  In this contribution, we derive a gas-liquid two-scale multi-fluid model with
capillarity effects along with a novel interface regularization approach. We
introduce this unified modelling capable of encompassing the interface
representation of both separated and disperse regimes, as it occurs in
atomization processes. Above a preset length threshold at large scale, a
multi-fluid diffuse interface model resolves the dynamics of the interface
while, at smallscale, a set of geometric variables is used to characterize the
interface geometry. These variables result from a reduced-order modelling of
the small-scale kinetic equation that describes a collection of liquid
inclusions. The flow model can be viewed as a two-phase two-scale mixture, and
the equations of motion are obtained thanks to the Hamilton's Stationary Action
Principle, which requires to specify the kinetic and potential energies at
play. We particularly focus on modelling the effects of capillarity on the
mixture's energy by including dependencies on additional variables accounting
for the interface's geometry at both scales. The regularization of the
largescale interface is then introduced as a local and dissipative process. The
local curvature is limited via a relaxation toward a modified Laplace
equilibrium such that an inter-scale mass transfer is triggered when the mean
curvature is too high. We propose an original numerical method and assess the
properties and potential of the modelling strategy on the relevant test-case of
a two-dimensional liquid column in a compressible gas flow.
