Jie Liao, Phase Field Model for Solidification with Boundary Interface Interaction, IFSL Volume 9, International Frontier Science Letters (Volume 9)
https://www.scipress.com/IFSL.9.1
Abstract:
    By incorporation the surface free energy in the free energy functional, a phase field model for solidification with boundary interface intersection is developed. In this model, the bulk equation is appropriately modified to account for the presence of heat diffusion inside the diffuse interface, and a relaxation boundary condition for the phase field variable is introduced to balance the interface energy and boundary surface energy in the multiphase contact region. The asymptotic analysis is applied on the phase field model to yield the free interface problem with dynamic contact point condition.
Keywords:
    Boundary Interface Interaction, Dynamic Contact Angle, Phase Field Model