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oai:recercat.cat:2445/187442025-11-21T05:48:19Zcom_2072_1057col_2072_478823col_2072_478917

00925njm 22002777a 4500 dc Magdaleno Escar, Francesc Xavier author Casademunt i Viader, Jaume author 2011-07-07T12:51:47Z 2011-07-07T12:51:47Z 1999 We find that solvability theory selects a set of stationary solutions of the Saffman-Taylor problem with coexistence of two unequal fingers advancing with the same velocity but with different relative widths ${\ensuremath{\lambda}}_{1}$ and ${\ensuremath{\lambda}}_{2}$ and different tip positions. For vanishingly small dimensionless surface tension ${d}_{0},$ an infinite discrete set of values of the total filling fraction $\ensuremath{\lambda}={\ensuremath{\lambda}}_{1}+{\ensuremath{\lambda}}_{2}$ and of the relative individual finger width $p={\ensuremath{\lambda}}_{1}/\ensuremath{\lambda}$ are selected out of a two-parameter continuous degeneracy. They scale as $\ensuremath{\lambda}\ensuremath{-}1/2\ensuremath{\sim}{d}_{0}^{2/3}$ and $|p\ensuremath{-}1/2|\ensuremath{\sim}{d}_{0}^{1/3}.$ The selected values of $\ensuremath{\lambda}$ differ from those of the single finger case. Explicit approximate expressions for both spectra are given. Dinàmica de fluids Fluid dynamics Two-finger selection theory in the Saffman-Taylor problem