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 counter-intuitively 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 non-trivial 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 to specifically control the speed of droplets or capsules in microchannels, based on their rheological properties.

The adhesion of two surfaces relies on the propagation of an adhesion front. What is the dynamics of the front when both surfaces are coated with a thin layer of viscous liquid? Standard criteria from fingering instabilities would predict a stable front since viscous fluid pushes away air of low viscosity. Surprisingly, the front propagation may be unstable and generally leads to growing fingers. We demonstrate with model experiments where the two adhering surfaces are slightly tilted by an angle $\alpha$ that the origin of this interfacial instability relies on feeding the front from the surrounding thin film. We show experimentally that the typical wavelength of the instability is mainly dictated by the thickness of the oil layers $h$ . In this wedge geometry, the propagation dynamics is found to follow a $t^{1/2}$ dependence and to saturate for an extension length of the order of $h/\alpha$ .