Author: Arthur Loison, Samuel Kokh, Marc Massot and Teddy Pichard We aim at modelling two-phase flows in regimes including both polydisperse sprays of droplets and separated flows. The typical configuration we have in mind in the injection at high pressure of a liquid into a surrounding gas, such that this liquid atomizes into thin droplets. Such a multi-scale flow is modelled through an Hamiltonian process with an energy combining both the small-scale and large-scale contributions through different variables. In this contribution, I will focus on the small scale description, that is the modelling of the droplets through a geometric method of moments, and the exchange of mass through the scales.