The evolution of a slender non-axisymmetric drop in an extensional flow

P. D. Howell, M. Siegel

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

Abstract

An asymptotic method for analysing slender non-axisymmetric drops, bubbles and jets in a general straining flow is developed. The method relies on the slenderness of the geometry to reduce the three-dimensional equations to a sequence of weakly coupled, quasi-two-dimensional Stokes flow problems for the cross-sectional evolution. Exact solution techniques for the flow outside a bubble in two-dimensional Stokes flow are generalized to solve for the transverse flow field, allowing large non-axisymmetric deformations to be described. A generalization to the case where the interior of the bubble contains a slightly viscous fluid is also presented. Our method is usedto compute steady non-axisymmetric solution branches for inviscid bubbles and slightly viscous drops. We also present unsteady numerical solutions showing how the eccentricity of the cross-section adjusts to a non-axisymmetric external flow. Finally, we use our theory to investigate how the pinch-off of a jet of relatively inviscid fluid is affected by a two-dimensional straining cross-flow.

Original languageEnglish (US)
Pages (from-to)155-180
Number of pages26
JournalJournal of Fluid Mechanics
Volume521
DOIs
StatePublished - Dec 20 2004

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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