# Physicists have solved the paradox of Leonardo, who described the strange movement of bubbles

(ORDO NEWS) — Some bubbles rise to the surface of the water not in a straight line, but in a spiral. Leonardo da Vinci discovered this strange phenomenon over 500 years ago, but only now has it been explained.

Artist, engineer and sculptor Leonardo da Vinci became one of the most famous personalities in history.

Today, a number of unusual observations and phenomena are associated with his name, including several paradoxes. In hydrodynamics, the Leonardo paradox is the strange behavior of bubbles rising in water.

About 500 years ago, the great Italian noticed that while most of the bubbles rush from below directly to the surface, some of them begin to oscillate and rise upward in a spiral.

He sketched out such a movement, which has come down to our time in a notebook of notes known as the Leicester Codex. The riddle of Leonardo’s paradox has survived to this day.

It was only recently possible to solve it.

Observations confirm that rather small – less than a millimeter in diameter – bubbles rise in the water more or less in a straight line, while larger ones oscillate from side to side, moving along a spiral path.

Miguel Herrada of the University of Seville and Jens Eggers of the University of Bristol made new calculations and showed that the critical size is 0.926 millimeters.

If the bubble diameter exceeds this value, it becomes unstable and loses its even spherical shape. Areas with greater and lesser bending appear on its surface.

Where the bend is greater, the water flows around the bubble faster, which means that its pressure is lower, causing the bubble to move sideways.

At the same time, the same decrease in pressure allows the strongly curved area to recover its shape and slightly “round”.

However, while remaining unstable, it deforms again, and the whole process repeats again, creating periodic oscillations from side to side.

As the authors write, when the critical dimensions are exceeded, “the bubble deforms in response to the forces acting on it from the side of the water, and vice versa, the shape of the bubble changes the characteristics of the water flow around it.”

The new work is not just a curious theoretical study. Bubbles that form and move in a liquid accompany a number of natural phenomena (including finger crunching ) and are actively used in industry.

Understanding their properties will allow you to better understand natural processes and optimize some stages of production.

Online: