Particle capture in binary solidification

We examine the interaction of a spherical foreign particle with a propagating solidification front in a binary alloy. Depending on the material properties and the speed of the front, the particle may be pushed ahead of the front, or engulfed and incorporated into the solid phase. We apply numerical boundary integral and continuation methods to determine the critical speed for particle capture, as a function of the system parameters. We reconcile the differing predictions of previous theoretical works, and show that many typical systems may obey a new scaling of the critical speed, as obtained here. We show that due to constitutional undercooling, the presence of solute decreases particle speeds by an order of magnitude below those for a single-component system. We briefly consider the case of spherical bubbles, where thermocapillary and solutocapillary effects play a large role.