Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science
Based on measurements of the specific dendrite surface area (S-nu), fraction of interdendritic liquid (phi), and primary dendrite spacing (lambda(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 mum s(-1), it is observed that S-nu = lambda(1)(-1) S*(-0.33) (3.38 - 3.29 phi + 8.85 phi(2)), where S* = D-l G(eff)/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.
Tewari, Surendra N. and Tiwari, R., "A Mushy-Zone Rayleigh Number to Describe Interdendritic Convection During Directional Solidification of Hypoeutectic Pb-Sb and Pb-Sn Alloys" (2003). Chemical & Biomedical Engineering Faculty Publications. 1.
Tewari, S.N., & Tiwari, R. (2003). A Mushy-Zone Rayleigh Number to Describe Interdendritic Convection During Directional Solidification of Hypoeutectic Pb-Sb and Pb-Sn Alloys. Metallurgical and Materials Transactions A: Physical Metallurgy and Materials Science 34A, 2365-2376
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