IJCsatellite IJCsatellite/PRL

14 January 2005

Phys. Rev. Lett. 94, 018501 (2005) http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype=pdf&id=PRLTAO000094000001018501000001&idtype=cvips

Stalactite Growth as a Free-Boundary Problem: A Geometric Law and Its Platonic Ideal

Martin B. Short,1 James C. Baygents,2,3 J. Warren Beck,1,4 David A. Stone,5 Rickard S. Toomey III,6 and Raymond E. Goldstein1,3

1Department of Physics, University of Arizona, Tucson, Arizona 85721, USA
2Department of Chemical and Environmental Engineering, University of Arizona, Tucson, Arizona 85721, USA
3Program in Applied Mathematics, University of Arizona, Tucson, Arizona 85721, USA
4Accelerator Mass Spectrometry Facility, University of Arizona, Tucson, Arizona 85721, USA
5Department of Soil, Water, and Environmental Science, University of Arizona, Tucson, Arizona 85721, USA
6Kartchner Caverns State Park, P.O. Box 1849, Benson, Arizona 85602, USA

(Received 11 August 2004; published 7 January 2005)

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. ?2005 The American Physical Society

URL: http://link.aps.org/abstract/PRL/v94/e018501 ~ doi:10.1103/PhysRevLett.94.018501
PACS: 91.65.-n, 47.15.Gf, 47.54.+r, 68.70.+w

薄膜状の流体力学、炭酸カルシウムの化学反応、二酸化炭素の輸送を考慮することにより、現実の鍾乳石の形状をよく再現するモデルの話


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