Phase-field models for phase transition

Models of solid/liquid phase change

• Model of solidification and crystal growth
  • Useful thermodynamic relations for phase change
  • Solidification of a pure substance and Stefan’s problem
  • Derivation of phase-field model
  • Equivalence between phase-field model and Stefan’s problem
  • Anisotropy function and phase-field model of crystal growth
  • References

Navier-Stokes/Korteweg model

• Isothermal Navier-Stokes/Korteweg model
  • Free energy functional with \(\rho\)
  • van der Waals equation of state and Maxwell construction
  • Free energy density and non-local pressure
  • Maxwell construction for bulk densities \(\rho_l\) and \(\rho_g\)
  • Pressure tensor and Korteweg tensor
  • Mathematical model of van der Waals fluids
  • Bibliography

Mass transfer through interfaces

• Mass transfer through interfaces
  • Gibbs-Thomson condition
  • Ostwald ripening
  • Droplet growth

Incompressible Liquid-Gas phase change

• Incompressible Liquid/gas phase change