Leonardo da Vinci’s paradox solved

Leonardo da Vinci observed five centuries ago that air bubbles, if they are large enough, periodically deviate, zigzag or spiral, from moving in a straight line. However, neither a quantitative description of the phenomenon nor a physical mechanism to explain this periodic movement had yet been found.

Now, researchers from the universities of Seville in Spain and Bristol in the United Kingdom have managed to solve this unknown about the instability of the trajectory of an air bubble rising in water.

Miguel Ángel Herrada, a professor at the University of Seville, and Jens Eggers, a professor at the University of Bristol, have discovered a mechanism that explains the unstable movement of bubbles rising in water. According to the researchers, the results may be useful to understand the movement of particles whose behavior is intermediate between a solid and a gas.

The authors of this new study have developed a numerical discretization technique to accurately characterize the air-water interface of the bubble, which allows simulating its movement and studying its stability. Their simulations agree well with high-precision measurements of unstable bubble motion and indicate that bubbles deviate from a straight path in water if their spherical radius exceeds 0.926 millimeters, a result within 2% of experimental values ​​obtained with water. ultrapure in the 1990s.

Sketch drawn by Leonardo illustrating the spiral movement of an ascending bubble (taken from his manuscript known as Codex Leicester). (Photo: University of Seville)

The researchers propose a mechanism for bubble track instability in which periodic tilting of the bubble changes the curvature, affecting rate of ascent and causing a wobble in the bubble track, tilting the upper side upward. of the bubble whose curvature has grown. Then, as the fluid moves faster and the fluid pressure drops around the high curvature surface, the pressure imbalance returns the bubble to its original position, restarting the periodic cycle.

The study is titled “Path instability of an air bubble rising in water”. And it has been published in the academic journal Proceedings of the National Academy of Sciences (PNAS). (Source: University of Seville)