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The present paper proposes a two-phase flow model that is able to account fortwo-scale kinematics and two-scale surface tension effects based on geometricvariables at small scale. At large scale, the flow and the full geometry of theinterface may be retrieved thanks to the bulk variables, while at small scalethe interface is accurately described by volume fraction, interfacial areadensity and mean curvature, called the geometric variables. Our work mainlyrelies on the Least Action Principle. The resulting system is an extension of aprevious work modeling small scale pulsation in which surface tension was nottaken into account at large or small scale. Whereas the original derivationassumes a cloud of monodispersed spherical bubbles, the present context allowsfor polydispersed, non-spherical bubbles. The resulting system of equationssolely involves small scale geometric variables, thus contributing in theconstruction of a unified model describing both large and small scales.

Derivation of a two-phase flow model with two-scale kinematics, geometric variables and surface tension using variational calculus