Brownian Motion Effects on the Particle Settling and its Application to Solidification Front in Metal Matrix Composites

Studying the interactions between the reinforcement particles and solidification front of metal-matrix composites (MMCs) and/or metal-matrix nanocomposites (MMNCs) synthesized using solidification processing is essential to understand the particle strengthening mechanism of these materials. Previous models describing such reinforcement particle and solidification front interactions predict that large particles will be engulfed by the solidification front while smaller particles and nanoparticles will be pushed. However, these models cannot explain the evidence in MMNCs produced by solidification processing that nanoparticles can indeed be engulfed and distributed throughout the material and are not necessarily concentrated in grain boundary or interdendritic regions. In this work, an analytical model of particle size effects on the particle settling due to gravity and the pushing/engulfment during solidification is described that accounts for both Stokes’ law and Brownian motion. The model shows a clear transition from Stokesian- to Brownian-dominant behaviors of ultra-fine nano-sized reinforcement particles, which indicates that these fine particles may be engulfed rather than pushed by the solidification front.