Infiltrations in Immiscible Fluids Systems

In this paper we prove a certain regularity property of configurations of immiscible fluids, filling a bounded container Ω and locally minimizing the interface energy ∑ i<j cij‖Sij‖, where Sij represents the interface between fluid i and fluid j, ‖ · ‖ stands for area or more general areatype functional, and cij is a positive coefficient. More precisely, we show that, under strict triangularity of the cij ’s, no infiltrations of other fluids are allowed between two main ones. A remarkable consequence of this fact is the almost-everywhere regularity of the interfaces. Our analysis is performed in general dimension n ≥ 2 and with volume constraints on fluids.