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A mushy-zone rayleigh number to describe interdendritic convection during directional solidification of hypoeutectic Pb-Sb and Pb-Sn alloys

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Abstract

Based on measurements of the specific dendrite surface area (S v), fraction of interdendritic liquid (φ), and primary dendrite spacing (λ 1) on transverse sections in a range of directionally solidified hypoeutectic Pb-Sb and Pb-Sn alloys that were grown at thermal gradients varying from 10 to 197 K cm−1 and growth speeds ranging from 2 to 157 µm s−1, it is observed that S v=λ 1 −1 S*−0.33 (3.38−3.29 φ+8.85 φ 2), where S*=D l Geff/V m 1 C o (k−1)/k, with D l being the solutal diffusivity in the melt, G eff being the effective thermal gradient, V being the growth speed, m l being the liquidus slope, C o being the solute content of the melt, and k being the solute partition coefficient. Use of this relationship in defining the mushy-zone permeability yields an analytical Rayleigh number that can be used to describe the extent of interdendritic convection during directional solidification. An increasing Rayleigh number shows a strong correlation with the experimentally observed reduction in the primary dendrite spacing as compared with those predicted theoretically in the absence of convection.

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Authors and Affiliations

  1. the Chemical and Biomedical Engineering Department, Cleveland State University, 44115, Cleveland, OH

    S. N. Tewari (Professor) & R. Tiwari (Graduate Student)

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  1. S. N. Tewari
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  2. R. Tiwari
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Tewari, S.N., Tiwari, R. A mushy-zone rayleigh number to describe interdendritic convection during directional solidification of hypoeutectic Pb-Sb and Pb-Sn alloys. Metall Mater Trans A 34, 2365–2376 (2003). https://doi.org/10.1007/s11661-003-0299-2

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  • DOI: https://doi.org/10.1007/s11661-003-0299-2

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