Derivation of a two‐phase flow model accounting for surface tension

Abstract This paper presents the derivation of a two‐phase flow model that incorporates surface tension effects using Hamilton's principle of stationary action. The Lagrangian functional, which defines the action consists of kinetic energy–accounting for interface characteristics–and potential energy. A key feature of the model is the assumption that the interface separating the two phases possesses its own internal energy, which satisfies a Gibbs form that includes both surface tension and interfacial area. Consequently, surface tension is considered in both the kinetic and potential energy terms that define the Lagrangian functional. By applying the stationary action principle, a set of partial differential equations (PDEs) governing the dynamics of the two‐phase flow is derived. This includes evolution equations for the volume fraction and interfacial area, incorporating mechanical relaxation terms. The final model is proven to be well‐posed, demonstrating hyperbolicity and satisfying Lax entropy conditions.