A non-equilibrium state diagram for liquid/fluid/particle mixtures.

The equilibrium structures of ternary oil/water/surfactant systems are often represented within a triangular composition diagram with various regions of the triangle corresponding to different equilibrium states. We transplant this idea to ternary liquid/fluid/particle systems that are far from equilibrium. Liquid/liquid/particle mixtures or liquid/gas/particle mixtures yield a wide diversity of morphologies including Pickering emulsions, bijels, pendular aggregates, spherical agglomerates, capillary suspensions, liquid marbles, powdered liquids, and particle-stabilized foams. This paper argues that such ternary liquid/fluid/particle mixtures can be unified into a non-equilibrium state diagram. What is common among all these systems is that the morphology results from an interplay between the preferential wettability of the particles, capillarity, and viscous forces encountered during mixing. Therefore all such systems share certain universal features, regardless of the details of the particles or fluids used. These features guide the construction of a non-equilibrium state diagram which takes the form of a triangular prism, where each triangular cross-section of the prism corresponds to a different relative affinity of the particles towards the two fluids. We classify the prism into regions in which the various morphologies appear and also emphasize the major difference between systems in which the particles are fully-wetted by one of the fluids vs. partially-wetted by both fluids. We also discuss how the state diagram may change with mixing intensity or with interparticle attractions.