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A dynamic model for the interaction between a solid particle and an advancing solid/liquid interface

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Abstract

Most models that describe the interaction of an insoluble particle with an advancing solid-liquid interface are based on the assumption of steady state. However, as demonstrated by experimental work, the process does not reach steady state until the particle is pushed for a while by the interface. In this work, a dynamic mathematical model was developed. The dynamic model demonstrates that this interaction is essentially non-steady state and that steady state eventually occurs only when solidification is conducted at subcritical velocities. The model was tested for three systems: aluminum-zirconia particles, succinonitrile-polystyrene particles, and biphenyl-glass particles. The calculated values for critical velocity of the pushing/engulfment transition were in the same range with the experimental ones.

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References

  1. S.N. Omenyi and A.W. Neumann: J. Appl. Phys., 1976, vol. 47 (9), pp. 3956–62.

    Article  CAS  Google Scholar 

  2. A.A. Chernov, D.E. Temkin, and A.M. Mel’nikova: Sov. Phys. Crystallogr., 1977, vol. 22 (6), pp. 656–58.

    Google Scholar 

  3. A.A. Chernov, D.E. Temkin, and A.M. Mel’nikova: Sov. Phys. Crystallogr., 1976, vol. 21 (4), pp. 369–73.

    Google Scholar 

  4. G.F. Bolling and J.A. Cissé: J. Cryst. Growth, 1971, vol. 10, pp. 56–66.

    Article  CAS  Google Scholar 

  5. C. Korber G. Rau, M.D. Causman, and E.G. Cravalho: J. Cryst. Growth, 1985, vol. 72, pp. 649–62.

    Article  CAS  Google Scholar 

  6. J. Pötschke and V. Rogge: J. Cryst. Growth, 1989, vol. 94, pp. 726–38.

    Article  Google Scholar 

  7. D.K. Shangguan, S. Ahuja, and D.M. Stefanescu: Metall. Trans. A, 1992, vol. 23A, pp. 669–80.

    CAS  Google Scholar 

  8. R. Sasikumar, T.R. Ramamohan, and B.C. Pai: Acta Metall., 1989, vol. 37 (7), pp. 2085–91.

    Article  Google Scholar 

  9. L. Hadgi: Phys. Rev. E, 1999, vol. 60 (5), pp 6180–83

    Article  Google Scholar 

  10. C. Schvezov: in Solidification 1999, W.H. Hofmeister, J.R. Rogers, N.B. Singh, S.P. Marsh, and P.W. Vorhees, eds., TMS, Warrendale, PA, 1999, pp. 251–61

    Google Scholar 

  11. A.V. Catalina and D.M. Stefanescu: in Solidification 1999, W.H. Hofmeister, J.R. Rogers, N.B. Singh, S.P. Marsh, and P.W. Vorhees, eds., TMS, Warrendale, PA, 1999, pp. 273–82.

    Google Scholar 

  12. S. Sen, B.K. Dhindaw, D.M. Stefanescu, A.V. Catalina, and P.A. Curreri: J. Cryst. Growth, 1997, vol. 173, pp. 574–84.

    Article  CAS  Google Scholar 

  13. A. Cotrell: Introduction to the Modern Theory of Metals, The Institute of Metals, London, 1988.

    Google Scholar 

  14. D.R. Uhlmann, B. Chalmers, and K.A. Jackson: J. Appl. Phys., 1964, vol. 35, pp. 2986–93.

    Article  CAS  Google Scholar 

  15. J. Happel and H. Brenner: Low Reynolds Number Hydrodynamics, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1965.

    Google Scholar 

  16. H. Brenner: Chem. Eng. Sci., 1961, vol. 16, pp. 242–51.

    Article  CAS  Google Scholar 

  17. L.G. Leal: Laminar Flow and Convective Transport Processes—Scaling Principles and Asymptotic Analysis, Butterworth-Heinemann, London, 1992.

    Google Scholar 

  18. D.M. Stefanescu, F.R. Juretzko, B.K. Dhindaw, A.V. Catalina, S. Sen, and P.A. Curreri: Metall. Mater. Trans. A, 1998, vol. 29A, pp. 1697–1706.

    Article  CAS  Google Scholar 

  19. D.M. Stefanescu, F.R. Juretzko, B.K. Dhindaw, S. Sen, and P.A. Curreri: NASA Microgravity Materials Science Conf., D.C. Gillies and D.E. McCauley, eds., NASA Marshall Space Flight Center, Huntsville, AL, 1999, p. 599.

    Google Scholar 

  20. A.V. Catalina: Ph.D. Dissertation, University of Alabama, Tuscaloosa, AL, Apr. 2000.

    Google Scholar 

  21. A.V. Catalina and D.M. Stefanescu: Modeling of Casting & Solidification Processes, 1999, C.P. Hong, J.K. Choi and D.H. Kim eds., Hanrimwon, Seoul, Korea, 2000, pp. 3–11.

    Google Scholar 

  22. J.O. Hinze: Turbulence, Mc-Graw-Hill, New York, NY, 1975, p. 463.

    Google Scholar 

  23. R.J. Brodkey: The Phenomena of Fluid Motions, Addison-Wesley, Reading, MA, 1967, p. 621.

    Google Scholar 

  24. J. Szekely: Fluid Flow Phenomena in Metal Processing, Academic Press, New York, NY, 1979, pp. 260–64.

    Google Scholar 

  25. J. Klein and E. Kumacheva: Science, 1995, vol. 269, pp. 816–19.

    Article  CAS  Google Scholar 

  26. J. Klein and E. Kumacheva: J. Chem. Phys., 1998, vol. 108 (16), pp. 6996–7009.

    Article  CAS  Google Scholar 

  27. T. Iida and R.I.L. Guthrie: The Physical Properties of Liquid Metals, Clarendon Press, Oxford, United Kingdom, 1988, p. 27.

    Google Scholar 

  28. K.A. Hoffmann and S.T. Chiang: Computational Fluid Dynamics for Engineers, Engineering Education SystemTN, Wichita, KS, 1993, vol. 1.

    Google Scholar 

  29. H. Lamb: Hydrodynamics, 6th ed., Cambridge University Press, Cambridge, MA, 1932.

    Google Scholar 

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Catalina, A.V., Mukherjee, S. & Stefanescu, D. A dynamic model for the interaction between a solid particle and an advancing solid/liquid interface. Metall Mater Trans A 31, 2559–2568 (2000). https://doi.org/10.1007/s11661-000-0200-5

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