  This paper addresses the derivation of a two-phase flow model accounting for
surface tension effects, by means of the Stationary Action Principle (SAP). The
Lagrangian functional, defining the Action, is composed of a kinetic energy,
accounting for interface feature, and a potential energy. The key element of
the model lies on the assumption that the interface separating the two phases
admits its own internal energy, satisfying a Gibbs form including both surface
tension and interfacial area. Thus surface tension is taken into account both
in the potential energy and the kinetic one which define the Lagrangian
functional. Applying the SAP allows to build a set of partial differential
equations modelling the dynamics of the two-phase flow. It includes evolution
equations of the volume fraction and the interfacial area, accounting for
mechanical relaxation terms. The final model is shown to be well posed
(hyperbolicity, Lax entropy).
