Blas Echebarria
Universitat Politècnica de Catalunya
 

We study directional solidification of dilute binary alloys by means of a phase-field formulation. Recently, phase-field models have become an important tool to simulate interfacial pattern formation in solidification and other systems. It avoids the problem of tracking of the interface through the introduction of an order parameter, or phase-field $\phi$, which varies
smoothly from one value in the liquid to another in the solid across an interfacial region. However, the resulting equations are stiff, due to the disparity of scales between the interface thickness and the diffusion length.
We use a recently derived phase-field model, whose thin interface limit yields a much less stringent restriction on the choice of interface thickness than previous formulations and permits to eliminate non-equilibrium effects at the interface. This allows us to make quantitative comparisons with experiments for realistic values of the physical parameters. We will use this formulation to study the onset of sidebranching and the cell to dendrite transition in directional solidification. We find that besides noise induced  sidebranches, there is also an oscillatory branch where sidebranches exist even in the absence of noise.