Multiscale Modeling of Particle-Solidification Front Dynamics, Part 3: Theoretical Aspects and Parametric Study (Preprint)

The development of the solidified microstructure in metal-matrix composites depends on complex interactions between non-planar solidification fronts and multiple particles. The problem is multiscale in nature; the motion of the particle (under the action of a nano-scale disjoining pressure force and a micro-scale viscous drag force) is dynamically coupled with the developing solidification front morphology, which is dependent on a variety of thermal conditions. Using computational techniques discussed in parts I and II, this paper seeks to describe the complicated nonlinear parametric dependencies of the phenomenon. The effects of four of the most important parameters in the particle-solidification front interaction are investigated, i.e. the Hamaker constant, the particle size, the thermal conductivity ratio of the particle to the melt, and the solid-liquid interfacial free energy. By performing simulations using the multiscale approach the dependencies of the critical velocity on these four parameters is clarified. Submitted for publication in the International Journal of Heat and Mass Transfer. Prepared in collaboration with Falk Corporation, Milwaukee, WI, and The University of Iowa, Iowa City, IA.