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Steady-state solidification of aqueous ammonium chloride

Published online by Cambridge University Press:  06 March 2008

S. S. L. PEPPIN ,
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
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
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Abstract

We report on a series of experiments in which a Hele-Shaw cell containing aqueous solutions of NH4Cl was translated at prescribed rates through a steady temperature gradient. The salt formed the primary solid phase of a mushy layer as the solution solidified, with the salt-depleted residual fluid driving buoyancy-driven convection and the development of chimneys in the mushy layer. Depending on the operating conditions, several morphological transitions occurred. A regime diagram is presented quantifying these transitions as a function of freezing rate and the initial concentration of the solution. In general, for a given concentration, increasing the freezing rate caused the steady-state system to change from a convecting mushy layer with chimneys to a non-convecting mushy layer below a relatively quiescent liquid, and then to a much thinner mushy layer separated from the liquid by a region of active secondary nucleation. At higher initial concentrations the second of these states did not occur. At lower concentrations, but still above the eutectic, the mushy layer disappeared. A simple mathematical model of the system is developed which compares well with the experimental measurements of the intermediate, non-convecting state and serves as a benchmark against which to understand some of the effects of convection. Movies are available with the online version of the paper.

JFM classification

Convection: Convection in porous media
Type
Papers
Information
Journal of Fluid Mechanics , Volume 599 , 25 March 2008 , pp. 465 - 476
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Anderson, D. M. & Worster, M. G. 1996 A new oscillatory instability in a mushy layer during the solidification of binary alloys. J. Fluid Mech. 307, 245–267.CrossRefGoogle Scholar
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
Chen, C. F. 1995 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. M. 1970 The origin of freckles in unidirectionally solidified castings. Metall. Trans. 1, 2193–2204.CrossRefGoogle Scholar
Davis, S. H. 2001 Theory of Solidification. Cambridge University Press.CrossRefGoogle Scholar
Emms, P. & Fowler, A. C. 1994 Compositional convection and freckle formation in the solidification of binary alloys. J. Fluid Mech. 262, 111–139.CrossRefGoogle Scholar
Flood, S. C. & Hunt, J. D. 1998 Columnar to equiaxed transition. ASM Handbook 15, 130–136.Google Scholar
Fowler, A. C. 1985 The formation of freckles in binary alloys. IMA J. Appl. Maths 35, 159–174.CrossRefGoogle Scholar
Guba, P. & Worster, M. G. 2006 Nonlinear oscillatory convection in mushy layers. J. Fluid Mech. 553, 419–443.CrossRefGoogle Scholar
Hellawell, A., Liu, S. & Lu, S. Z. 1997 Dendrite fragmentation and the effects of fluid flow in castings. JOM-J. Min. Met. Mat. Soc. 49, 18–20.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., Sparks, R. S. J., Wilson, J. R. & Hallworth, M. A. 1993 Cooling and crystallization at an inclined plate. Earth Planet. Sci. Lett. 79, 319–328.CrossRefGoogle Scholar
Huppert, H. E. & Worster, M. G. 1985 Dynamic solidification of a binary melt. Nature 314, 703–707.CrossRefGoogle Scholar
Jackson, K. A., Hunt, J. D., Uhlmann, D. R. & Seward, T. P. 1966 On the origin of the equiaxed zone in castings. Trans. Metall. Soc. AIME 236, 149–158.Google Scholar
Kear, B. H. 1986 Advanced metals. Sci. Am. 255, 159–167.CrossRefGoogle Scholar
Kerr, R. C., Woods, A. W., Worster, M. G. & Huppert, H. E. 1990 Solidification of an alloy cooled from above. Part II: nonequilibrium interfacial kinetics. J. Fluid Mech. 217, 331–348.CrossRefGoogle Scholar
Kurz, W. & Fisher, D. J. 1989 Fundamentals of Solidification, 3rd Edn. Aedermannsdorf: Trans Tech. Publications.Google Scholar
Loper, D. E. & Roberts, P. H. 2001 Mush-chimney convection. Stud. Appl. Maths 106, 187–227.CrossRefGoogle Scholar
Martorano, M. A., Beckermann, C. & Gandin, Ch.-A. 2003 A solutal interaction mechanism for the columnar-to-equiaxed transition in alloy solidification. Metall. Mater. Trans. A 34, 1657–1674.CrossRefGoogle Scholar
McDonald, R. J. & Hunt, J. D. 1970 Convective fluid motion within the interdendritic liquid of a casting. Metall. Trans. 1, 1787–1788.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
Ni, J. & Incropera, F. P. 1995 Extension of the continuum model for transport phenomena occurring during metal alloy solidification – I. The conservation equations. Intl J. Heat Mass Transfer 38, 1271–1296.CrossRefGoogle 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
Press, W. H., Teukolsky, S. A., Vetterling, W. T., & Flannery, B. P. 1992 Numerical Recipes in C, 2nd Edn. Cambridge University Press.Google Scholar
Roberts, P. H. & Loper, D. E. 1983 Towards a theory of the structure and evolution of a dendrite layer. In Stellar and Planetary Magnetism (ed. Soward, A. M.), pp. 329–349. Gordon & Breach.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., Jahrling, K. & Jaupart, C. 1992 The planform of compositional convection and chimney formation in a mushy layer. Nature 359, 406–408.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.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. 1997 Convection in mushy layers. J. Fluid Mech. 29, 91–122.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

Peppin et al. supplementary material

Movie 1.  The time-lapse movie shows the solidification of a 23 wt% solution of aqueous NH4Cl. The pulling speed is initially 2 microns per second (point b in figure 4) and the mushy layer is relatively uniform. Eventually the speed is decreased to 0.5 microns per second (point a in figure 4) and several chimneys form. Plumes of buoyant fluid can be seen emanating from the chimneys. The speed is then increased back to 2 microns per second and the chimneys disappear. The entire movie represents 1 hour and 10 minutes of real time. The width of the Hele-Shaw cell is 12 centimetres.

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Video 2.7 MB

Peppin et al. supplementary material

Movie 2.  In this movie a 25 wt% NH4Cl solution is being translated at 6 microns per second (point c in figure 4). Secondary crystals can be seen in the supercooled melt above the mushy layer. The entire time-lapse movie represents 1 hour and 10 minutes of real time.

Download Peppin et al. supplementary material(Video)
Video 1.3 MB

Peppin et al. supplementary material

Movie 3.  This movie illustrates the disappearance of the mushy layer during the solidification of a 21 wt% solution translated at 1 micron per second (point d in figure 4). Although the initial concentration was above the eutectic concentration of 19.7 wt% the growing solid is the pure composite eutectic and no mushy layer appeared. The entire time-lapse movie represents 1 hour and 40 minutes of real time. The gradations on the ruler at the left are in millimetres.

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Peppin et al. supplementary material

Movie 4.  This final movie shows a 'breathing mode' which occurred during the solidification of a 23 wt% solution. This system has the same initial concentration as in movie 1, but the pulling speed is intermediate between the speeds used there. Here the pulling speed is 1 micron per second, which is near to the chimney-extinction boundary (figure 4), and the chimneys form and die out and then form again in phase. The entire time-lapse movie represents 12 hours of real time.

Download Peppin et al. supplementary material(Video)
Video 1.7 MB