Droplet Size Distribution in Emulsions.

The droplet size in emulsions is known to affect the rheological properties and plays a crucial role in many applications of emulsions. Despite its importance, the underlying mechanisms governing droplet size in emulsification remain poorly understood. We investigate the average drop size and size distribution upon emulsification with a high-shear mixer for model oil-in-water emulsions stabilized by a surfactant. The size distribution is found to be a log-normal distribution resulting from the repetitive random breakup of drops. High-shear emulsification, the usual way of making emulsions, is therefore found to be very different from turbulent emulsification given by the Kolmogorov-Hinze theory, for which power-law distributions of the drop size are expected. In agreement with this, the mean droplet size does not follow a scaling with the Reynolds number of the emulsification flow but rather a capillary number scaling based on the viscosity of the continuous phase.

Motion of Viscous Droplets in Rough Confinement: Paradoxical Lubrication.

We study the sedimentation of highly viscous droplets confined inside Hele-Shaw cells with textured walls of controlled topography. In contrast with common observations on superhydrophobic surfaces, roughness tends here to significantly increase viscous friction, thus substantially decreasing the droplets mobility. However, reducing confinement induces a jump in the velocity as droplets can slide on a lubricating layer of the surrounding fluid thicker than the roughness features. We demonstrate that increasing the viscosity of the surrounding liquid may counterintuitively enhance the mobility of a droplet sliding along a rough wall. Similarly, a sharp change of the droplet mobility is observed as the amplitude of the roughness is modified. These results illustrate the nontrivial friction processes at the scale of the roughness, and the coupling between viscous dissipation in the drop, in the front meniscus, and in the lubricating film. They could enable one to specifically control the speed of droplets or capsules in microchannels, based on their rheological properties.