Moving contact lines and rivulet instabilities. part 2. lone waves on flat rivulets

Ralph H. Weiland*, Stephen H Davis

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

38 Scopus citations


A rivulet is a narrow stream of liquid located on a solid surface and sharing a curved interface with the surrounding gas. Long-wave instabilities are investigated for flat rivulets on a vertical wall. Three cases of contact-line conditions are investigated: (i) fixed contact lines, (ii) moving contact lines having fixed contact angles and (iii) moving contact lines whose contact angles vary smoothly with contact-line speeds. For case (i), the straight, unidirectional rivulet is stable below a critical Reynolds number. For case (ii), the rivulet is unconditionally unstable. For case (iii), the variation, G 1 ≡ [dα/dU CL ] UCL = 0 , in contact angle a with contact-line speed U CL stabilizes the rivulet and if G 1 is large enough can completely stabilize the flow. The analysis lends support to the idea that contact-angle steepening with contact-line motion is a purely dissipative process.

Original languageEnglish (US)
Pages (from-to)261-280
Number of pages20
JournalJournal of fluid Mechanics
StatePublished - Jan 1 1981

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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