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Physics of Fluids / Volume 22 / Issue 1 / ARTICLES / Others

Phys. Fluids 22, 017102 (2010); http://dx.doi.org/10.1063/1.3291075 (15 pages)

Morphological instability of the solid-liquid interface in crystal growth under supercooled liquid film flow and natural convection airflow

Kazuto Ueno and Masoud Farzaneh

NSERC/Hydro-Quebec/UQAC Industrial Chair on Atmospheric Icing of Power Network Equipment (CIGELE) and Canada Research Chair on Engineering of Power Network Atmospheric Icing (INGIVRE), Université du Québec à Chicoutimi, 555 Boulevard de l’Université, Chicoutimi, Québec G7H 2B1, Canada

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(Received 1 May 2009; accepted 12 December 2009; published online 11 January 2010; publisher error corrected 13 January 2010)

Ringlike ripples on the surface of icicles are an example of morphological instability of the ice-water interface during ice growth under supercooled water film flow. The surface of icicles is typically covered with ripples of about 1 cm in wavelength, and the wavelength appears to be almost independent of external temperature, icicle radius, and volumetric water flow rate. One side of the water layer consists of the water-air surface and growing ice is the other. This is one of the more complicated moving phase boundary problems with two interfaces. A recent theoretical work [ K. Ueno, Phys. Rev. E 68, 021603 (2003) ] to address the underlying instability that produces ripples is based on the assumption of the absence of airflow around icicles. In this paper, we extend the previous theoretical framework to include a natural convection airflow ahead of the water-air surface and consider whether the effect of natural convection airflow on the wavelength of ripples produced on an ice surface is essential or not.

© 2010 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. THEORY
    1. Governing equations
    2. Boundary conditions at the ice-water interface and water-air surface
      1. Hydrodynamic boundary conditions
      2. Thermodynamic boundary conditions
    3. Perturbation
    4. Equations of flow and temperature distributions in the air boundary layer
    5. Equations of flow and temperature distributions in the water layer
    6. Linearization of boundary conditions
    7. Dispersion relation
  3. RESULTS
    1. Solutions of temperature distributions in the air boundary layer
    2. Approximate solutions of flow and temperature distributions in the water layer
    3. Wavelength and translation velocity of ripples
    4. Heat flux at the ice-water interface and water-air surface
  4. SUMMARY AND DISCUSSION

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KEYWORDS and PACS

Keywords

film flow, ice, liquid films, natural convection, supercooling, water

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3291075

PUBLICATION DATA

ISSN

1070-6631 (print)  
1089-7666 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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    References

    N. Ogawa and Y. Furukawa, “Surface instability of icicles,” Phys. Rev. E 66, 041202 (2002).

    K. Ueno, “Pattern formation in crystal growth under parabolic shear flow,” Phys. Rev. E 68, 021603 (2003).

    K. Ueno, “Pattern formation in crystal growth under parabolic shear flow II,” Phys. Rev. E 69, 051604 (2004).

    K. Ueno, “Characteristics of the wavelength of ripples on icicles,” Phys. Fluids 19, 093602 (2007)PHFLE6000019000009093602000001.

    M. B. Short, J. C. Baygents, and R. E. Goldstein, “A free-boundary theory for the shape of the ideal dripping icicle,” Phys. Fluids 18, 083101 (2006)PHFLE6000018000008083101000001.

    T. G. Myers, J. P. F. Charpin, and S. J. Chapman, “The flow and solidification of a thin fluid film on an arbitrary three-dimensional surface,” Phys. Fluids 14, 2788 (2002)PHFLE6000014000008002788000001.


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