Researchers from the Universities of Seville and Bristol have solved the mystery of the unsteady trajectory of an air bubble rising in water. Professor Miguel Ángel Herrada of the University of Seville and Jens G. Eggers of the University of Bristol discovered a mechanism that explains the unstable motion of bubbles rising in water. Findings published in a prestigious journal Proceedings of the National Academy of SciencesIt can give an idea about the behavior of particles between solid and gas states.

Five centuries ago, Leonardo da Vinci observed that air bubbles, if they are large enough, periodically deviate from linear motion in a zigzag or spiral pattern. However, no quantitative explanation of the phenomenon or physical mechanism has been found to explain this periodic motion.

A drawing by Leonardo (from the manuscript known as the Leicester Codex) showing the spiraling motion of a rising balloon. Credit: University of Seville

The authors of this new paper have developed a numerical discretization technique to accurately characterize the air-water surface of a balloon, which allows to model its motion and investigate its stability. Their simulations closely match high-precision measurements of unstable bubble motion and show that bubbles deviate from a straight path in water when their spherical radius exceeds 0.926 millimeters; this is a result within 2% of the experimental values ​​achieved with ultrapure water in the 1990s.

The researchers propose a bubble trajectory instability mechanism in which periodic tilting of the bubble changes its curvature, thereby affecting the upward velocity, and tilting the side of the bubble with increasing upward curvature causes the bubble trajectory to oscillate. Then, as the fluid moves faster and the fluid pressure drops around the high curvature surface, the pressure imbalance pushes the balloon back to its original position, restarting the periodic cycle.