Stalactite growth as a free-boundary problem: A geometric law and its platonic ideal

Martin B. Short, James C. Baygents, J. Warren Beck, David A. Stone, Rickard S. Toomey, Raymond E. Goldstein

Research output: Contribution to journalArticle

64 Scopus citations

Abstract

The chemical mechanisms underlying the growth of cave formations such as stalactites are well known, yet no theory has yet been proposed which successfully accounts for the dynamic evolution of their shapes. Here we consider the interplay of thin-film fluid dynamics, calcium carbonate chemistry, and CO2 transport in the cave to show that stalactites evolve according to a novel local geometric growth law which exhibits extreme amplification at the tip as a consequence of the locally-varying fluid layer thickness. Studies of this model show that a broad class of initial conditions is attracted to an ideal shape which is strikingly close to a statistical average of natural stalactites.

Original languageEnglish (US)
Article number018501
JournalPhysical review letters
Volume94
Issue number1
DOIs
StatePublished - Jan 14 2005

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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