Leonardo da Vinci (Photo: IMAGO, imagebroker)

Scientists have cracked Leonardo da Vinci’s 500-year-old paradox. It can now be explained why air bubbles in water above a certain size do not rise in a straight line.

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Leonardo da Vinci discovered more than five centuries ago that an air bubble rising in water deviates from its straight path to the water surface as soon as it has reached a certain size. The bubble then tends to zigzag or spiral towards the surface. The phenomenon is also called “Leonardo’s paradox”.

So far, the rise of the bubble could not be explained concretely by either a physical mechanism or a quantitative description, although there have been numerous attempts to explain the rise, both experimentally and theoretically.

Leonardo da Vinci is famous for a variety of inventions, his art and his studies of man, which also resulted in the famous depiction of the Vitruvian man. His observation that air bubbles above a certain size in water do not rise straight up has not yet been clarified.


Physical mechanism found that solves “Leonardo’s Paradox”.

Now the researchers Miguel Ángel Herrada from the Spanish University of Seville and Jens G. Eggers from the British University of Bristol have discovered a suitable mechanism. They recently published their findings in the journal PNAS. In their simulation, they take both the flow and the bubble deformation into account.

Determining and calculating the trajectory of rising air bubbles in water represents a numerical and theoretical challenge, because the physical properties of water cause various effects and interactions that affect air bubbles and their flow character.

The size of the bubble causes it to tip

As the researchers describe in the journal, the mechanism is based on the interaction of the flow and bubble deformation. From a sphere radius of 0.926 millimeters, the movement of the bubble changes.

Because the bubble becomes unstable due to its size, the curvature changes, the air bubble deforms and begins to tilt. This affects the path and the speed. The more curved side rises more strongly and a periodic movement occurs. This is because the water pressure around the surface decreases as it rises, so the bladder returns to its original position and the whole thing starts all over again.

Leonardo da Vinci's sketch of the Leonardo Paradox (Photo: Universidad de Sevilla)

Leonardo da Vinci collected his scientific notes, writings and sketches in the Codex Leicester manuscript. He also sketched the spiral movement of an ascending bubble there, as shown in a section here.

University of Seville

Relevant for various industrial and environmental applications

Even if da Vinci’s observation dates back several centuries, it is relevant today. According to the scientists, the bubble movement plays a role in natural phenomena in industry and the environment, such as in oceanography or chemical engineering.

The results could also help science to understand the movement of particles, such as impurities, which behave somewhere between a solid and a gas.

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J. A. Allen

Author, blogger, freelance writer. Hater of spiders. Drinker of wine. Mother of hellions.

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