The unstable and expanding interface between reacting liquids: theoretical interpretation of negative surface tension

When a chemical reaction between two immiscible liquids creates surfactant molecules at the interface between them, the interfacial surface tension decreases with increasing amount of surfactant. In particular, an interfacial reaction that is faster than the time scale of system's equilibration can cause a marked increase in the interfacial area due to the surface tension becoming effectively negative. Under these highly nonequilibrium conditions, the interface roughens and develops a variety of interfacial structures ranging from "ripples" to micelle-like formations; in systems of droplets, this process can lead to cycles of droplet elongation and self-division into smaller progenies. In the present work, the emergence and implications of negative surface tension over a "reactive" interface are studied theoretically and using computer simulations. The onset of interfacial instabilities can be described analytically using the methods of linear stability analysis of the continuum theory. For longer times, Molecular Dynamics simulations are implemented which reproduce the formation and increase of interfacial "ripples" at the initial stage, when the interface is a monolayer of surfactant, and widening of the reactive/mixing layer at later times.