Soft Matter, Hard Rules: When Emulsions Flow Just Like Sand

What is it about?

Think about spreading mayonnaise on bread. Is it a solid or a liquid? The answer depends on how much pressure you put on the knife and how densely the droplets of oil are packed inside the egg yolk suspension. “Mayo" is just one of many examples of emulsions, including cosmetic creams, ice cream, and butter, in which we know from every day experiences that their flow is surprisingly difficult to predict. At first sight, emulsions seem very different from sand: their droplets are liquid and can deform, whereas sand grains are rough and rigid. Yet, our study shows that dense emulsions follow remarkably similar flow laws to granular suspensions, albeit with much smaller friction (resistance to motion). The key to unifying these disparate systems is pressure. We developed a new kind of rheometer, the “Capillarytron", that allows us to directly control the osmotic pressure on the droplets. Increasing pressure deforms the spherical droplets and allows them to slide past each other at progressively higher packing densities, shifting the point at which emulsion jam up and behave like solids. Once this pressure-dependent jamming point is accounted for, measurements made at different droplet densities and flow rates all collapse onto the same underlying rheological laws. In other words, the apparent complexity of emulsion rheology can largely be understood through a simple idea: pressure moves jamming, while the underlying flow laws remain the same even way beyond the jamming point.

Featured Image

Photo by Sara Cervera on Unsplash

Photo by Sara Cervera on Unsplash

Why is it important?

For decades, the flow of materials such as emulsions, foams and other soft amorphous materials has often been described using empirical laws. One of the most famous is the Herschel–Bulkley law, which relates the stress needed to make a material flow to how fast it is flowing. Although this law works remarkably well, its parameters have often lacked a clear physical interpretation. Our results provide a different perspective. They show that the rheology of emulsions can be understood using the same underlying framework as granular suspensions, with droplet softness entering primarily through a pressure-dependent jamming point. This gives a physical interpretation to the parameters appearing in conventional rheological laws and provides a unified description from weakly compressed, Newtonian emulsions to highly compressed, yielding materials. More broadly, the result suggests that the distinction between “granular” and “soft” materials may be less fundamental than it first appears. Sand grains, droplets and potentially other deformable particles can follow the same collective rules; what changes is how pressure modifies the point at which the material jams. This perspective could provide a useful framework for understanding other densely packed soft materials, including foams and, potentially, biological tissues, where cells can also deform, rearrange and undergo rigidity transitions.

Perspectives