Derivation of a two-phase flow model with two-scale kinematics and surface tension by means of variational calculus

International audienceThe present paper proposes a definition of a two-phase interface that relies on a probability density function. This definition enables to introduce a scale separation in the definition this interface and to define fields that characterize the geometry of the interface. Relying on these fields, we propose a two-phase flow model that is able to account for small and large scale separation of the interface description by means of supplementary convected geometric variables. The model accounts for two-scale kinematics and two-scale surface tension. At large scale, the flow and the full geometry of the interface may be retrieved thanks to the bulk variables and the volume fraction, while at small scale the interface dynamics is accurately recovered through the interfacial area density fluctuation and the mean curvature