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Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study
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We study the singular effects of vanishingly small surface tension on the dynamics of finger competition in the Saffman-Taylor problem, using the asymptotic techniques described by Tanveer [Philos. Trans. R. Soc. London, Ser. A 343, 155 (1993)] and Siegel and Tanveer [Phys. Rev. Lett. 76, 419 (1996)], as well as direct numerical computation, following the numerical scheme of Hou, Lowengrub, and Shelley [J. Comput. Phys. 114, 312 (1994)]. We demonstrate the dramatic effects of small surface tension on the late time evolution of two-finger configurations with respect to exact (nonsingular) zero-surface-tension solutions. The effect is present even when the relevant zero-surface-tension solution has asymptotic behavior consistent with selection theory. Such singular effects, therefore, cannot be traced back to steady state selection theory, and imply a drastic global change in the structure of phase-space flow. They can be interpreted in the framework of a recently introduced dynamical solvability scenario according to which surface tension unfolds the structurally unstable flow, restoring the hyperbolicity of multifinger fixed points.
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PAUNÉ I XURIGUERA, Eduard, SIEGEL, Michael, CASADEMUNT I VIADER, Jaume. Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study. _Physical Review E_. 2002. Vol. 66, núm. 4, pàgs. 046205. [consulta: 21 de gener de 2026]. ISSN: 1539-3755. [Disponible a: https://hdl.handle.net/2445/18692]