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In this work we explore means for modeling fluid flows that involve a liquid and a gas separated by an interface that exhibits variations across different space scales. More specifically we will consider that the interface can transition between two topology regimes. In some regions the interface can be described at the bulk scale (separate phase regime). In other regions, it will take the form of extremely small droplets so that accounting for their shape at the bulk scale is not reasonnable (disperse phase) and that require a dedicated microscopic modeling. We will examine how the Hamilton Stationary Action Principle and the second law of thermodynamics can be used as valuable tools for developing such models, particularly for describing mass transfer from the large scale to the small scales of interface.
