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The Saffman‐Taylor Fingers in the Limit of Very Large Surface Tension
Author(s) -
Pomeau Y.
Publication year - 1985
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1002/sapm198573175
Subject(s) - inviscid flow , curvilinear coordinates , surface tension , limit (mathematics) , mathematical analysis , instability , mathematics , dimensionless quantity , viscous liquid , boundary (topology) , infinity , nonlinear system , surface (topology) , mechanics , physics , geometry , thermodynamics , quantum mechanics
In long rectangular Hele‐Shaw cells the Saffman‐Taylor instability generates steady advancing fingers of the less viscous fluid. The structure of these fingers is determined by the solution of a system of nonlinear integrodifferential equations for two unknown functions of the curvilinear coordinate defined along the boundary of the finger. The surface tension appears in these equations through a dimensionless coefficient called k . I analyze the solution when this coefficient tends to infinity. In this limit, the inviscid fluid tends to fill almost completely the cell, except for a thin layer of viscous fluid left on the sides of thickness of order k −½ .