Sliding drops
with Bruno Andreotti, Jens Eggers, Nolwenn Le Grand, Laurent Limat, Ivo Peters, Emmanuelle Rio, Jacco Snoeijer, Howard Stone, Koen Winkels, …
These images show the in-plane velocity field of tracer particles moving near the surface of drops sliding down an incline (here towards the right hand side). The left picture shows an oval drop at low inclinations, seen from above, and the right picture a drop at higher velocities, displaying a cusp at the rear. Note that in both cases the velocity field on the drop perimeter is normal to the contact line. This means that the relevant wetting speed (front half) or dewetting speed (rear half), which selects the contact angle, is given by the projection of the global drop velocity onto the contact line normal (Rio et al., PRL 2005).
The video above shows a drop of silicon oil sliding at low speed down a fluor-polymer coated substrate. The left hand side shows the drop from above, the right hand side a lateral view perpendicular to the direction of motion. The side-view includes a reflection of the drop in the substrate, which causes the view to be right-left symmetric. Note that although the side view shows a small increase in the advancing contact angle, together with a decrease in the receding contact angle, the shape of the drop as seen from above remains close to that of a static drop.
At slightly higher speed the rear of the drop becomes conical, and a transverse curvature gradient replaces the usual longitudinal gradient as the capillary driving force of the flow. This flow has a self-similar structure (Limat et al 2004, Le Grand et al 2005, Snoeijer et al 2005). The cone apex is still rounded at a scale that depends on velocity, but is directly and surprisingly linked to a microscopic length scale, interpreted as a hydrodynamic cut-off length (e.g. slip length) (Peters et al 2009, Winkels et al 2011, Snoeijer et al 2011).
The video above shows a drop running at a speed slightly above its dynamical wetting transition, where the cusped tail starts leaving a trail of small droplets behind. The mass of the drop does not significantly change over time however, as it simultaneously collects the droplets left on its track by its predecessor. The appearance of the corner/cusp (near-)singularity at the rear and the pearling transition is a consequence of diverging viscous stresses in the vicinity of the contact line.
The following PhD theses (in french) contain detailed descriptions of our experiments:
Last modified: 30 Jan 2016