Infiltrations in immiscible fluids systems

Abstract

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<jc_ij‖S_ij‖, where S_ij represents the interface between fluid i and fluid j, ‖·‖ stands for area or more general area-type functional, and c_ij is a positive coefficient. More precisely, we show that, under strict triangularity of the c_ij, 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.