Liquid droplet migration under static and dynamic conditions: Analytical model, phase-field simulation and experiment

An analytical model describing liquid droplet and dendrite arm migration due to temperature gradient zone melting (TGZM) is derived rigorously for both static and dynamic conditions. For the dynamic case of TGZM with superimposed directional solidification, criteria for critical pulling velocity and critical droplet position are proposed, which yield constant relative droplet positions with respect to the liquidus and solidus. With a pulling velocity lower or higher than the critical pulling velocity, the droplet migrates through the liquidus isotherm into the bulk liquid, or through the solidus isotherm into the entirely solid region, respectively. For a given pulling velocity, the droplets located above the critical position move into the bulk liquid, while the others sink into the bulk solid. The model is quantitatively validated by phase-field simulations for succinonitrile-acetone alloys and compared with experimental results using time-averaged dendrite arm migrating velocities. An excellent match of the models and reasonable agreement between the model predictions and the experiment are obtained.