Inserted: 5 sep 1998
Last Updated: 6 mar 2007
Journal: Arch. Rational Mech. Anal.
Volume: 144 (1998)
We make the connection between the geometric model for capillarity with line tension and the Cahn-Hilliard model for two-phase fluids. To this aim we add to the usual Cahn-Hillierd (or Ginzburg-Landau) energy an additional boundary term given by the integral of a further double-well potential. We show that in certain regimes of the paramters involved the singular limit of these energies lead to a coupled problem of bulk and surface phase transitions, and under certain assumptions agrees with the relaxation of the capillary energy with line tension.
Keywords: Line tension, singular perturbation, surface tension, Cahn-Hilliard model