Model for particle capture by the solid-liquid interface during solidification of metal matrix nanocomposites

Abstract

A sharp-interface model for solidification of nanocomposites with nanoparticle-interface interaction is presented. The main novelty of the work is that the engulfment or non-engulfment of nanoparticles is modelled as a function of the local interface velocity and a particle size-based critical velocity. This is incorporated through a variable partitioning coefficient while solving the nanoparticle conservation equation which is modelled similar to an alloying constituent. The movement of nanoparticles is governed by nanoparticle-interface interaction and by diffusion due to Brownian motion. The model couples a sharp-interface solidification model, species transport model and nanoparticle transport model. Thus, the engulfment and the resultant distribution of nanoparticles in the solidified region can be predicted for different combinations of initial undercooling and nanoparticle size. The effect of accumulated nanoparticles on the solute transport and solidification rate is also included in the model. Results show that the engulfment of smaller nanoparticles is very low resulting in high accumulation near the interface. This results in a high restriction to solute diffusion and solidification. Combined variation of initial undercooling and particle size shows that the average engulfment values for initial undercooling of 0.3, 0.5, and 0.7 are 2.75 %, 7.75 % and 21.50 % for r* = 0.1, 15.5 %, 53.5 %, and 82.5 % for r* = 0.5, and 38.0 %, 77.75 %, and 93.25 % for r* = 0.9. Thus, the engulfment of nanoparticles into the solid improves with increase in nanoparticle size and with the increase in solidification rate.