Non-reciprocal coalescence-breakup dynamics in flowing concentrated emulsions

Dense stabilized emulsions are mixtures of immiscible fluids where the high-volume fraction droplet dispersed phase is stabilized against coalescence by steric interactions. The production of emulsions-a key process in food, cosmetics and chemical industries-involves high-shear flows, elastic and steric interactions, and proceeds thanks to coalescence and breakup of droplets and interfaces. The complex interplay between all these interactions is key in determining both small-scale droplet morphology as well as large-scale emulsion rheology. It is well known that at a critical volume fraction, ϕ_c, the emulsion loses stability, undergoing an extremely rapid process where the fluid components in the emulsion exchange roles. This process, called catastrophic phase inversion, which resembles in several respects a dynamical phase transition, has remained widely elusive from an experimental and theoretical point of view. In this work, we present state-of-the-art experimental and numerical data to support a dynamical-system framework capable of precisely highlighting the dynamics occurring in the system as it approaches the catastrophic phase inversion. Our study clearly highlights that at high volume fractions, the droplet population starts to fluctuate wildly, leading to dramatic changes in the emulsion's rheology and stability. Additionally, we show that at approaching the critical volume fractions, the dynamics can be simplified as being controlled by the evolution of a correlation length represented, in our systems, by the size of the largest droplet. This dynamics shares a close connection with non-reciprocal phase transitions where two different physical mechanisms, coalescences and breakups, can get out of balance leading to large non-symmetric periodic excursions in phase space. We clarify the phenomenology observed and quantitatively explain the essential aspects of the highly complex dynamics of flowing stabilized emulsions undergoing catastrophic phase inversion. More generally, our approach sets the basis for the definition and modeling of a vast number of dynamical phase transitions in hydrodynamic systems out-of-equilibrium where the flow, or other advection mechanisms, can enhance both aggregation and breakup of aggregates.