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.