Free surface flows

Splash formation after disc impact

Side view of a disc impacting on a water surface. On the bottom left a rim is formed but remains intact, on the right this rim destabilizes and ejects droplets as a result of a higher impact speed.

Jumping in a pool and landing flat on your belly can be a painful experience. The image above shows a controlled experiment of this phenomenon, where we pull a circular disc down at a constant speed. Just before the disc hits the water surface, there is a layer of air that needs to be pushed away. In a perfectly symmetric system, the peak force is actually experienced before there is contact between the disc and the water surface. This has a big influence on the initial state of the splash wave and sets an initial length scale for the rim that is formed and thereby also influences the size of the ejected droplets.

[1] I.R. Peters, D. van der Meer and J.M. Gordillo, Splash wave and crown breakup after disc impact on a liquid surface, J. Fluid Mech. 724, 553-580 (2013) [pdf]

Non-axisymmetric cavity collapse

Underwater view of a collapsing cavity with a mode-20 perturbation.

The impact of a perfectly circular disc on a water surface results in a cylindrical cavity that – in a two-dimensional horizontal plane – collapses towards a single point. This is an example of a finite-time singularity, where properties such as velocities and pressures diverge. But what happens if there is a small perturbation on top of this circular geometry? Will such a perturbation amplify itself, or will it die out? In the case of a collapsing cavity, such a perturbation will keep its absolute amplitude, while at the same time oscillates with a frequency that diverges towards the moment of pinch-off. This can result in fascinating free-surface shapes as shown in the figure above.

[1]O.R. Enríquez, I.R. Peters, S. Gekle, L.E. Schmidt, D. Lohse and D. van der Meer, Collapse and pinch-off of a non-axisymmetric impact-created air cavity in water, J. Fluid Mech. 701, 40-58 (2012) [pdf]
[2] O.R. Enríquez, I.R. Peters, S. Gekle, L.E. Schmidt, D. van der Meer and D. Lohse, Non-axisymmetric impact creates pineapple-shaped cavity, Phys. Fluids 23, 091106 (2011) [pdf]
[3] O.R. Enríquez, I.R. Peters, S. Gekle, L.E. Schmidt, M. Versluis, D. van der Meer and D. Lohse, Collapse of non-axisymmetric cavities, Phys. Fluids 22, 091104 (2010) [pdf]

Air flow in a collapsing cavity

Air flow in a collapsing cavity, visualised using smoke and a laser sheet shining into the cavity from above.

When you throw a stone into a pond, you can hear a very distinct “plomp” sound. The larger the stone, the lower the frequency of this sound. This sound is created by the bubble that is entrained by the stone. The bubble is entrained because the surface cavity closes roughly halfway, as shown in the image above where we created such a cavity using a circular disc. During this collapse, air is pushed out of this cavity. Using surface tracking techniques, direct visualisation of the airflow using smoke and a laser sheet, and numerical simulations, we have shown that just before the pinch-off compressibility of the air starts to play an important role. Even more surprising: for a short moment, the air inside the cavity can reach supersonic speeds!

[1] I.R. Peters, S. Gekle, D. Lohse, and D. van der Meer, Air flow in a collapsing cavity, Phys. Fluids 25, 032104 (2013) [pdf]
[2] S. Gekle, I.R. Peters, J.M. Gordillo, D. van der Meer, and D. Lohse, Supersonic air flow due to solid-liquid impact, Phys. Rev. Lett. 104, 024501 (2010) [pdf]

Dynamic contact lines

A small millimetre-sized droplet of silicone oil sliding down an inclined plane (sliding from top to bottom in this image). As the drop slides faster, its tail forms a sharp corner from which eventually droplets pinch-off.

Look outside your window on a rainy day, and you’ll see a lot of droplets sitting on the glass surface with a range of different shapes. The shape of a rain droplet on a window depends on its size and wetting properties. What is a bit more difficult to see is the shape of the droplets that are not sitting still but are sliding down. Especially the rear part of these droplets can change in shape a lot, from nicely round to very pointy, depending on the speed at which it is sliding. As the sliding speed increases further, the droplet starts to pinch-off small droplets at its tail.

[1] K.G. Winkels, I.R. Peters, F. Evangelista, M. Riepen, A. Daerr, L. Limat, and J.H. Snoeijer, Receding contact lines: from sliding drops to immersion lithography, Eur. Phys. J. Special Topics 192, 195–205 (2011) [pdf]
[2] I.R. Peters, J.H. Snoeijer, A. Daerr, and L. Limat, Coexistence of Two Singularities in Dewetting Flows: Regularizing the Corner Tip, Phys. Rev. Lett. 103, 114501 (2009) [pdf]