An Mysterious Paradox about Liquids Posed by Leonardo da Vinci That Confused Scientists for Centuries. Now, we have the answer.
More than 500 years ago, while observing air bubbles rising to the surface of the water, Leonardo da Vinci noticed that they moved in a spiral or meandering pattern rather than traveling straight up. For centuries, this strange phenomenon remained unexplained and became known as the “Leonardo Paradox.”
An explanation for the “Leonardo Paradox” has been found. (Image: iStock).
Now, two scientists have uncovered the answer by developing simulations that align with highly accurate measurements. The research results were published on January 17 in the journal Proceedings of the National Academy of Sciences.
Professor Miguel Ángel Herrada from the University of Seville and Professor Jens G. Eggers from the University of Bristol explored the mechanisms explaining the unstable motion of air bubbles as they rise to the water’s surface.
According to the authors, the research findings indicate that bubbles can reach a critical radius, continuously being pushed into new paths of movement due to the interaction between the surrounding water flow and their shape changes.
“The motion of bubbles in water plays a central role in many natural phenomena, from chemical industries to environmental concerns,” Miguel Herrada and Jens Eggers noted regarding the significance of explaining the Leonardo Paradox.
A drawing by Leonardo da Vinci depicting the strange movement of air bubbles in water. (Image: University of Seville).
What da Vinci observed five centuries ago has been confirmed by other scientists: air bubbles with a radius smaller than a millimeter tend to rise straight to the surface, while larger bubbles exhibit a wobbling motion that leads to spiral or meandering paths.
Herrada and Eggers used the Navier–Stokes equations, a mathematical model used to calculate the flow of liquids and gases, to simulate the complex interactions between air bubbles and their surrounding water.
The research team accurately identified the critical spherical radius that triggers this wobbling as 0.926 mm—roughly the size of a pencil tip—and described the mechanisms leading to these erratic movements.
Bubbles exceeding the critical radius become increasingly unstable, creating a tilt that alters their curvature. This increases the velocity of the water around the bubble’s surface, causing the wobbling motion.
Subsequently, the bubbles return to their original position due to the pressure imbalance created by the deformations, repeating the process cyclically.
“Previously, it was believed that the very act of rising to the surface made the bubbles unstable, but we demonstrate a new mechanism based on the interaction between flow and bubble deformation,” the authors concluded.
