A free-boundary theory for the shape of the ideal dripping icicle

Martin B. Short, James C. Baygents, Raymond E. Goldstein

Research output: Contribution to journalArticlepeer-review

33 Scopus citations


The growth of icicles is considered as a free-boundary problem. A synthesis of atmospheric heat transfer, geometrical considerations, and thin-film fluid dynamics leads to a nonlinear ordinary differential equation for the shape of a uniformly advancing icicle, the solution to which defines a parameter-free shape which compares very favorably with that of natural icicles. Away from the tip, the solution has a power-law form identical to that recently found for the growth of stalactites by precipitation of calcium carbonate. This analysis thereby explains why stalactites and icicles are so similar in form despite the vastly different physics and chemistry of their formation. In addition, a curious link is noted between the shape so calculated and that found through consideration of only the thin coating water layer.

Original languageEnglish (US)
Article number083101
JournalPhysics of Fluids
Issue number8
StatePublished - Aug 2006

ASJC Scopus subject areas

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


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