One might expect dense suspensions to form droplets in much the same way as highly viscous fluids. Although this sounds intuitive, Marc Miskin and Heinrich Jaeger would argue otherwise, having assembled evidence to suggest that the particles in a suspension bring about strikingly different behaviour — tantamount to a new class of topological transition (Proc. Natl Acad. Sci. USA http://doi.org/hq9; 2012).

Experimenting with suspensions of varying density and viscosity, Miskin and Jaeger showed that the rate of detachment scaled with the radius of the neck of the forming droplet. Whereas high viscosity fluids are expected to exhibit linear scaling, the suspensions they tested showed sublinear scaling. Changing the experimental conditions, such as packing fraction and nozzle size, did little to recover the linear scaling — the exponent remained the same.

Credit: © TURBO/CORBIS

The first clue to what might be happening came when high-speed imaging revealed deformations in the surface of the neck. The authors noted that immediately before break-up, the thinning suspension was reduced to just two particles connected by a liquid stream. These observations prompted them to develop a new description for the process, based on the forces associated with the microscopic surface deformations.

The model incorporates the fact that the curvature of the neck's surface accommodates variations in packing — providing a built-in feedback mechanism between packing and pressure. This corroborates the picture suggested by high-speed imaging, and makes sense of experimental evidence downplaying the importance of viscous stresses on the observed scaling behaviour.

One of the more remarkable outcomes of the model is the prediction that droplets form as they would in pure, inviscid liquid when the particle size approaches that of the nozzle — rather than the opposite limit, in which the suspension more closely resembles a homogeneous fluid. This surprising prediction is borne out in Miskin and Jaeger's measurements. The particles create a pressure that matches the pressure in a pure liquid only when the mean curvature of their menisci approaches that of the forming droplet.

In this way, particle size shows up in the system as an intrinsic length scale that in turn encodes a memory of its initial conditions. This memory effect rules out the idea that suspension droplets are formed through a self-similar scaling mechanism — in stark contrast to the case for pure liquids — meaning that theories relying on the analogy do away with crucial details of what goes on near the nozzle tip.