A NOTE ON THE MOTION OF BUBBLES IN A HELE-SHAW CELL AND POROUS MEDIUM
From MaRDI portal
Publication:3266250
DOI10.1093/qjmam/12.3.265zbMath0091.18502OpenAlexW2023269164MaRDI QIDQ3266250
Philip G. Saffman, G. I. Taylor
Publication date: 1959
Published in: The Quarterly Journal of Mechanics and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1093/qjmam/12.3.265
Non-Newtonian fluids (76A05) PDEs in connection with fluid mechanics (35Q35) Flows in porous media; filtration; seepage (76S05)
Related Items
Discrete point spectrum of linear stability operator for Saffman-Taylor bubbles with nonzero surface tension ⋮ Inclusion shaping and extremal property of the Taylor-Saffman bubble ⋮ Rotation invariance for steady Hele–Shaw flows ⋮ On the motion of unsteady translating bubbles in an unbounded Hele-Shaw cell ⋮ Nonsymmetric Saffman–Taylor fingers ⋮ The shape and motion of gas bubbles in a liquid flowing through a thin annulus ⋮ Bubble rise in a Hele-Shaw cell: bridging the gap between viscous and inertial regimes ⋮ The role of added mass in the theory of Hele-Shaw cell bubbles ⋮ Infinite stream of Hele–Shaw bubbles ⋮ Complex variable methods in Hele–Shaw moving boundary problems ⋮ Principle of minimum energy dissipation rate in steady Hele-Shaw flows ⋮ The interaction of multiple bubbles in a Hele-Shaw channel ⋮ Topography of the lubrication film under a pancake droplet travelling in a Hele-Shaw cell ⋮ Approximate solutions to droplet dynamics in Hele-Shaw flows ⋮ Penguin huddling: a continuum model ⋮ A pancake droplet translating in a Hele-Shaw cell: lubrication film and flow field ⋮ Analytic theory for the determination of velocity and stability of bubbles in a Hele-Shaw cell. I: Velocity selection ⋮ Extremum principles for selection in the Saffman–Taylor finger and Taylor–Saffman bubble problems ⋮ Rigorous results in existence and selection of Saffman–Taylor fingers by kinetic undercooling ⋮ Prediction of bubble velocity in a Hele–Shaw cell: Thin film and contact angle effects ⋮ CONFORMAL SLIT MAPS IN APPLIED MATHEMATICS ⋮ Viscous fingering as a paradigm of interfacial pattern formation: Recent results and new challenges ⋮ Miscible droplets in a porous medium and the effects of Korteweg stresses ⋮ Existence and selection of steady bubbles in a Hele-Shaw cell ⋮ Bubbles in a Hele–Shaw cell: Numerical simulation of three-dimensional effects ⋮ Multiple steady bubbles in a Hele-Shaw cell ⋮ The effect of surface tension on steadily translating bubbles in an unbounded Hele-Shaw cell ⋮ The influence of invariant solutions on the transient behaviour of an air bubble in a Hele-Shaw channel ⋮ Retarded motion of bubbles in Hele–Shaw cells ⋮ Multiple bubbles and fingers in a Hele-Shaw channel: complete set of steady solutions ⋮ Analytic solution to an interfacial flow with kinetic undercooling in a time-dependent gap Hele-Shaw cell ⋮ Variational finite element methods for waves in a Hele-Shaw tank ⋮ Nonexistence of classical steady Hele-Shaw bubble ⋮ Selection of a Hele-Shaw Bubble via Exponential Asymptotics ⋮ Selection in the Saffman-Taylor finger problem and the Taylor-Saffman bubble problem without surface tension ⋮ Doubly periodic array of bubbles in a Hele-Shaw cell ⋮ Modelling finger propagation in elasto-rigid channels ⋮ Laplacian and diffusional growth: A unified theoretical description for symmetrical and parity-broken patterns ⋮ Sensitivity of Saffman–Taylor fingers to channel-depth perturbations ⋮ Bifurcations of drops and bubbles propagating in variable-depth Hele-Shaw channels ⋮ Film thickness distribution in gravity-driven pancake-shaped droplets rising in a Hele-Shaw cell ⋮ Multiple steadily translating bubbles in a Hele-Shaw channel ⋮ Generalised Hele-Shaw flow: A Schwarz function approach ⋮ Instability of the displacement fronts of non-Newtonian fluids in a Hele-Shaw cell ⋮ Analytical solutions of seepage theory problems. Inverse method, variational theorems, optimization and estimates (a review) ⋮ Integrability-preserving regularizations of Laplacian Growth ⋮ Dynamics of a high-Reynolds-number bubble rising within a thin gap ⋮ Hele–Shaw flows with a free boundary produced by multipoles ⋮ Unnamed Item