Effects of small surface tension in Hele-Shaw multifinger dynamics: An analytical and numerical study

Document Type

Article

Publication Date

10-10-2002

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. © 2002 The American Physical Society.

Identifier

41349107347 (Scopus)

Publication Title

Physical Review E Statistical Physics Plasmas Fluids and Related Interdisciplinary Topics

External Full Text Location

https://doi.org/10.1103/PhysRevE.66.046205

ISSN

1063651X

PubMed ID

12443297

First Page

13

Issue

4

Volume

66

Grant

9704746

Fund Ref

National Science Foundation

This document is currently not available here.

Share

COinS