Phase field modeling with large interface thickness and undercooling

• A new formulation of phase field model for large interface thickness and undercooling.
• The Gibbs–Thomson equation satisfied easier with more weighting from the hyperbolic tangent profile of the phase field variable.
• One-dimensional isothermal and non-isothermal examples with different interface thicknesses and weighting factors.
• Curvature-driven growth with different interface thickness.
• Simple proof for the role of weighting factor in the new formulation.

The interface thickness is the most crucial parameter in the phase field model (PFM) for the accuracy and the computability. However, the Gibbs–Thomson equation can be satisfied only when the interface thickness is sufficiently small, especially with a large undercooling, but this greatly limits the applications of PFM to a realistic problem. The temperature correction in the thin-interface model partially resolves the problem, but the range is rather limited. In this report, we propose a new formulation of PFM by adding extra terms stabilizing the hyperbolic tangent profile of the phase-field, and this allows us to use a much larger interface thickness for simulation, even with a large undercooling. Several benchmark comparisons with analytical solutions are carried out and discussed.