April 13, 2024

Unsolved for 500 Years: Researchers Crack Leonardo da Vinci’s Paradox

By University of Seville
February 3, 2023

The scientists propose a mechanism for the instability of the bubble trajectory whereby periodic tilting of the bubble changes its curvature, therefore impacting the upward speed and triggering a wobble in the bubbles trajectory, tilting up the side of the bubble whose curvature has actually increased. Then, as the fluid moves faster and the fluid pressure falls around the high-curvature surface area, the pressure imbalance returns the bubble to its initial position, restarting the periodic cycle.
Reference: “Path instability of an air bubble rising in water” by Miguel A. Herrada and Jens G. Eggers, 17 January 2023, Proceedings of the National Academy of Sciences.DOI: 10.1073/ pnas.2216830120.

Five centuries back, Leonardo da Vinci observed air bubbles deviating from a straight path in a zigzag or spiral motion. However, the cause of this routine movement stayed unidentified previously.
Researchers from the universities of Seville and Bristol have actually resolved the secret surrounding the unstable path of an air bubble rising in water.
Professors Miguel Ángel Herrada of the University of Seville and Jens G. Eggers of the University of Bristol have uncovered a system that explains the unpredictable movement of bubbles rising in water. The findings, released in the prominent journal Proceedings of the National Academy of Sciences, could supply insights into the habits of particles that fall between solid and gas states.
Leonardo da Vinci observed 5 centuries ago that air bubbles, if huge enough, occasionally deviate in a zigzag or spiral from a straight-line motion. Nevertheless, no quantitative description of the phenomenon or physical system to discuss this regular movement had ever been found.
Leonardos sketch showing the spiral movement of an ascending bubble (from his manuscript called the Codex Leicester). Credit: Universidad de Sevilla
The authors of this brand-new paper have developed a numerical discretization method to identify specifically the bubbles air-water user interface, which enables them to mimic its motion and explore its stability. Their simulations closely match high-precision measurements of unsteady bubble motion and show that bubbles deviate from a straight trajectory in water when their round radius surpasses 0.926 millimeters, an outcome within 2% of experimental values acquired with ultrapure water in the 90s.