Singular effects of surface tension in evolving Hele-Shaw flows

Michael Siegel, Saleh Tanveer, Wei Shen Dai

Research output: Contribution to journalArticlepeer-review

48 Scopus citations

Abstract

In this paper, we present evidence to show that a smoothly evolving zero-surface tension solution of the Hele-Shaw equations can be singularly perturbed by the presence of arbitrarily small non-zero surface tension in order-one time. These effects are explained by the impact of 'daughter singularities' on the physical interface, whose formation was suggested in a prior paper (Tanveer 1993). For the case of finger motion in a channel, it is seen that the daughter singularity effect is strong enough to produce the transition from a finger of arbitrary width to one with the selected steady-state width in 0(1) time.

Original languageEnglish (US)
Pages (from-to)201-236
Number of pages36
JournalJournal of Fluid Mechanics
Volume323
DOIs
StatePublished - Sep 25 1996

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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