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 journalArticle

24 Citations (Scopus)

Abstract

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
Volume18
Issue number8
DOIs
StatePublished - Aug 2006

Fingerprint

free boundaries
Calcium Carbonate
Calcium carbonate
Fluid dynamics
Ordinary differential equations
Physics
calcium carbonates
fluid dynamics
Heat transfer
Thin films
Coatings
Water
differential equations
heat transfer
chemistry
coatings
physics
synthesis
thin films
water

ASJC Scopus subject areas

  • Mechanics of Materials
  • Computational Mechanics
  • Physics and Astronomy(all)
  • Fluid Flow and Transfer Processes
  • Condensed Matter Physics

Cite this

A free-boundary theory for the shape of the ideal dripping icicle. / Short, Martin B.; Baygents, James C; Goldstein, Raymond E.

In: Physics of Fluids, Vol. 18, No. 8, 083101, 08.2006.

Research output: Contribution to journalArticle

Short, Martin B. ; Baygents, James C ; Goldstein, Raymond E. / A free-boundary theory for the shape of the ideal dripping icicle. In: Physics of Fluids. 2006 ; Vol. 18, No. 8.
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