David Quéré

The aerodynamic wall

We study the trajectory of dense projectiles subjected to gravity and drag at large Reynolds number. We show that two types of trajectories can be observed: if the initial velocity is smaller than the terminal velocity of free fall, we observe the classical Galilean parabola: if it is larger, the projectile decelerates with an asymmetric trajectory first drawn by Tartaglia, which ends with a nearly vertical fall, as if a wall impeded the movement. This regime is often observed in sports, fireworks, watering, etc. and we study its main characteristics.

On the shape of giant soap bubbles

Significance Surface tension dictates the spherical cap shape of small sessile drops, whereas gravity flattens larger drops into millimeter-thick flat puddles. In contrast with drops, soap bubbles remain spherical at much larger sizes. However, we demonstrate experimentally and theoretically that meter-sized bubbles also flatten under their weight, and we compute their shapes. We find that mechanics does not impose a maximum height for large soap bubbles, but, in practice, the physicochemical properties of surfactants limit the access to this self-similar regime where the height grows as the radius to the power 2/3. An exact analogy shows that the shape of giant soap bubbles is nevertheless realized by large inflatable structures. We study the effect of gravity on giant soap bubbles and show that it becomes dominant above the critical size ℓ=a2/e0, where e0 is the mean thickness of the soap film and a=γb/ρg is the capillary length (γb stands for vapor–liquid surface tension, and ρ stands for the liquid density). We first show experimentally that large soap bubbles do not retain a spherical shape but flatten when increasing their size. A theoretical model is then developed to account for this effect, predicting the shape based on mechanical equilibrium. In stark contrast to liquid drops, we show that there is no mechanical limit of the height of giant bubble shapes. In practice, the physicochemical constraints imposed by surfactant molecules limit the access to this large asymptotic domain. However, by an exact analogy, it is shown how the giant bubble shapes can be realized by large inflatable structures.