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In this contribution, we derive a gas-liquid two-scale multi-fluid model withcapillarity effects along with a novel interface regularization approach. Weintroduce this unified modelling capable of encompassing the interfacerepresentation of both separated and disperse regimes, as it occurs inatomization processes. Above a preset length threshold at large scale, amulti-fluid diffuse interface model resolves the dynamics of the interfacewhile, at smallscale, a set of geometric variables is used to characterize theinterface geometry. These variables result from a reduced-order modelling ofthe small-scale kinetic equation that describes a collection of liquidinclusions. The flow model can be viewed as a two-phase two-scale mixture, andthe equations of motion are obtained thanks to the Hamilton's Stationary ActionPrinciple, which requires to specify the kinetic and potential energies atplay. We particularly focus on modelling the effects of capillarity on themixture's energy by including dependencies on additional variables accountingfor the interface's geometry at both scales. The regularization of thelargescale interface is then introduced as a local and dissipative process. Thelocal curvature is limited via a relaxation toward a modified Laplaceequilibrium such that an inter-scale mass transfer is triggered when the meancurvature is too high. We propose an original numerical method and assess theproperties and potential of the modelling strategy on the relevant test-case ofa two-dimensional liquid column in a compressible gas flow.

A unified two-scale gas-liquid multi-fluid model with capillarity and interface regularization through a mass transfer between scales