An analytical solution of the critical interface velocity for the encapturing of insoluble particles by a moving solid/liquid interface

An analytical model for the particle pushing phenomenon that occurs between spherical particles and advancing curved solid/liquid interfaces during solidification of pure melts is presented. An expression for the critical interface velocity for encapturing particles by moving solid/liquid interfaces has been developed for the steady-state condition. As a first step, the actual shape of the interface behind the particle is computed in terms of the thermal conductivity ratio of the particle to that of the melt and the temperature gradient ahead of the interface; based on assumed subject, the critical interface velocity is calculated using the force balance between the attractive forces and repulsive forces acting on the particle. The critical interface velocity under steady-state conditions in aluminum containing SIC particle (10 mu m) comes out to be 5800 mu m/s according to the present model; this calculated velocity is much closer to the experimental observations of Wu et al., as compared to the predictions of the models proposed by earlier workers.