Dynamics of a viscous thread on a non-planar substrate

Mark Bowen*, John R. King

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


We derive a general reduced model for the flow of a slender thread of viscous fluid on a grooved substrate. Specific choices of the substrate topography allow further analytic progress to be made, and we subsequently focus on a convection-diffusion equation governing the evolution of viscous liquid in a wedge geometry. The model equation that arises also appears in the context of foam drainage, and we take the opportunity to review and compare the results from both applications. After summarising the constant mass results, we introduce a time-dependent fluid influx at one end of the wedge. The analytical results are supported by numerical computations.

Original languageEnglish
Pages (from-to)39-62
Number of pages24
JournalJournal of Engineering Mathematics
Issue number1
Publication statusPublished - 2013 Jun


  • Asymptotics
  • Capillary flow
  • Self-similarity
  • Thin film

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)


Dive into the research topics of 'Dynamics of a viscous thread on a non-planar substrate'. Together they form a unique fingerprint.

Cite this