Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-20T08:37:00.125Z Has data issue: false hasContentIssue false
  • English
  • Français

Steady-state mushy layers: experiments and theory

Published online by Cambridge University Press:  14 October 2021

S. S. L. Peppin ,
P. Aussillous ,
Herbert E. Huppert  and
M. Grae Worster
S. S. L. Peppin
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
P. Aussillous
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
Herbert E. Huppert
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
M. Grae Worster
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

A new facility has been developed to investigate the directional solidification of transparent aqueous solutions forming mushy layers in a quasi-two-dimensional system. Experiments have been conducted on NaCl–H2O solutions by translating a Hele-Shaw cell at prescribed rates between fixed heat exchangers providing a temperature gradient of approximately 1°C mm−1. The mush–liquid interface remained planar at all freezing velocities larger than 8 μm s−1, while steepling occurred at lower velocities. No significant undercooling of the mush–liquid interface was detected at freezing velocities up to 12 μm s−1. Mathematical predictions of the steady-state temperature profile and mushy-layer thickness as functions of freezing rate are in excellent agreement with experimental measurements.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 570 , 10 January 2007 , pp. 69 - 77
Copyright
Copyright © Cambridge University Press 2007

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

†

Present address: Groupe Ecoulements de Particules, IUSTI, Polytech' Marseille, Université de Provence, CNRS UMR 6595, 5 rue Enrico Fermi, 13453 Marseille cedex 13, France.

References

REFERENCES

Aussillous, P., Sederman, A. J., Gladden, L. F., Huppert, H. E. & Worster, M. G. 2006 Magnetic resonance imaging of structure and convection in solidifying mushy layers. J. Fluid Mech. 552, 99–125.CrossRefGoogle Scholar
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics Cambridge University Press.Google Scholar
Bergman, M. I. & Fearn, D. R. 1994 Chimneys on the Earth's inner-outer core boundary? Geophys. Res. Lett. 21, 477–480.CrossRefGoogle Scholar
Brattkus, K. 1995 Directional solidification into static stability. J. Fluid Mech. 304, 143–159.CrossRefGoogle Scholar
Burden, M. H., Hebditch, D. J. & Hunt, J. D. 1973 Macroscopic stability of a planar, cellular or dendritic interface during directional freezing. J. Cryst. Growth 20, 121–124.CrossRefGoogle Scholar
Chen, C. F. 1991 Experimental study of convection in a mushy layer during directional solidification. J. Fluid Mech. 293, 81–98.CrossRefGoogle Scholar
Chen, F. & Chen, C. F. 1991 Experimental study of directional solidification of aqueous ammonium chloride solution. J. Fluid Mech. 227, 567–586.CrossRefGoogle Scholar
Chung, C.-A. & Worster, M. G. 2002 Steady state chimneys in a mushy layer. J. Fluid Mech. 455, 387–411.CrossRefGoogle Scholar
Copley, S. M., Giamei, A. F., Johnson, S. M. & Hornbecker, M. F. 1970 The origin of freckles in unidirectionally solidified castings. Metall. Trans. 1, 2193–2204.CrossRefGoogle Scholar
Coriell, S. R. & McFadden, G. B. 1989 Buoyancy effects on morphological instability during directional solidification. J. Cryst. Growth 94, 513–521.CrossRefGoogle Scholar
Fowler, A. C. 1985 The formation of freckles in binary alloys. IMA J. Appl. Maths 35, 159–174.CrossRefGoogle Scholar
Hills, R. N., Loper, D. E. & Roberts, P. H. 1983 A thermodynamically consistent model of a mushy zone. Q. J. Mech. Appl. Maths 36, 505–539.CrossRefGoogle Scholar
Huppert, H. E. 1990 The fluid mechanics of solidification. J. Fluid Mech. 212, 209–240.CrossRefGoogle Scholar
Huppert, H. E. & Hallworth, M. A. 1993 Solidification of NH4Cl and NH4Br from aqueous solutions contaminated with CuSO4: the extinction of chimneys. J. Cryst. Growth 130, 495–506.CrossRefGoogle Scholar
Huppert, H. E. & Worster, M. G. 1985 Dynamic solidification of a binary melt. Nature 314, 703–707.CrossRefGoogle Scholar
Incropera, F. P. & DeWitt, D. P. 1996 Fundamentals of Heat and Mass Transfer, 4th Edn. John Wiley & Sons.Google Scholar
Loper, D. E. & Roberts, P. H. 2001 Mush-chimney convection. Stud. Appl. Maths 106, 187–227.CrossRefGoogle Scholar
Mullins, W. W. & Sekerka, R. F. 1964 Stability of a planar interface during solidification of a dilute binary alloy. J. Appl. Phys. 35, 444–451.CrossRefGoogle Scholar
Press, W. H., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. 1992 Numerical Recipes in C, 2nd Edn. Cambridge University Press.Google Scholar
Rubinsky, B. & Ikeda, M. 1985 A cryomicroscope using directional solidification for the controlled freezing of biological material. Cryobiology 22, 55–68.CrossRefGoogle Scholar
Sarazin, J. R. & Hellawell, A. 1998 Channel formation in Pb-Sn, Pb-Sb and Pb-Sn-Sb alloys and comparison with the system NH4Cl-H20. Metall. Trans. 19A, 1861–1871.Google Scholar
Schulze, T. M. & Worster, M. G. 1999 Weak convection, liquid inclusions and the formation of chimneys in mushy layers. J. Fluid Mech. 388, 197–215.CrossRefGoogle Scholar
Solomon, T. H. & Hartley, R. R. 1998 Measurements of the temperature field of mushy and liquid regions during solidification of aqueous ammonium chloride. J. Fluid Mech. 358, 87–106.CrossRefGoogle Scholar
Tait, S. & Jaupart, C. 1992 Compositional convection in a reactive crystalline mush and melt differentiation. J. Geophys. Res. 97, 6735–6756.CrossRefGoogle Scholar
Wettlaufer, J. S., Worster, M. G. & Huppert, H. E. 1997 Natural convection during solidification of an alloy from above with application to the evolution of sea ice. J. Fluid Mech. 344, 291–316.Google Scholar
Worster, M. G. 1986 Solidification of an alloy from a cooled boundary. J. Fluid Mech. 167, 481–501.CrossRefGoogle Scholar
Worster, M. G. 1991 Natural convection in a mushy layer. J. Fluid Mech. 224, 335–359.CrossRefGoogle Scholar
Worster, M. G. 1992 Instabilities of the liquid and mushy regions during solidification of alloys. J. Fluid Mech. 237, 649–669.CrossRefGoogle Scholar
Worster, M. G. 2000 Solidification of fluids. In Perspectives in Fluid Dynamics (ed. Batchelor, G. K., Moffatt, H. K. & Worster, M. G.), pp. 393–446. Cambridge University Press.Google Scholar
Worster, M. G. & Kerr, R. C. 1994 The transient behaviour of alloys solidified from below prior to the formation of chimneys. J. Fluid Mech. 269, 23–44.CrossRefGoogle Scholar