A Free Energy Model for Curved Surfaces and Curved Thin Films in Emulsions

ABSTRACT

The formulation of surface thermodynamics for flat surfaces has been done so as to be free of the Gibbs surface construction. The advantage of these formulations is that it allows the choice of thermodynamic field variables that is more general than the traditional construction. However, a generalization to curved surfaces including thin films that exist in emulsion structures has not been published. The Hansen-Cahn construction is developed in a setting that allows curvature terms to be added to the free energy expression. The Laplace equation extended to include bending elasticity and spontaneous bending elasticity is derived by computing functional derivatives of the free energy. Results for both single interfaces and double interfaces are reported. Stability conditions for profile fluctuations are developed to include these additional properties.