  In this contribution, we introduce a versatile formalism to derive unified
two-phase models describing both the separated and disperse regimes. It relies
on the stationary action principle and interface geometric variables. The main
ideas are introduced on a simplified case where all the scales and phases have
the same velocity and that does not take into account large-scale capillary
forces. The derivation tools yield a proper mathematical framework through
hyperbolicity and signed entropy evolution. The formalism encompasses a
hierarchy of small-scale reduced-order models based on a statistical
description at a mesoscopic kinetic level and is naturally able to include the
description of a disperse phase with polydispersity in size. This hierarchy
includes both a cloud of spherical droplets and non-spherical droplets
experiencing a dynamical behaviour through incompressible oscillations. The
associated small-scale variables are moments of a number density function
resulting from the Geometric Method Of Moments (GeoMOM). This method selects
moments as small-scale geometric variables compatible with the structure and
dynamics of the interface; they are defined independently of the flow topology
and, therefore, this model pursues the goal of unifying the modelling of a
fully-coupled two-scale flow. It is particularly showed that the resulting
dynamics provides closures for the interface area density equation obtained
from the averaging approach. The extension to mass transfer from one scale to
the other including capillary phenomena, as well as the extension to multiple
velocities are possible and proposed in complementary works.
