More than 500 years ago, Leonardo da Vinci was watching air bubbles floating in the water, as befits Renaissance sages. During this time, he noticed that some bubbles were inexplicably spinning or zigzagging instead of rising directly to the surface.

For centuries no one has been able to provide a satisfactory explanation for this strange, repetitive deviation in the movement of certain bubbles in the water, called the "Leonardo Paradox".

Two scientists have finally solved the long-standing puzzle, according to a study published Tuesday in the journal Proceedings of the National Academy of Sciences.

According to the research, there is an interaction between the water flow around the bubbles and the subtle deformations in their shape. This places some bubbles in a critical zone of circular motion that pushes them on new and unstable paths.

Authors Miguel Herrada and Jens Eggers, fluid physics researchers at the University of Seville and the University of Bristol, respectively; "The movement of bubbles in water plays a central role for a wide variety of natural phenomena, from the chemical industry to the environment.The buoyancy of a single balloon serves as a well-studied model, both experimentally and theoretically."

The explanation continued: "However, despite all these efforts and enormous computational power, it has not been possible to reconcile experiments with numerical models of the exact hydrodynamic equations for a water-deformable air bubble. This is especially true of the intriguing observation made by Leonardo da Vinci."

In fact, bubbles are so common in our daily lives that we may forget that they are dynamically complex and difficult to study experimentally. Air bubbles rising in water; The fluidity is affected by a number of forces, such as surface friction and environmental pollutants, which deform the bubble and change the dynamics of the surrounding water.

Air bubbles with a spherical radius of less than a millimeter tend to follow a straight path upward through the water, while bubbles of larger radius periodically develop spiral or zigzag trajectories. Leonardo da Vinci pointed to this fact, and many scientists have since confirmed it.

Herrada and Eggers used the Navier-Stokes equations, a mathematical approach to describing the motion of viscous fluids, to simulate the complex interaction between air bubbles and their aqueous media. The team determined the spherical radius (0.926 millimeters, or about the size of a pencil tip) that triggered this tilt, thereby identifying the possible mechanism behind the wobble motion.

A balloon beyond the critical radius becomes more unstable, creating a slope that changes the balloon's curvature. The curvature change increases the velocity of the water around the surface of the balloon, which initiates the wobble motion. The balloon then returns to its original position due to the pressure imbalance created by the curved shape and repeats this process in a regular cycle.

As well as resolving a 500-year-old paradox, this new study also sheds light on a number of other questions about the variable behavior of bubbles and other objects that don't fit into easy classification.

"While it was previously believed that the water carrying the balloon became unstable, we have now proven a new mechanism based on the interaction between flow and balloon deformation," said Herrada and Eggers. "This mechanism also opens the door to investigating the small perturbations found in most environments that affect a particle between a solid and a gas."