École polytechnique: The physics of droplet hurdles race

The 40 centimetre hurdle could be an event in the Micro-Olympic Games, if they existed. It is in fact an experiment conducted in partnership between the Hydrodynamics Laboratory (LadHyX*) and the laboratoire Physique et Mécanique des Milieux Hétérogènes (Physics and Mechanics of Heterogeneous Media Laboratory, PMMH*). A drop placed on a hydrophobic surface – which repels water – moves very easily, reaching speeds of around one metre per second. The aim of this experiment, the results of which have just been published in Applied Physics Letters, is to understand the evolution of this speed when obstacles are placed in the path of the drops.

While naturally hydrophobic materials exist, such as lotus leaves, the 40 cm tracks used here are etched in aluminium and then soaked in a solution containing micrometre-sized silica beads. “After the solvent has evaporated, we obtain a hydrophobic texture on which a drop can be held without spreading, rather like a fakir on a nail board,” describes Hélène de Maleprade (X 2009) who carried out this experiment during her thesis. Small indentations 1 mm high and 1.5 mm wide, spaced 4 to 12 mm apart depending on the track, act as hurdles. Finally, drops are made with a water-glycerol mixture, whose viscosity can be varied, and placed on the starting line. Tilting the track a few degrees launches the race, recorded by a high-speed camera.

“Using scaling laws, we capture the physical ingredients that allow us to account for the observations” explains the scientist. For example, the shocks experienced by the drop against the hurdles as it passes over them are modelled by an overall frictional force that counterbalances the driving effect of gravity. The drops’ speed falls by at least a factor of 10 compared to a flat racetrack. This slowdown is significantly greater than in a previous study where the obstacles were much closer from each other. By increasing the viscosity, the scientists also probed the transition from an “inertial” regime, where shocks dominate the slowdown, to a “viscous” regime, where the liquid drops roll with little or no feel for the obstacles. “Surprisingly, even a drop with a viscosity one hundred times higher than water remains sensitive to the effect of shocks,” emphasises Hélène de Maleprade, now a post-doctoral fellow at the IRPHE in Marseille. Among the potential follow-up experiments, the scientists are wondering how other liquids with viscoelastic properties, or even small solid beads, would behave in such a situation.