Basic concepts of phase-field theory: two-phase

• Fundamentals of phase-field theory
  • Free energy functional with \(\phi\) and double-wells
  • Euler-Lagrange equation and chemical potential
  • Fundamental solution of Euler-Lagrange equation
  • Alternative forms of double-wells
  • Properties of equilibrium solutions
  • Bibliography
  • Appendices
• Time-evolution: Cahn-Hilliard and Allen-Cahn models
  • Cahn-Hilliard (CH) model for conservative order parameter
  • Allen-Cahn model for non-conservative order parameter
  • Conservative Allen-Cahn (CAC) model
• Model of incompressible Navier-Stokes with interface-capturing equation
  • Bulk and local densities
  • Mass balance
  • Incompressible two-phase flows without phase change
  • Bibliography
• 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
• Thermodynamics of phase transition (to be written)
  • Common tangent construction
  • Droplet growth
  • Ostwald ripening
  • Models of phase change