Leonardo da Vinci’s mystery of the path of water bubbles solved

Leonardo da Vinci's mystery of the path of water bubbles solved

A pair of scientists have found a mechanism to answer a question asked by Leonardo da Vinci 500 years ago: why do water bubbles not rise in a straight line? The result may lead to a better understanding of particle movements under certain conditions.

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The upward movement of bubbles in water towards the surface is not always a constant straight line. Sometimes they draw zigzag routes, or even a spiral, for no obvious reason.

Since Leonardo da Vinci’s initial observation 5 centuries ago, scientists have yet to obtain a mathematical description of the phenomenon, nor discover the physics behind these apparently chaotic motions.

Now, professors Miguel Ángel Herrada (University of Seville) and Jens G. Eggers (University of Bristol) have published an article with their findings on the mystery. They developed a numerical technique to accurately describe bubbles in hyper-clean water, which allowed them to simulate trajectory instability.

Once mathematically simulated, the phenomenon can be studied, bringing results consonant with high precision measurements of movement and unstable bubble shapes in hyper-clean water. According to the new study, air bubbles in water deviate from the straight line if they have a radius above 0.926 millimeters.

The authors then proposed a mechanism for this instability: the periodic inclination of the bubble alters its curvature, affecting the rate of ascent and causing the bubble trail to oscillate, tilting the side of the bubble upwards.

As the bubble moves faster, the pressure drops around the “surface” where the curvature is most pronounced. The pressure imbalance returns the oscillating bubble to its original position, restarting the cycle.

This answer to a 500-year-old problem could be a step towards a broader understanding of the movement of particles with an intermediate behavior between solid and gas.

The study was published in the Proceedings of the National Academy of Sciences.

Source: PNAS, University of Seville