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Article overview
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Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study | | E Pauné
; M Siegel
; J Casademunt
; | | Date: |
30 Sep 2002 | | Journal: | Phys Rev E, 66 (4 Pt 2), 046205 | | Abstract: | 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. | | Source: | PubMed, pmid12443297 | | Other source: | [GID 929361] nlin.PS/0204052 | | Services: | Forum | Review | Favorites | |
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