Sharp interface numerical simulation of directional solidification of binary alloy in the presence of a ceramic particle Yi Yang, J.W. Garvin, H.S. Udaykumar * Department of Mechanical and Industrial Engineering, University of Iowa, Iowa City, IA-52242, United States Received 15 May 2006; received in revised form 10 April 2007 Available online 3 July 2007 Abstract A sharp interface technique is employed to study the interaction of a solid–liquid interface in a solidifying binary alloy with a ceramic particle in the melt. The application targeted is solidification of a metal–matrix composite. A level-set based sharp interface numerical method is used to study the directional solidification process in the presence of the particle. The transport of solute and heat are com- puted. The directional solidification calculations are first validated against stability theory. The Mullins–Sekerka stability spectrum is reproduced with good agreement with the theory. The interaction of the cellular interface with a ceramic particle in the melt is then com- puted. It is shown that, in contrast to the case of a pure material, the ratio of thermal conductivity of the particle to the melt plays no role in determining the front morphology and the result of the particle–front interaction. The diffusion of species controls the evolution of the phase front around the particle. The implications of the results for particle–front interactions in a binary alloy are discussed. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Alloy solidification; Particle–front interactions 1. Introduction Solidification front and particle interaction is very important to applications such as metal–matrix composites (MMCs) processing. Experiments show [1–3] that a particle that is approached by a (planar) solidification front can react in one of the following ways: (1) it may be pushed along with the moving front, (2) it may be engulfed in the front instantaneously, or (3) it may be pushed followed by engulfment. There are different theoretical models, mainly in pure melts, that purport to predict which one of the above three scenarios will occur. An overview of the experimental and theoretical work on front–particle interactions can be found in Asthana and Tewari [1] (see also [2,3]). Most of the theoretical work on front–particle interac- tion has focused on the rather idealized, even contrived sit- uation of the approach of a planar solidification front in a pure material towards a ceramic particle suspended in the melt. Furthermore, in these studies the front solidifies towards the particle at a controlled rate, by means of a directional solidification process. However, in actual cast- ing processes of interest to MMC processing such idealized conditions are unlikely to be met. More realistic scenar- ios include solidification in the presence of pure under- cooled melts or directionally solidified impure materials. In these situations, typically, the solidification front that approaches a particle assumes morphologies that are com- plex in shape, such as dendritic or cellular structures. The- oretical work on non-planar fronts interacting with particles has been lacking. Recently, Yang et al. [4] have computed the interaction of a non-planar solidification front with an embedded ceramic particle. They have shown that during dendrite–particle interactions, the particles will eventually be engulfed by the side branches, a mechanism that will lead to particles being segregated at grain bound- aries in the final solid, rather than being located within the 0017-9310/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2007.04.037 * Corresponding author. Tel.: +1 319 384 0832; fax: +1 319 335 5669. E-mail address: ush@icaen.uiowa.edu (H.S. Udaykumar). www.elsevier.com/locate/ijhmt Available online at www.sciencedirect.com International Journal of Heat and Mass Transfer 51 (2008) 155–168