Numerical method determining the time-dependent position of a minority phase sphere in the Fe-Cu alloy droplet

A numerical method was developed to track the dynamic positions of the L2 phase sphere inside the Fe-Cu alloy droplet. Firstly, the temperature field distribution within alloy droplet was calculated, and the variation in thermal gradient was analyzed. Secondly, the migration behavior of the sphere was analyzed based on Marangoni convection. Finally, the theoretical position of the 10 μm sphere was determined. The results demonstrated that there is a little difference in temperature between the center and the surface of the droplet, but its gradient is very different. Moreover, the maximum migration times for the L2 phase sphere were determined to be ~0.02 s, 0.07 s, and 0.14 s within 300μm, 600μm, and 900μm alloy droplets, respectively. In addition, it was also found that the same-sized spheres can reach the same relative position, i.e., 0.485R. This means the final position of the sphere within the different alloy droplets is independent of the droplet size.