Basic concepts of phase-field theory: two-phase

Fundamentals of phase-field theory

• Principe de moindre action
  • Action \(\mathscr{S}\) et Lagrangien \(\mathcal{L}\)
  • Principe de stationnarité et dérivée variationnelle
  • Équations d’Euler-Lagrange
  • Application: loi du mouvement de Newton
• 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
  • Common tangent for a flat interface
  • Properties of equilibrium solutions
  • Appendices
  • References

Dynamics: time-evolution

• 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
  • References

Coupling with incompressible Navier-Stokes

• Derivation of incompressible Navier-Stokes with interface-capturing equation model
  • Mass balance & interface equation
  • Derivation of constitutive laws
  • Model of incompressible Navier-Stokes with interface-capturing equation
  • Appendix: details for deriving constitutive laws
  • References

Contact angle

• Contact angle
  • Law of Young-Dupré
  • Boundary condition for diffuse interface
  • References