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28 March 2024
 
  » arxiv » nlin.PS/0204052

 Article overview


Effects of small surface tension in Hele-Shaw multifinger dynamics: an analytical and numerical study
E. Paune ; M. Siegel ; J. Casademunt ;
Date 19 Apr 2002
Subject Pattern Formation and Solitons; Exactly Solvable and Integrable Systems; Statistical Mechanics | nlin.PS cond-mat.stat-mech nlin.SI
AbstractWe 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 in [S. Tanveer, Phil. Trans. R. Soc. Lond. A 343, 155 (1993)]and [M. Siegel, and S. Tanveer, Phys. Rev. Lett. 76, 419 (1996)] as well as direct numerical computation, following the numerical scheme of [T. Hou, J. Lowengrub, and M. Shelley,J. Comp. 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 (non-singular) 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 structually unstable flow, restoring the hyperbolicity of multifinger fixed points.
Source arXiv, nlin.PS/0204052
Other source [GID 929361] pmid12443297
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