Compressed frictionless emulsions follow the laws of granular rheology

The rheology of particulate materials, from granular slurries to emulsions and foams, has been an active area of study for decades. Building on earlier findings that grains and soft sphere systems obey an analogous granular rheology, we show using an osmotic pressure-controlled rheometer that this framework also extends to frictionless and deformable emulsions. These measurements reveal that the constitutive flow rules follow [$\mu(J), \phi(J)$] relations similar to granular suspensions, but with a compressibility law that describes how the jamming volume fraction increases with pressure owing to droplet deformability. This pressure-imposed framework is validated by quantitatively predicting conventional volume-imposed stress–strain measurements across Newtonian, yielding, and shear-thinning regimes without adjustable parameters. Remarkably, pressure emerges as the key parameter that collapses all rheological data, far above and below jamming, onto a universal curve with a single critical exponent of -2.4. This result implies that the flow of emulsions, from dilute to dense foam-like structures, can be understood within a unified picture. From a microscopic perspective, these results are surprising, but can be rationalized using emulsion properties as inputs into the theory. Our approach gives predictive power to the study of flow in a variety of compressible materials, from adhesive emulsions and foams to biological tissues.