shaw cells: theory
• The Penetration of a Finger into a Viscous Fluid in a Channel and Tube
• Interface conditions for two-phase displacement in Hele-Shaw cells
• The effect of surface tension on the shape of fingers in a Hele Shaw cell
• Inexact Newton Methods
• Analysis of New Phenomena in Shear Flow of Non-Newtonian Fluids
• Self-dilating viscous fingers in wedge-shaped Hele-Shaw cells
• A numerical study of the effect of surface tension and noise on an expanding Hele–Shaw bubble
• The primary and inverse instabilities of directional viscous fingering