Hostname: page-component-7f64f4797f-l842n Total loading time: 0 Render date: 2025-11-04T05:47:23.729Z Has data issue: false hasContentIssue false
  • English
  • Français

Convective instability in ammonium chloride solution directionally solidified from below

Published online by Cambridge University Press:  26 April 2006

Falin Chen ,
Jay W. Lu  and
Tsung L. Yang
Falin Chen
Affiliation:
Institute of Applied Mechanics, National Taiwan University, Taipei, Taiwan 10764, ROC
Jay W. Lu
Affiliation:
Institute of Applied Mechanics, National Taiwan University, Taipei, Taiwan 10764, ROC
Tsung L. Yang
Affiliation:
Institute of Applied Mechanics, National Taiwan University, Taipei, Taiwan 10764, ROC
Get access Rights & Permissions [Opens in a new window]

Abstract

The stabilities of salt-finger and plume convection, two major flows characterizing the fluid dynamics of NH4Cl solutions cooling from below, are investigated by theoretical and experimental approaches. A linear stability analysis is implemented to study theoretically the onset of salt-finger convection. Special emphasis is placed on the competition between different instability modes. It is found that in most of the cases considered, the neutral curve consists of two separated monotonic branches with a Hopf bifurcation branch in between; the right-hand monotonic branch corresponding to the boundary-layer-mode convection is more unstable than the left-hand monotonic branch corresponding to the mushy-layer mode. We also conducted a series of experiments covering wide ranges of bulk fluid concentration C∞ and bottom temperature TB to study the stability characteristics of plume convection. From the measurement of both temperature and concentration of the interstitial fluid in the mushy layer, we verify that during the progress of solidification the melt in the mush is in a thermodynamic equilibrium state except at the melt/mush interface where most of the solidification occurs. The critical Rayleigh number of the onset of plume convection is found to be Rccm = 1.1 × 107Π* (see (22)), where Π* is the permeability of the mush. This relation is believed to be valid up to supereutectic NH4Cl solutions.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 276 , 10 October 1994 , pp. 163 - 187
Copyright
© 1994 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.)

Article purchase

Temporarily unavailable

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.Google Scholar
Chen, C. F. & Chen, F. 1991 Experimental study of directional solidification of aqueous ammonium chloride solution. J. Fluid Mech. 227, 567.Google Scholar
Chen, F., Yang, T. L. & Lu, J. W. 1993 Influence of convection on crystallization of directionally solidified binary solutions. J. Appl. Phys. 74, 7531.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.Google Scholar
Coriell, S. R., Cordes, M. R., Boettinger, W. J. & Sekerka, R. F. 1980 Convective and interfacial instability during unidirectional solidification of binary alloy. J. Cryst. Growth 49, 13.Google Scholar
Fowler, A. G. 1985 The formation of freckles in binary alloys. IMA J. Appl. Maths 35, 159.Google Scholar
Head, M. J. 1983 The use of miniature four-electrode conductivity probes for high resolution measurement of turbulent density or temperature variations in salt-stratified water flows. PhD dissertation, University of California, San Diego.
Huppert, H. E. 1990 The fluid mechanics of solidification. J. Fluid Mech. 212, 209.Google 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.Google Scholar
Keller, H. B. 1976 Numerical Solutions of Two Point Boundary Value Problems. SIAM.
Kerr, R. C., Woods, A. W., Worster, M. G. & Huppert, H. E. 1990 Solidification of an alloy cooled from above. Part 1. Equilibrium growth. J. Fluid Mech. 216, 323.Google Scholar
Powell, M. J. D. 1970 Numerical Methods for Nonlinear Algebraic Equations (ed. P. H. Rabinowitz). Gordon & Breach.
Rasenat, S., Busse, F. H. & Rehberg, I. 1989 A theoretical and experimental study of double-layer convection. J. Fluid Mech. 199, 519.Google Scholar
Sample, A. K. & Hellawell, A. 1984 The mechanism of formation and prevention of channel segregation during alloy solidification. Metall. Trans. 15A, 2163.Google Scholar
Tait, S., Jahrling, K. & Jaupart, C. 1992 The planform of compositional convection and chimney formation in a mushy layer. Nature 359, 406.Google Scholar
Tait, S. & Jaupart, C. 1989 Compositional convection in viscous melts. Nature 338, 571.Google Scholar
Tait, S. & Jaupart, C. 1992 Compositional convection in a reactive crystalline mush and melt differentiation. J. Geophys. Res. 97, 6735.Google Scholar
Worster, M. G. 1992 Instabilities of the liquid and mushy regions during solidification of alloys. J. Fluid Mech. 237, 649.Google Scholar