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Stochastic convective transport in presence of fragmented dendrites in a solidifying binary melt

  • S. Ganguly (a1) and S. Chakraborty (a1)

Abstract

A comprehensive integrated model of stochastic convective transport in a solidifying binary melt is presented in this work. The detailed transport phenomena in the particle and bulk phases are coupled together through a stochastic Eulerian-Lagrangian formalism, capturing the physical mechanisms and consequences of particle agglomeration, de-agglomeration, and the underlying hydrodynamic interactions. The interactions between random thermo-fluidic fluctuations in the continuum carrier phase and the associated growth/dissolution of particle phases are modeled by employing a Langevin formalism. Representative case studies highlighting the implications of the dynamics of the fragmented dendrites on the overall convective patterns in an electromagnetically-stirred semi-solid binary melt are subsequently presented, so as to emphasize on the comprehensive physical bases and to illustrate the fundamental approach of the present predictive methodology.

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[1] Young, G.W., Davis, S.H., Phys. Rev. B 34, 3388 (1986)
[2] Turner, J., Huppert, H.E., Sparks, R., J. Petrol. 27, 397 (1986)
[3] Thompson, M.E., Szekely, Y.J., J. Fluid Mech. 187, 409 (1988)
[4] Huppert, H.E., J. Fluid Mech. 212, 209 (1990)
[5] Li, Q., Beckermann, C., Phys. Rev. E 57, 3176 (1998)
[6] Kumar, P., Chakraborty, S., Srinivasan, K., Dutta, P., Metall. Mater. Trans. B 34, 899 (2003)
[7] Tsiveriotis, K., Brown, R.A., Phys. Rev. B 48, 13495 (1993)
[8] M.C. Flemings, Solidification Processing (McGraw-Hill, New York, 1974)
[9] Flemings, M.C., Metall. Trans. A 22, 957 (1991)
[10] Batchelor, G.K., J. Fluid Mech. 52, 245 (1972)
[11] Sasikumar, R., Kumar, M., Acta Metall. Mater. 39, 2503 (1991)
[12] Hadji, L., Phys. Rev. E 65, 022201 (2002)
[13] Chakraborty, S., Kumar, A., Phys. Rev. Lett. 95, 024504 (2005)
[14] Bennon, W.D., Incropera, F.P., Int. J. Heat Mass Transfer 30, 2161 (1987)
[15] D. Gidaspow, Appl. Mech. Rev.39, 1 (1986)
[16] Happel, J., AIChE. J. 4, 197 (1958)
[17] Karma, A., Phys. Rev. Lett. 70, 3439 (1993)
[18] Han, Q., Hunt, J.D., J. Crystal Growth 140, 398 (1994)
[19] Maxey, M.R., Riley, J.J., Phys. Fluids 26, 883 (1983)
[20] Bafaluy, J., Senger, B., Voegel, J.C., Schaaf, P., Phys. Rev. Lett. 70, 623 (1993)
[21] Wojtaszczyk, P., Avalos, J.B., Phys. Rev. Lett. 80, 754 (1998)
[22] Yamakawa, H., J. Chem. Phys. 53, 436 (1970)
[23] Hur, J.S., Shaqfeh, E.S.G., Larson, R.G., J. Rheol. 44, 713 (2000)
[24] Jendrejack, R.M., Schwartz, D.C., Pablo, J.J.de, Graham, M.D., J. Chem. Phys. 120, 2513 (2004)
[25] Koke, J., Modigell, M., J. Non-Newtonian Fluid. Mech. 112, 141 (2003)
[26] Petera, J., Kotynia, M., Int. J. Heat Mass Transfer 47, 1483 (2004)
[27] Gautham, B.P., Kapur, P.C., Mater. Sci. Eng. 393, 223 (2005)
[28] Higashitani, K., Ogawa, R., Hosokawa, G., Matsuno, Y., J. Chem. Eng. Jap. 15, 299 (1982)
[29] Van Dongen, P.G.J., Ernst, M.H., J. Stat. Phys. 37, 301 (1984)
[30] M. Elimelech, J. Gregory, X. Jia, R.A. Williams, Particle Deposition and Aggregation, Measurement, Modelling and Simulation (Butterworth-Heinemann, Woburn, 1995)
[31] N.A. Fuchs, The Mechanics of Aerosols (Pergamon, New York, 1964)
[32] Klett, J.D., Davis, M.H., J. Atmos. Sci. 30, 107 (1973)
[33] Kusters, K.A., Wijers, J.G., Thoenes, D., Chem. Eng. Sci. 52, 107 (1997)
[34] Selomulya, C., Bushell, G., Amal, R., Waite, T.D., Chem. Eng. Sci. 58, 327 (2003)
[35] Pandya, J.D., Spielman, L.A., Chem. Eng. Sci. 38, 1983 (1983)
[36] J.C. Flesch, P.T. Spicer, S.E. Pratsinis, AIChE. J. 45, 1114 (1999)
[37] Meakin, P., Phys. Rev. A 27, 1495 (1983)
[38] Mandelbrot, B.B., Passoja, D.E., Paullay, A.J., Nature 308, 721 (1984)
[39] Li, J. M., Lu, L., Su, Y., Lai, M.O., J. Appl. Phys. 86, 2526 (1999)
[40] K.J. Falconer, The Geometry of Fractal Sets (Cambridge University Press, Cambridge, 1986)
[41] Einstein, A., Ann. Phys. 19, 289 (1906)
[42] P.E. Kloeden, E. Platen, Numerical Solution of Stochastic Differential Equations (Springer-Verlag, Berlin, 1999)
[43] S.V. Patankar, Numerical Heat Transfer and Fluid Flow (Hemisphere, Washington, DC, 1980)
[44] Swaminathan, C.R., Voller, V.R., Int. J. Heat Mass Transfer 40, 2859 (1997)
[45] Voller, V.R., Int. J. Heat Mass Transfer 40, 2869 (1997)
[46] Kirkwood, D.H., Int. Mater. Rev. 39, 173 (1994)
[47] Spencer, D.B., Mehrabian, R., Flemings, M.C., Metall. Trans. 3, 1925 (1972)
[48] Y. Ito, M.C. Flemings, J.A.Cornie, in Nature and properties of semisolid Materials, edited by J.A. Sekhar, J.A. Dantzig (TMS, Warrendale, PA, 1991), p. 3

Keywords

Stochastic convective transport in presence of fragmented dendrites in a solidifying binary melt

  • S. Ganguly (a1) and S. Chakraborty (a1)

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