Domain of convergence of perturbative solutions for Hele-Shaw flow near interface collapse

Adriana J. Pesci, Raymond E. Goldstein, Michael J. Shelley

Research output: Contribution to journalArticlepeer-review

Abstract

Recent work [Phys. Fluids 10, 2701 (1998)] has shown that for Hele-Shaw flows sufficiently near a finite-time pinching singularity, there is a breakdown of the leading-order solutions perturbative in a small parameter ∈ controlling the large-scale dynamics. To elucidate the nature of this breakdown we study the structure of these solutions at higher order. We find a finite radius of convergence that yields a new length scale exponentially small in ∈. That length scale defines a ball in space and time, centered around the incipient singularity, inside of which perturbation theory fails. Implications of these results for a possible matching of outer solutions to inner scaling solutions are discussed.

Original languageEnglish (US)
Pages (from-to)2809-2811
Number of pages3
JournalPhysics of Fluids
Volume11
Issue number10
DOIs
StatePublished - Oct 1999

ASJC Scopus subject areas

  • Computational Mechanics
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Fluid Flow and Transfer Processes

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