Saturday, January 28, 2023

A 500-year-old ‘paradox’ by Leonardo da Vinci has finally been resolved, says a study

More than 500 years ago, Leonardo da Vinci was observing air bubbles floating in water, as you do when you’re a Renaissance-era scholar, when he noticed that some bubbles, inexplicably, instead spiraled or Started zigzagging. to the surface of the water.

For centuries, no one has come up with a satisfactory explanation for this strange periodic deviation in the movement of some bubbles through water, which has been called “Leonardo’s paradox”.

A pair of scientists now believe they have solved a long-standing puzzle by developing new simulations that match high-precision measurements of the effect, according to a published study.

The results suggest that bubbles can reach a critical radius that pushes them into new and unstable paths due to interactions between the flow of water around them and subtle distortions of their shape.

Authors Miguel Herrada and Jens Eggers, fluid physics researchers at the University of Seville and the University of Bristol, respectively, said in the study:

“The motion of bubbles in water plays a central role in a wide range of natural phenomena, from the chemical industry to the environment.”

“The buoyant rise of a single bubble serves as a well-studied paradigm both experimentally and theoretically.”

“However, despite these efforts, and the immediate availability of enormous computing power, it has not been possible to reconcile experiments with numerical simulations of the full hydrodynamic equations for deformable air bubbles in water.”

“This is especially true of the intriguing observation, already made by Leonardo da Vinci, that sufficiently large air bubbles move periodically, rather than ascending in a straight line.”

In fact, bubbles are so ubiquitous in our daily lives that it can be easy to forget that they are dynamically complex and often difficult to study experimentally. Air bubbles rising in water are affected by a number of intermolecular forces, such as fluid viscosity, surface friction, and any surrounding contaminants, which distort the shape of the bubble and change the dynamics of the water flowing through it.

What da Vinci noted and other scientists have confirmed is that air bubbles with circular radii that are much smaller than a millimeter follow a straight path through water, while larger bubbles follow a wobbly path. resulting in periodic whorls or zigzags. trajectory.

Herrada and Eggers used the Navier–Stokes equations, a mathematical framework for describing the movement of viscous fluids, to simulate the complex interactions between air bubbles and their aqueous medium. The team was able to identify the sphere radius that triggers this wobble (0.926 millimetres, which is about the size of a pencil tip) and describe the possible mechanism behind the undulating motion.

A bubble that has exceeded the critical radius becomes more unstable, producing a tilt that changes the bubble’s curvature. The change in curvature increases the speed of the water around the surface of the bubble, which initiates the rocking motion. The bubble then returns to its original position due to the pressure imbalance created by the deformations in its curved shape and repeats the process in a periodic cycle.

In addition to resolving a 500-year-old paradox, the new study may shed light on many other questions about the trading behavior of bubbles and other commodities that defy easy categorization.

Herrada and Eggers concluded in the study:

“While it was previously believed that the bubble wake becomes unstable, we now demonstrate a new mechanism based on the interaction between bubble flow and deformation.”

“This opens the door to the study of tiny contaminants present in most practical settings, simulating a particle somewhere between a solid and a gas.”

Nation World News Desk
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