Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-28T07:12:44.795Z Has data issue: false hasContentIssue false
  • English
  • Français

Flow focusing instability in a solidifying mushy layer

Published online by Cambridge University Press:  26 April 2006

A. O. P. Chiareli  and
M. Grae Worster
A. O. P. Chiareli
Affiliation:
Institute of Theoretical Geophysics, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, UK
M. Grae Worster
Affiliation:
Institute of Theoretical Geophysics, 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 stability of the flow of interstitial liquid in a mushy layer driven by expansion or contraction upon solidification is analysed. The full perturbation equations are reduced in a particular aymptotic limit that allows the principal mechanisms controlling instability to be identified. Comparisons are made with the acid-etching instabilities in porous rocks. The full equations are then solved to determine the parametric dependences of the instability. It is found that, though the potential for instability exists, it is unlikely to occur in practice.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 297 , 25 August 1995 , pp. 293 - 305
Copyright
© 1995 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

Amberg, G. & Homsy, G. M. 1993 Nonlinear analysis of buoyant convection in binary solidification with application to channel formation. J. Fluid Mech. 252, 79–98.Google Scholar
Bear, J. 1988 Dynamics of Fluids in Porous Media. Dover.
Chadam, J., Hoff, D., Merino, E., Ortoleva, P. & Sen, A. 1986 Reactive infiltration instabilities. IMA J. Appl. Maths 36, 7–221.Google Scholar
Chen, F, Lu, J. W. & Yang, T. L. 1994 Convective instability in ammonium chloride solution directionally solidified from below. J. Fluid Mech. 276, 163–187.Google Scholar
Chiareli, A. O. P. 1994 Fluid flow and macrosegregation in mushy layers. PhD thesis, Northwestern University.
Chiareli, A. O. P, Huppert, H. E. & Worster, M. G. 1994 Segregation and flow during the solidification of alloys. J. Cryst. Growth. 139, 134–146.Google 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.Google Scholar
Emms, P. W. & Fowler, A. C. 1994 Compositional convection in the solidification of a binary alloy. J. Fluid Mech. 262, 111–139.Google Scholar
Flemings, M. C. 1974 Solidification Processing. McGraw Hill.
Fowler, A. C. 1985 The formation of freckles in binary alloys. IMA J. Appl. Maths 35, 159–174.Google Scholar
Hills, R. N., Loper, D. J. & Roberts, P. H. 1983 A thermodynamically consistent model of a mushy zone. Q. J. Appl. Maths 36, 505–539.Google Scholar
Hinch, E. J. & Bhatt, B. S. 1990 Stability of an acid front moving through porous rock. J. Fluid Mech. 212, 279–288.Google Scholar
Sherwood, J. D. 1987 Stability of a plane reaction front in a porous medium. Chem. Engng Sci. 42, No. 7, 1823-1829.Google Scholar
Tait, S., Jahrling, K. & Jaupart, C. 1992 The planform of compositional convection and chimney formation in a mushy layer. Nature 359, 406–408.Google Scholar
Worster, M. G. 1986 Solidification of an alloy from a cooled boundary. J. Fluid Mech. 167, 481–501.Google Scholar
Worster, M. G. 1991 Natural convection in a mushy layer. J. Fluid Mech. 224, 335–359.Google Scholar
Worster, M. G. 1992a The dynamics of mushy layers. In Interactive Dynamics of Convection and Solidification (ed. S. H. Davis, H. E. Huppert, U. Müller & M. G. Worster). NATO ASI E219, pp. 113–138. Kluwer.
Worster, M. G. 1992b Instabilities of the liquid and mushy regions during solidification of alloys. J. Fluid Mech. 237, 649–669.Google Scholar