Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-18T20:58:47.928Z Has data issue: false hasContentIssue false
  • English
  • Français

The growth of compositionally stratified solid above a horizontal boundary

Published online by Cambridge University Press:  26 April 2006

Andrew W. Woods  and
Herbert E. Huppert
Andrew W. Woods
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge, CB3 9EW, UK
Herbert E. Huppert
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge, CB3 9EW, UK
Get access Rights & Permissions [Opens in a new window]

Abstract

The compositional stratification in solid formed by cooling a binary alloy from below is investigated theoretically and experimentally. It is shown that in order to grow composite solid the boundary temperature needs to be below the eutetic temperature. Two separate cases are considered. In the first, heavy fluid is released on solidification. The solid growth is then governed by the diffusive transport of heat and composition. The resultant solid is shown to have a fixed composition until the far-field conditions change. In the second case, light fluid is released on solidification. This generates turbulent compositional convection in the melt which significantly increases the transport of heat and composition across the solid/melt interface. As a result, the fraction of heavy component in the solid initially increases, but subsequently decreases to conserve mass. A simple theoretical model, using the approximation of a flat solid/melt interface is developed; this predicts differences in the thermal flux in saturated and undersaturated melts. Laboratory experiments involving aqueous solutions of sodium carbonate cooled from below which released light fluid displayed compositional convection and stratification of the solid as predicted.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 199 , February 1989 , pp. 29 - 53
Copyright
© 1989 Cambridge University Press

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

Adornato, P. M. & Brown, R. A., 1987 Convection and segregation in directional solidification of dilute and non-dilute binary alloys: effects of ampoule and furnace design. J. Cryst. Growth 80, 115.Google Scholar
Carslaw, H. S. & Jaegar, J. C., 1986 Conduction of Heat in Solids. Oxford University Press.
Chen, C. F. & Turner, J. S., 1980 Crystallisation in a double-diffusive system. J. Geophys. Res. 85, 2573.Google Scholar
Coriell, S. R., Cordes, M. R., Boettinger, W. J. & Sekerka, R. F., 1981 Convective and interfacial stability during unidirectional solidifiation of a binary allow. J. Cryst. Growth 49, 13.Google Scholar
Elliott, R.: 1983 Eutectic Solidification Processing. Butterworths.
Fowler, A. C.: 1985 The formation of freckles in binary alloys. IMA J. Appl. Maths. 35, 159.Google Scholar
Howard, L. N.: 1964 Convection at high Rayleigh number. Proc. 11th Intl Cong. Appl. Mech., p. 1109. Springer.
Huppert, H. E., Sparks, R. S. J., Wilson, J. R., Hallworth, M. A. & Leitch, A. M., 1987 Laboratory experiments with aqueous solutions modelling processes in a magma chamber II. Cooling and crystallization along inclined planes. In Origins of Igneous Layering (ed. I. Parsons), p. 539. Reidel.
Huppert, H. E. & Worster, M. G., 1985 Dynamic solidification of a binary alloy. Nature 314, 703.Google Scholar
Hurle, D. T. J. & Jakeman, E. 1968 Morphological stability of lamellar eutectics. J. Cryst. Growth 3–4, 594.Google Scholar
Hurle, D. T. J., Jakeman, E. & Wheeler, A. A., 1982 Effect of solutal convection on the morphological stability of a binary alloy. J. Cryst. Growth 58, 163.Google Scholar
Kerr, R. C.: 1984 Crystallisation and compositional convection in geological fluid mechanics. Ph.D. thesis, Cambridge University.
Krishnamurti, R.: 1970 On the transition to turbulent convection. J. Fluid Mech. 42, 295.Google Scholar
Kurz, W. & Fisher, D. J., 1986 Fundamentals of Solidification. Trans Tech Publishers.
Langer, J. S.: 1980 Instabilities and pattern formation in crystal growth. Rev. Mod. Phys. 52, 1.Google Scholar
Leitch, A. M.: 1985 Laboratory models of magma chambers. Ph.D. thesis, A. N. U., Canberra, Australia.
Linden, P. F. & Shirtcliffe, T. G. L. 1978 The diffusive interface in double-diffusive convection. J. Fluid Mech. 87, 417.Google Scholar
McBirney, A. R. & Noyes, R. M., 1979 Crystallisation and layering of the Skaergaard intrusion. J. Petrol. 20, 487.Google Scholar
Mollard, F. R. & Flemings, M. C., 1967 Growth of composites from the melt, Parts I and II, Trans. Met., AIME 239, 1526 and 1534.Google Scholar
Mullins, W. W. & Sekerka, R. F., 1964 Stability of a planar interface during the solidification of a binary alloy. J. Appl. Phys. 35, 444.Google Scholar
Turner, J. S.: 1979 Buoyancy Effects in Fluids. Cambridge University Press.
Turner, J. S., Huppert, H. E. & Sparks, R. S. J. 1986 Komatiites II – experimental and theoretical investigations of post emplacement cooling and crystallisation. J. Petrol. 27, 397.Google Scholar
Weast, Q. C. (ed.) 1971 Handbook of Chemistry and Physics. Cleveland: C. R. C.
Worster, M. G.: 1983 Convective flow problems in geological fluid mechanics. Ph.D. thesis, Cambridge University.
Worster, M. G.: 1986 Solidification of an alloy from a cooled boundary. J. Fluid Mech. 167, 481.Google Scholar