Leonardo da Vinci's paradox of the periodic motion of bubbles cracked

Leonardo da Vinci’s paradox of the periodic motion of bubbles cracked

Leonardo’s sketch showing the spiral motion of an ascending bubble from his manuscript known as the Codex Leicester

Prof. Miguel Ángel Herrada, of the University of Seville, and Prof. Jens G. Eggers, of the University of Bristol, discovered a mechanism to explain the unstable motion of bubbles rising in water. According to the researchers, the results, which are published in the journal PNASit can be useful to understand the motion of particles whose behavior is intermediate between a solid and a gas.

Leonardo da Vinci noticed five centuries ago that air bubbles, if large enough, periodically deviate from straight-line motion in a zigzag or spiral pattern. However, no quantitative description of the phenomenon or physical mechanism to explain this periodic motion has ever been found.

The authors of this new paper developed a numerical discretization technique to precisely characterize the air-water interface of the bubble, which allows them to simulate 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 path in water when their spherical radius exceeds 0.926 millimeters, a result within 2% of the experimental values ​​obtained with water ultrapure in the 90s.

The researchers propose a bubble trajectory instability mechanism whereby periodic tilting of the bubble changes its curvature, thereby affecting the upward velocity and causing a wobble in the bubble trajectory, tilting up the part of the bubble whose curvature has increased.

Then, as the fluid moves faster and the fluid pressure drops around the high-curvature surface, the pressure imbalance brings the bubble back to its original position, restarting the periodic cycle.

More information:
Miguel A. Herrada et al., Path instability of an air bubble rising in water, Proceedings of the National Academy of Sciences (2023). DOI: 10.1073/pnas.2216830120

Provided by the University of Seville

Citation: Leonardo da Vinci’s Paradox of the Periodic Motion of Cracked Bubbles (2023, January 17) Retrieved January 17, 2023, from https://phys.org/news/2023-01-leonardo-da-vinci-paradox-periodic.html

This document is subject to copyright. Except for any fair dealing for the purpose of private study or research, no part may be reproduced without written permission. The content is provided for informational purposes only.

Leave a Comment

Your email address will not be published. Required fields are marked *