A Spanish and English researcher solved Leonardo da Vinci’s paradox

Fluid mechanics expert Miguel Angel Herrada, from the University of Seville, has been found together with Professor Jens G Eggers, from the University of Bristol (United Kingdom), a mechanism explaining the unstable motion of bubbles rising in the water.

The results are published in a journal PNAScan be useful for understanding the movement of particles, because of their behavior between solids and gases.

Leonardo da Vinci observed five centuries ago that an air bubble, if large enough, floats periodically movement in a straight line, either zigzag or spiral. However, neither a quantitative description of the phenomenon nor a physical mechanism to explain it has been found.

Leonardo’s sketch illustrates the spiral motion of the rising bubble and an x-ray of the structure of the movement of water around the bubble for a critical radius. / Leicester Codex/USA

Air bubbles deviate from a straight line as they rise in water if their radius is greater than 0.926 millimeters

The authors of this new study have developed a technique numerical discretization to accurately characterize the air-water interface of the bubbles, which makes it possible to simulate their movement and study their stability. Their model is consistent with high-precision measurements of unstable bubble motion.

Deflection occurs when the radius of the bubble is round exceed 0.926 millimetersresults within 2% of the experimental values ​​obtained with ultrapure water in the 1990s.

Herrada and Eggers proposed a mechanism of bubble trajectory instability in which its periodic tendency to change curvature. This affects the rate of ascent and causes a wobble in the bubble’s path: the curvature increases and the sides of the bubble tilt up.

Then, as the fluid moves faster and the fluid pressure drops around the high curvature surface, the pressure imbalance returns the bubbles to their original position, restarting the periodic cycle.

Reference

Herrada, MA et al. “Path of instability of air bubbles rising in water”. PNAS (2023)

Right: Creative Commons.

Stuart Martin

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