Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-26T14:01:09.465Z Has data issue: false hasContentIssue false
  • English
  • Français

An experimental study of shear-enhanced convection in a mushy layer

Published online by Cambridge University Press:  10 October 2008

JEROME A. NEUFELD  and
J. S. WETTLAUFER
JEROME A. NEUFELD
Affiliation:
Department of Geology and Geophysics, Yale University, New Haven, CT 06520, USA
J. S. WETTLAUFER
Affiliation:
Department of Geology and Geophysics, Yale University, New Haven, CT 06520, USA Department of Physics, Yale University, New Haven, CT 06520, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

The influence of an external shear flow on the evolution of a solidifying array of dendritic crystals, termed a mushy layer, is investigated through controlled cooling of an aqueous ammonium chloride solution in a laboratory flume. The controlled cooling produces a mushy layer that grows at a constant rate from the base of the flume over which a laminar shear flow is applied. We find a critical flow speed above which a spatiotemporal variation of the solid fraction of the layer appears with a planform transverse to the flow direction. The presence of this distinctive pattern of spanwise crevasses is compared with a simplified stability analysis in which the motion of the external fluid over the corrugated mush–liquid interface produces a pressure perturbation that drives flow and phase change within the mushy layer. This flow leads to a pattern of solidification and dissolution that is compared to the experimental results. The physical mechanism underlying the pattern formation is confirmed by the agreement between the theoretical predictions and experimental results. Finally, the comparison between theory and experiment provides a value for the mushy layer permeability, the evolution of which is of relevance to a host of geophysical, biological and engineering systems.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 612 , 10 October 2008 , pp. 363 - 385
Copyright
Copyright © Cambridge University Press 2008

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.)

References

REFERENCES

Aubert, J., Amit, H., Hulot, G. & Olson, P. 2008 Thermochemical flows couple the Earth's inner core growth to mantle heterogeneity. Nature 454, 758–761.CrossRefGoogle ScholarPubMed
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
Beavers, G. S. & Joseph, D. D. 1967 Boundary conditions at a naturally permeable wall. J. Fluid Mech. 30, 197–207.CrossRefGoogle Scholar
Belonoshko, A. B., Skorodumova, N. V., Rosengren, A. & Johansson, B. 2008 Elastic anisotropy of Earth's inner core. Science 319, 797–800.CrossRefGoogle ScholarPubMed
Chen, C. F. & Chen, F. 1991 Experimental study of directional solidification of aqueous ammonium chloride solution. J. Fluid Mech. 227, 567–586.CrossRefGoogle Scholar
Chen, F., Lu, J. W. & Yang, T. L. 1994 Conective instability in ammonium chloride solution directionally solidified from below. J. Fluid Mech. 276, 163–187.CrossRefGoogle Scholar
Chung, C. A. & Chen, F. 2001 Morphological instability in a directionally solidifying binary solution with an imposed shear flow. J. Fluid Mech. 436, 85–106.CrossRefGoogle Scholar
Copley, S. M., Giamei, A. F., Johnson, S. M. & Hornbecker, M. F. 1970 The origin of freckles in binary alloys. Metall. Trans. 1, 2193–2204.CrossRefGoogle Scholar
Davis, S. H. 1990 Hydrodynamic interactions in directional solidification. J. Fluid Mech. 212, 241–262.CrossRefGoogle Scholar
Davis, S. H. 2001 Theory of Solidification. Cambridge University Press.CrossRefGoogle Scholar
Feltham, D. L. & Worster, M. G. 1999 Flow-induced morphological instability of a mushy layer. J. Fluid Mech. 391, 337–357.CrossRefGoogle Scholar
Glicksman, M. E., Coriell, S. R. & McFadden, G. B. 1986 Interaction of flows with the crystal-melt interface. Annu. Rev. Fluid Mech. 18, 307–335.CrossRefGoogle Scholar
Huppert, H. E., Hallworth, M. A. & Lipson, S. G. 1993 Solidification of NH4Cl and NH4Br from aqueous solutions contaminated by CuSO4: the extinction of chimneys. J. Cryst. Growth 130, 495–506.CrossRefGoogle Scholar
Krembs, C., Tuschling, K. & von Juterzenka, K. 2002 The topography of the ice-water interface – its influence on the colonization of sea ice by algae. Polar Biol. 25, 106–117.CrossRefGoogle Scholar
Neufeld, J. A. & Wettlaufer, J. S. 2008 Shear-enhanced convection in a mushy layer. J. Fluid Mech. 612, 339–361.CrossRefGoogle Scholar
Neufeld, J. A., Wettlaufer, J. S., Feltham, D. L. & Worster, M. G. 2006 Corrigendum to flow-induced morphological instability of a mushy layer. J. Fluid Mech. 549, 442–443.Google Scholar
Peppin, S. S. L., Aussillous, P., Huppert, H. E. & Worster, M. G. 2007 Steady-state mushy layers: experiments and theory. J. Fluid Mech. 570, 69–77.CrossRefGoogle Scholar
Sarazin, J. R. & Hellawell, A. 1988 Channel formation in Pb-Sn, Pb-Sb, and Pb-Sn-Sb alloy ingots and comparison with the system NH4Cl-H2O. Metall. Trans. A 19, 1861–1871.CrossRefGoogle Scholar
Tait, S. & Jaupart, C. 1989 Compositional convection in viscous melts. Nature 338, 571–574.CrossRefGoogle Scholar
Tait, S. & Jaupart, C. 1992 Compositional convection in a reactive crystalline mush and melt differentiation. J. Geophys. Res. 97 (B5), 6735–6756.CrossRefGoogle Scholar
Vella, D. & Wettlaufer, J. S. 2007 Finger rafting: a generic instability of floating elastic sheets. Phys. Rev. Lett. 98, 088303.CrossRefGoogle ScholarPubMed
Washburn, E. W. (Ed.) 2003 International Critical Tables of Numerical Data, Physics, Chemistry and Technology. Knovel.Google Scholar
Wettlaufer, J. S., Worster, M. G. & Huppert, H. E. 1997 a Natural convection during solidification of an alloy from above with application to the evolution of sea ice. J. Fluid Mech. 344, 291–316.CrossRefGoogle Scholar
Wettlaufer, J. S., Worster, M. G. & Huppert, H. E. 1997 b The phase evolution of young sea ice. Geophys. Res. Lett. 24, 1251–1254.CrossRefGoogle Scholar
Widell, K., Fer, I. & Haugan, P. M. 2006 Salt release from warming sea ice. Geophys. Res. Lett. 33, L12501, doi:10.1029/2006GL026262.CrossRefGoogle Scholar
Worster, M. G. 1986 Solidification of an alloy from a cooled boundary. J. Fluid Mech. 167, 481–501.CrossRefGoogle Scholar
Worster, M. G. 1992 a The dynamics of mushy layers. In Interactive Dynamics of Convection and Solidification (ed. Davis, S. H., Huppert, H. E., Müller, U., Worster, M. G.), pp. 113–138. Kluwer.CrossRefGoogle Scholar
Worster, M. G. 1992 b 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