Pressure in the Landau-Ginzburg functional: Pascal’s law, nucleation in fluid mixtures, a meanfield theory of amphiphilic action, and interface wetting in glassy liquids

We set up the problem of finding the transition state for phase nucleation in multi-component fluid mixtures, within the Landau-Ginzburg density functional. We establish an expression for the coordinate-dependent local pressure that applies to mixtures, arbitrary geometries, and certain non-equilibrium configurations. The expression allows one to explicitly evaluate the pressure in spherical geometry, a la van der Waals. Pascal’s law is recovered within the Landau-Ginzburg density functional theory, formally analogously to how conservation of energy is recovered in the Lagrangian formulation of mechanics. We establish proper boundary conditions for certain singular functional forms of the bulk free energy density that allow one to obtain droplet solutions with thick walls in essentially closed form. The hydrodynamic modes responsible for mixing near the interface are explicitly identified in the treatment; the composition at the interface is found to depend only weakly on the droplet size. Next we develop...