An analytical model for the interaction between an insoluble particle and an advancing solid/liquid interface
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INTRODUCTION
THE particle/interface interaction has been a subject of research over the past three decades, due to its relevance to a wide range of phenomena, including particle distribution in ceramic particulate-reinforced metal matrix composites (MMCs), [~] growth of monotectics, [2,3] inclusion segregation in castings, [41frost heave in soils, [5] and emulsion of organic cell suspensions in ice in cryobiology. [6] In particulate-reinforced MMCs, e.g., A1/SiCp, the particle distribution in the matrix is one of the major microstructural features which determines the properties and performance of the composite material produced either by melt processing (MP) or powder metallurgy (PM). In the melt processing of MMCs, the particle distribution is determined by the various interactions involved in the different phases of processing. These include the incorporation of particles into the metallic melt, particle dispersion and particle-particle interaction in the melt, and the interaction between particles and an advancing solid/ liquid interface during solidification. In an MMC casting, the first two interactions largely determine the macroscopic distribution of particles in the matrix, while the third primarily determines the microscopic particle distribution, i.e., at the level of grains. The particles can be distributed either uniformly or along grain boundaries, the latter being detrimental to the performance of MMCs. This phenomenon has recently aroused further interest in understanding the interaction between particles and the solid/liquid interface, t~,7-m A large number of experimental observations (e.g., References 1, 5, 6, and 8 through 18) have demonstrated that when the interface encounters particles, it can either push them along or engulf them. It has been generally D. SHANGGUAN, formerly Assistant Research Engineer, The University of Alabama, is now Manufacturing Engineer, Electronics Division, Ford Motor Company, Dearborn, MI 48121. S. AHUJA, Graduate Research Assistant, and D.M. STEFANESCU, University Research Professor, are with the Department of Metallurgical and Materials Engineering, The University of Alabama, Tuscaloosa, AL, 35487-0202. Manuscript submitted April 5, 1991. METALLURGICAL TRANSACTIONS A
accepted that there exists a critical velocity for the pushing/engulfment transition of particles by an advancing solid/liquid interface. If the interface velocity is below the critical velocity, the particles will be pushed. On the other hand, if the interface velocity exceeds the critical velocity, the particles will be engulfed. Engulfment will normally lead to uniform distribution of particles, while pushing will result in particle segregation. It is thus of great interest to characterize the critical velocity as a function of material parameters and processing variables and ultimately to control particle distribution in the matrix. Previous studies include experimental measurement of the critical velocity for the pushing/engulfment transition in organic materials, [~2-~6]water, [~2,~6-~8]and me
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