PART V.C. Phase-field models for phase transition

Liquid/gas phase change with fluid flows

• 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
  • References
• Incompressible Liquid/gas phase change

Models of solid/liquid phase change without fluid flow

• 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
• Dissolution with a grand-potential formulation
  • Sharp interface model of dissolution
  • Grand-potential functional energy
  • Quadratic free energy
  • Equivalent phase-field model
  • References
• Mass transfer through interfaces
  • Gibbs-Thomson condition
  • Ostwald ripening
  • Droplet growth