Dynamics of Mushy Layers on a Finite Domain

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Mushy layers are regions of intermixed liquid and solid which can arise during the solidification of binary alloys, generally consisting of dendritic solids with solute-rich liquid in the interstices. They occur due to an instability resulting from the buildup of rejected solute along the solidification front. Liquid ahead of the front becomes supercooled, so disturbances to the interface grow more rapidly than the interface itself. A simple experiment has a tank filled with a uniform solution at uniform temperature being placed upon a cold surface. Early on, a small solid layer forms at the bottom capped by a rapidly advancing mushy layer. Typical modeling efforts have made at least one of two assumptions, that the tank is of infinite depth or that the diffusion of solute is negligible. This dissertation investigates the finite-domain problem in the presence of solute diffusion, highlighting new interfacial dynamics and other behaviors that arise in this case.