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In this work, we investigate an original strategy in order to derive astatistical modeling of the interface in gas-liquid two-phase flows throughgeometrical variables. The con- tribution is two-fold. First it participates inthe theoretical design of a unified reduced- order model for the description oftwo regimes: a disperse phase in a carrier fluid and two separated phases. Thefirst idea is to propose a statistical description of the in- terface relyingon geometrical properties such as the mean and Gauss curvatures and define aSurface Density Function (SDF). The second main idea consists in using such aformalism in the disperse case, where a clear link is proposed between localstatistics of the interface and the statistics on objects, such as the numberdensity function in Williams-Boltzmann equation for droplets. This makesessential the use of topolog- ical invariants in geometry through theGauss-Bonnet formula and allows to include the works conducted on sprays ofspherical droplets. It yields a statistical treatment of populations ofnon-spherical objects such as ligaments, as long as they are home- omorphic toa sphere. Second, it provides an original angle and algorithm in order to buildstatistics from DNS data of interfacial flows. From the theoretical approach,we identify a kernel for the spatial averaging of geometrical quantitiespreserving the topological invariants. Coupled to a new algorithm for theevaluation of curvatures and surface that preserves these invariants, weanalyze two sets of DNS results conducted with the ARCHER code from CORIA withand without topological changes and assess the approach.

Statistical modeling of the gas-liquid interface using geometrical variables: toward a unified description of the disperse and separated phase flows