Journal of Crystal Growth 267 (2004) 724–737 Drag on a particle being pushed by a solidiﬁcation front and its dependence on thermal conductivities J.W. Garvin, H.S. Udaykumar* Department of Mechanical and Industrial Engineering, The University of Iowa, 3026 Seamans Center, Iowa City, IA 52242-1527, USA Received 8 May 2003; accepted 1 March 2004 Communicated by J.J. Derby Abstract A particle approached by an advancing solidiﬁcation front may be set in motion under the inﬂuence of forces that act across the narrow gap between it and the advancing solidiﬁcation front. This particle motion induces a drag that promotes engulfment of the particle in the advancing solidifying medium. This drag force experienced by a particle being steadily pushed by a solidiﬁcation front is studied numerically. A sharp-interface method is used to track both the phase boundary and the particle. The method employed in this paper allows for inclusion of the effects of thermal property differences between the particle and the melt. The dependency of the drag on the thermal conductivity ratio of the particle to the melt, as well as on the thickness of the thin gap between the solidifying interface and the particle, is examined. The results of the present calculations are compared with those of previous analyses. It is shown that previously used expressions for the drag on a particle may not correctly account for the effects of thermal conductivity of the particle. r 2004 Elsevier B.V. All rights reserved. PACS: 02.60.Cb; 02.70.c Keywords: A1. Computer simulation; A1. Directional solidiﬁcation; A1. Drag; A1. Particle; A1. Solidiﬁcation; A1. Thermal conductivity 1. Introduction Particle-solidiﬁcation front interactions are im- portant in the growth of crystals from melts containing inclusions or reinforcements. The latter situation arises for instance in casting or direc- tional solidiﬁcation of metal-matrix composite structural components. The interaction between the embedded particle and the front determines the microstructural and hence strength properties of the solidiﬁed material. When a particle is ap- proached by an advancing solidiﬁcation front, the fate of the particle is determined by the forces that the solid and melt impose on the particle [1–13]. ARTICLE IN PRESS *Corresponding author. Tel.: +1-319-384-0832; fax: +1- 319-335-5669. E-mail address: hs-kumar@uiowa.edu (H.S. Udaykumar). 0022-0248/$-see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2004.03.074