On the rôle of Stokes lines in the selection of Saffman–Taylor fingers with small surface tension

DOI10.1017/S0956792599003848zbMath0949.76022OpenAlexW2134943453MaRDI QIDQ4486076

S. Jonathan Chapman

Publication date: 11 December 2000

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

Full work available at URL: https://doi.org/10.1017/s0956792599003848

zbMATH Keywords

small surface tensionSaffman-Taylor problemStokes linesselection of Saffman-Taylor fingers

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Capillarity (surface tension) for incompressible viscous fluids (76D45) Other free boundary flows; Hele-Shaw flows (76D27)

Related Items (17)

Do waveless ships exist? Results for single-cornered hulls ⋮ Free surface flow past topography: A beyond-all-orders approach ⋮ Exponential asymptotics for steady parasitic capillary ripples on steep gravity waves ⋮ Complex singularities near the intersection of a free surface and wall. Part 1. Vertical jets and rising bubbles ⋮ Unnamed Item ⋮ The role of exponential asymptotics and complex singularities in self-similarity, transitions, and branch merging of nonlinear dynamics ⋮ Rigorous results in existence and selection of Saffman–Taylor fingers by kinetic undercooling ⋮ Existence and selection of steady bubbles in a Hele-Shaw cell ⋮ The effect of surface tension on steadily translating bubbles in an unbounded Hele-Shaw cell ⋮ A REVIEW OF ONE-PHASE HELE-SHAW FLOWS AND A LEVEL-SET METHOD FOR NONSTANDARD CONFIGURATIONS ⋮ On the growth of the mixing zone in miscible viscous fingering ⋮ Analytic solution to an interfacial flow with kinetic undercooling in a time-dependent gap Hele-Shaw cell ⋮ Nonexistence of classical steady Hele-Shaw bubble ⋮ Exponential asymptotics of localised patterns and snaking bifurcation diagrams ⋮ Selection of a Hele-Shaw Bubble via Exponential Asymptotics ⋮ Corner and finger formation in Hele-Shaw flow with kinetic undercooling regularisation ⋮ Local smoothing effect and existence for the one-phase Hele–Shaw problem with zero surface tension

This page was built for publication: On the rôle of Stokes lines in the selection of Saffman–Taylor fingers with small surface tension