More than 500 years ago, Leonardo da Vinci was watching air bubbles float up through water–as you do when you’re a Renaissance-era polymath–when he noticed that some bubbles inexplicably started spiraling or zigzagging instead of making a straight ascent to the surface.
For many centuries, no one has been able to explain the strange periodic motion of bubbles through water. This phenomenon was known as “Leonardo’s paradox”
A pair of scientists have developed new simulations to match the high-precision measurements of this effect. The study, published in Proceedings of National Academy of Sciences on Tuesday , is now out.
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 the subtle deformations of their shapes.
“The motion of bubbles in water plays a central role for a wide range of natural phenomena, from the chemical industry to the environment,” said authors Miguel Herrada and Jens Eggers, who are fluid physics researchers at the University of Seville and the University of Bristol respectively, in the study. “The buoyant rise of a single bubble serves as a much-studied paradigm, both experimentally and theoretically.”
“Yet, in spite of these efforts, and in spite of the ready availability of enormous computing power, it has not been possible to reconcile experiments with numerical simulations of the full hydrodynamic equations for a deformable air bubble in water,” the team continued. “This is true in particular for the intriguing observation, made already by Leonardo da Vinci, that sufficiently large air bubbles perform a periodic motion, instead of rising along a straight line.”
Indeed, bubbles are so ubiquitous in our daily lives that it can be easy to forget that they are dynamically complicated and often tricky to experimentally study. Water bubbles that rise in the atmosphere are affected by many forces, including fluid viscosity and surface friction. These forces can alter the shape of bubbles as well as the dynamic of the surrounding water.
Clinicians have confirmed that bubbles smaller in diameter than one millimeter follow an upward trajectory through water. However, larger bubbles tend to develop wobbles that result in periodic spirals or zigzag paths.
Herrada used Eggers’ Navier-Stokes equations to model the complicated interaction between air bubbles with their fluid medium. This tilt–0 is caused by a spherical radius. The team was able to identify the radius. 926 millimeters, which is about the size of a pencil tip–and describe the possible mechanism behind the squiggly motion.
A bubble that has exceeded the critical radius becomes more unstable, producing a tilt that changes the curvature of the bubble. The shift in curvature increases the velocity of water around the surface of the bubble, which kicks off the wobble motion. Due to pressure imbalances caused by deformations of its curvature, the bubble returns to its initial position and continues the cycle on a periodic basis.
In addition to resolving a 500-year-old paradox, the new study could shed light on a host of other questions about the mercurial behavior of bubbles, and other objects that defy easy categorization.
“While it was previously believed that the bubble’s wake becomes unstable, we now demonstrate a new mechanism, based on the interplay between flow and bubble deformation,” Herrada and Eggers concluded in the study. “This opens the door to the study of small contaminations, present in most practical settings, which emulate a particle somewhere in between a solid and a gas.”
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