Perhaps of the many facets of Leonardo da Vinci, that of a painter is the best known thanks to paintings such as La Gioconda or The Last Supper. But whether it was because of his perfectionist desire in this regard or out of simple curiosity, Da Vinci also stood out as a scientist. His studies on human anatomy are meticulous, but there is an aspect of the natural sciences that he failed to resolve: the movement of the bubbles.
So intrigued did he leave the matter to the Florentine genius that the problem received the name of Leonardo’s Paradox. A paradox that has just been resolved, but what exactly is it? The paradox is based on the movement of the bubbles. Not from bubbles like soap bubbles, but from air bubbles trapped in the water.
A bubble in this context is a quantity of a gas (air) trapped under a liquid (water) whose extension is delimited by the surface tension of the water. Since water is heavier than air, the bubbles rise. The problem, Da Vinci observed, was that this movement was not always uniform or rectilinear but rather on some occasions the bubble showed a strange tendency to zigzag.
Why and how the bubbles did this dance as they rose had become an enigma for researchers. Until now. A couple of researchers have unraveled the enigma as recently announced by the University of Seville.
In a study published in the Proceedings of the National Academy of Sciences, researchers report that the keys to the movement of bubbles. The first, Da Vinci had already observed this, is size: it is only after a certain size that the bubbles begin to deviate (unlike, for example, carbonated drinks, where the bubbles rise in a straight line).
But from 0.926 millimeters in diameter, the bubbles become unstable, according to the calculations of the new study. The movement appears by an interaction between the flow of the bubble and the deformation of the same. Therein lies the second key to the finding: when the bubble is tilted, it is deformed, generating an asymmetry that implies that its different sides flow differently. That is, the hydrodynamics of the bubble change, causing it to change direction.
As it picks up speed, the pressure of the liquid on the bubble changes, exerting a force that deforms the bubble again, this time returning it to its original shape. This causes the bubble to stop listing and return to its original rise. after that the process is repeated.
To reach their conclusions, the researchers started from the Navier-Stokes equations. A complex mathematical framework that is used to describe the movement of viscous fluids taking friction into account. Due to its complexity, this is not the only problem that these equations still have to solve.
and this is precisely one of the potential achievements of this research. Beyond predicting the movement of simple air bubbles in water, understanding the interactions between fluids (and gases) can help answer questions of all kinds, from how pollutants diffuse into the sea to how pollutants stay in the air. planes. Perhaps this last doubt would have also intrigued Leonardo himself.
Image | Leonardo da Vinci
