Reduced critical solidification front velocity of particle engulfment due to an interface active solute in the liquid me
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2/3 ⭈ sl1/3 a ⭈ R
4/3
冢冣
[1]
with a new algorithm to calculate the value of ⌬ for different metal/ceramic systems. Equation [1] was obtained under the following physical and mathematical simplifications. (1) A single, spherical particle was considered. (2) A planar solidification front was considered far from the particle; however, the curvature of the interface behind the particle was taken into account by comparing the local Laplace pressure and the “disjoining pressure”[2] (in the model, the interfacial and drag forces were described as functions of this local curvature, while the role of the curvature due to the ratio of heat conductivities of the particle and the melt was neglected). (3) The effect of gravity and especially of liquid convection was neglected. (4) The effect of the solutal field was neglected; i.e., Eq. [1] is strictly valid only for pure metals. Equation [1] was found to describe perfectly the experimental results of Stefanescu et al.[3] obtained under microgravity conditions for the Al/ZrO2 system, designed in a way that the previous conditions are satisfied. However, in order to describe the PET event under industrial conditions of producing particle-reinforced MMCs, all of the previous simplifications should be replaced by more realistic conditions. This can be done by introducing correction factors into the expression for the “standard” critical velocity described by Eq. [1]. The goal of the present article is to derive an approximated equation for the critical interface velocity, corrected due to the presence of a solute in the liquid metal. This correction will be based on the equation of Mukai and Lin[4] describing the so-called interfacial gradient force. This equation will be incorporated into the force balance to obtain a corrected equation for the critical velocity of PET. Therefore, conditions (1) through (3) will be kept as previously given; however, condition (4) above will be modified as follows. (a) The presence of an interface active solute in the liquid will be taken into account, with a concentration buildup
G. KAPTAY, Professor and Head, Department of Physical Chemistry, and Dean, Faculty of Materials and Metallurgical Engineering, is with the University of Miskolc, Miskolc, Hungary. Contact e-mail:fkmkap@ gold.uni-miskolc.hu Manuscript submitted September 11, 2001. METALLURGICAL AND MATERIALS TRANSACTIONS A
at the solid-liquid interface due to its distribution coefficient k, leading to its concentration gradient in the liquid, and consequently to an interfacial energy gradient at the particle/liquid interface near the solidification front. (b) The isolines of the interfacial energy are approximately parallel to the solid/liquid interface (Figure 1). (c) The interfacial energy gradient is approximately constant and is determined solely by the concentration gradient of the solute (the effect of the temperature gradient can be neglected[4]). (d) The sum of the front-particle separation (h0) and the diameter of the particle (2R) are much lower than the thickness of t
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