Shape selection of Saffman-Taylor fingers

Journal Article · Mon May 12 04:00:00 EDT 1986 · Phys. Rev. Lett.; (United States)

DOI:https://doi.org/10.1103/PhysRevLett.56.2036· OSTI ID:5731911

Combescot, R; Dombre, T; Hakim, V; Pomeau, Y; Pumir, A

Among all problems of pattern selection the one posed by the Saffman-Taylor finger is yet unsolved, although numerics and experiments indicate the very simple property that the relative width of the finger tends to (1/2) in the low--surface-tension limit. We explain this by performing an expansion beyond all orders leading to the formulation of a nonlinear eigenvalue problem with a discrete set of solutions. In particular we predict that the relative width of the finger tends to (1/2) as the surface tension to the power (2/3).

• Research Organization: Groupe de Physique des Solides, Ecole Normale Superieure, F-75231 Paris Cedex 05, France
• OSTI ID: 5731911
• Journal Information: Phys. Rev. Lett.; (United States), Journal Name: Phys. Rev. Lett.; (United States) Vol. 56:19; ISSN PRLTA
• Country of Publication: United States
• Language: English

Related Subjects

640410* -- Fluid Physics-- General Fluid Dynamics
656000 -- Condensed Matter Physics
75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
CONVECTIVE INSTABILITIES
FLOW MODELS
INSTABILITY
INTERFACES
MATHEMATICAL MODELS
NONLINEAR PROBLEMS
PLASMA INSTABILITY
SURFACE PROPERTIES
SURFACE TENSION