Viscous fingering as a paradigm of interfacial pattern formation: Recent results and new challenges
Open Access
- 1 September 2004
- journal article
- Published by AIP Publishing in Chaos: An Interdisciplinary Journal of Nonlinear Science
- Vol. 14 (3), 809-824
- https://doi.org/10.1063/1.1784931
Abstract
We review recent results on dynamical aspects of viscous fingering. The Saffman¿Taylor instability is studied beyond linear stability analysis by means of a weakly nonlinear analysis and the exact determination of the subcritical branch. A series of contributions pursuing the idea of a dynamical solvability scenario associated to surface tension in analogy with the traditional selection theory is put in perspective and discussed in the light of the asymptotic theory of Tanveer and co-workers. The inherently dynamical singular effects of surface tension are clarified. The dynamical role of viscosity contrast is explored numerically. We find that the basin of attraction of the Saffman¿Taylor finger depends on viscosity contrast, and that the sensitivity to this parameter is maximal in the usual limit of high viscosity contrast. The competing attractors are identified as closed bubble solutions. We briefly report on recent results and work in progress concerning rotating Hele-Shaw flows, topological singularities and wetting effects, and also discuss future directions in the context of viscous fingerinKeywords
This publication has 67 references indexed in Scilit:
- Physics of Fluids, 2004
- Nonlinear Saffman-Taylor InstabilityPhysical Review Letters, 2004
- Microscopic Selection of Fluid Fingering PatternsPhysical Review Letters, 2001
- On the tip-splitting instability of viscous fingersJournal of Fluid Mechanics, 2000
- Numerical study of Hele-Shaw flow with suctionPhysics of Fluids, 1999
- Radial displacement of a fluid annulus in a rotating Hele–Shaw cellPhysics of Fluids, 1999
- On nonlinear interface dynamics in Hele-Shaw flowsEuropean Journal of Applied Mathematics, 1995
- Pattern selection in fingered growth phenomenaAdvances in Physics, 1988
- Fingering in Hele-Shaw cellsJournal of Fluid Mechanics, 1986
- Interfaces and falling drops in a Hele-Shaw cellEuropean Journal of Physics, 1984