# Leonardo da Vinci wondered why not all bubbles rise straight up. Now there is an answer

The hardest questions are often the easiest to ask. But five centuries later, the bubble problem appears to have been largely solved.

Joost van Egmond

Anyone with a fish tank has probably noticed. Otherwise, you may have seen it in your kettle or in a glass of soda. Bubbles don’t always go straight. But why not? Why do irregular bubbles zigzag to the surface of the liquid?

Some have also referred to this issue as Leonardo’s paradox, after the artist and inventor Leonardo da Vinci, who was interested in it already in the 16th century. He noted that it was a matter of size; Big bubbles make that winding path, and smaller bubbles go straight up.

Miguel Herrada and Jens Eggers, from the Universities of Seville and Bristol respectively, have managed to pinpoint an exact figure for this: the zigzag effect occurs when the radius of a bubble is more than 0.926 mm. And most importantly, they can discuss what is happening, They write in the magazine PNAS.

Of this size, the bubble becomes unstable during ascent. It deforms a bit, so the bubble curve will be steeper on one side than the other. This steeply curved side rises a little faster and starts interacting with the liquid. Then it flows more quickly after the bubble, so that the pressure drops slightly and the bubble expands on that side. This causes it to return to its original straight upward trajectory, after which the mechanism starts up again.

### Why is the bubble so complex

As simple as it may seem, it was not for the calculation. The authors agree that the bullish bubble is a very difficult field to study. The mathematical theory of how a bubble moves can seldom agree with experimental observations, especially in water. This is partly because the viscosity of water is very low, which means that the effects it has on the bubble are very subtle.

Above all, interaction is what makes it complicated; The forces exerted by the water cause the bubble to change shape, which affects the flow of water, which changes the shape of the bubble again, and so on until the bubble reaches the surface somewhere. All of this is hard to put into a model. Not to mention the skew you get if there is anything in the water that disrupts the bubble’s pure path.

This unpredictability also has its advantages. Bubbles are regularly used to generate random numbers that are used to secure Internet connections or to make computer games less predictable.

So both scientists are quick to stress that their model has its limitations. It applies to “ultrapure” water, and was also used in a series of experiments in the 1990s that produced a working model of smaller bubbles. Even then, Hirada and Eggers noted a small deviation, though less than 2 percent. For true bubble purists, a bit of a mystery remains.