How to create the perfect beer tornado
Bottles can usually be emptied more quickly if they are moved in a circular motion. However, researchers have now shown that a higher rotational speed is not always better.
If you want to empty a bottle as quickly as possible, a so-called tornado helps: you move the bottle in a circular motion until the liquid rotates and a vortex forms inside it. If the bottle opening then points downwards, air penetrates and reaches the surface of the liquid through the centre of the vortex, allowing it to drain quickly. This phenomenon is well known in everyday life, but there have been hardly any scientific studies on it to date. A team led by physicist Aurore Caquas from the Université Paris-Saclay has now changed this. In laboratory experiments, the research group has investigated how water tanks can be emptied as quickly as possible. As she reports in the journal "Physical Review Fluids", there is an optimum rotational speed for cylindrical vessels that produces a perfect tornado.
Instead of experimenting with beer bottles, the experts filled a cylindrical Plexiglas tank about 40 centimetres high with a diameter of 29 centimetres with water and placed it on a rotating platform. They worked with two tank openings of different sizes: one with a diameter of just under 1.3 centimetres and the other with a diameter of around 2 centimetres.
During the tornado experiments, the liquid inside the tank exhibited a more complicated behaviour than expected. Depending on the amount of liquid, the diameter of the outlet and the rotational speed, Caquas and her team found three different states. At low rotational speeds, a "glug-glug regime" initially develops: Individual air bubbles first enter the opening of the tank before the liquid drains out. At higher speeds, an unstable vortex forms at some point - a kind of tornado, but it is not strong enough to allow the air to flow from the tank opening to the water surface in the long term. This only becomes possible at even higher rotational speeds in the third phase, when the tornado stabilises and then resembles a vortex over the drain of a bathtub.
As it turns out, the duration of the three different states depends heavily on the shape of the vessel, the amount of liquid and the speed of rotation. This means that depending on how fast a bottle is rotated, the transitions between the glug-glug, unstable and stable tornado phases can take a long time under certain circumstances. Although a very high rotational speed causes the water to flow out extremely quickly in the stable tornado regime, the rapid rotation also extends the service life of the unstable regime. In extreme cases, this can extend the time it takes to empty the vessel so much that the process is faster without any rotation at all (i.e. in the pure glug-glug phase).
As the physicists discovered, there is an optimum rotation speed at which the lifetimes of the first two phases are quite short and at the same time the stable tornado is so well formed that the water flows out quickly. At this speed, the time required to empty the tank is minimised. For the working group's special test setup, the optimum rotation speed (depending on the size of the outlet) was around three to four revolutions per minute. However, if it exceeded eight revolutions per minute, the tank emptied more slowly than when it was stationary.
As the shape of the tested tank - as well as the contents - differs from a beer bottle, the result cannot be transferred one-to-one to the everyday example. In order to calculate the optimum rotation speed for a beer tornado, it would be necessary to analyse the different bottle shapes - and the possible effects of carbon dioxide in the liquid. However, the same is most likely true here: faster rotation does not necessarily lead to a better result.
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