A mystery of fluid dynamics that was first noticed by Leonardo—and that’s flummoxed scientists for centuries—has apparently been solved. And we are glad for it.

Over 500 years ago, da Vinci was watching bubbles floating in water. When you’re the greatest polymath of all time, that’s what you do. At some point, he noticed a few of the bubbles moving erratically, zig-zagging this way and that, instead of floating straight up to the surface. Da Vinci made the drawing below in his notebook and then scribbled some thoughts. The notes were written backwards, as per his usual.

After the fact, scientists were baffled for centuries by the riddle of why the movement of bubbles in water sometimes changes. The problem became known as “Leonardo’s paradox.” The answer may have been recently discovered by two scientists who published a paper in Proceedings of the National Academy of Sciences. The authors are Miguel Herrada and Jens Eggers, two fluid physics researchers at the University of Seville and the University of Bristol respectively. The two developed new simulations that match previous high precision measurements of bubbles acting in water. In the paper, their findings 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.”

In their paper, Herrada and Eggers further write that “the motion of bubbles in water plays a central role for a wide range of natural phenomena, from the chemical industry to the environment. The buoyant rise of a single bubble serves as a much-studied paradigm, both experimentally and theoretically.”

Long before Herrada and Eggers took a crack at solving the gaseous dilemma, da Vinci observed that bubbles with a spherical radius smaller than a millimeter tended to drift straight up while larger bubbles often developed a wobble. Taking that as a cue, Herrada and Eggers used mathematical formulas called the Navier-Stokes equations to confirm da Vinci’s observations. They found that an increase in the spherical radius of a bubble to beyond 0.926 millimeters can be the mechanism that triggers the wobbly behavior. In other words, if a bubble becomes larger, it can become unstable producing a tilt that alters the curvature of the bubble, also increasing the velocity of the water around the bubble and ultimately resulting in the wobbly behavior.

Along with solving the age old Leonardo paradox, the new study may also have other applications. Eggers and Herrada conclude their paper by saying, “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. 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.”

All of which makes me wonder why it took so long to solve what by most appearances is an straight forward riddle. I think I know why. Other than water, most liquids that contain bubbles also have alcohol. Also, in the context of past experimentation, municipal water sources have only been safe to drink in most civilized countries for a century, if that. That being the case, previous researchers probably used alcoholic beverages like sparkling wine and beer for experimental purposes. It doesn’t take a da Vinci to imagine the researchers of old taking a nip from the control beaker/container now and again. And before you know it, one’s thinking could become cloudy, bubbles or not.

Otherwise, it’s curious how the properties of liquids have long fascinated man. Aside from bubbles in water, there are what’s called legs or tears in a glass of wine. These magical droplets have entranced mankind for millennia. But over a century ago, someone became obsessed with the phenomenon. His name was Carlo Marangoni. He was Italian. Of course, he was Italian. And the phenomenon of legs/tears moving in a glass of wine is named after him. It’s called the Marangoni Effect.

The effect was first identified by James Thompson, a British physicist (and brother of Lord Kelvin) in 1855. But it was Marangoni who studied it for his doctoral dissertation at the University of Padua. He published the results in 1865. However, a complete theoretical treatment on the effect was given by J. Willard Gibbs in his work On the Equilibrium of Heterogeneous Substances, written between1875-78. Hence the proper name is the Gibbs–Marangoni effect.

Regardless of name, the Marangoni effect, as I choose to call it, can be described as (and I’m quoting here) “the mass transfer along an interface between two phases due to a gradient of the surface tension. In the case of temperature dependence, this phenomenon may be called thermos-capillary convection (or Bénard–Marangoni convection).”

In layman’s terms, the above means this. If it’s wine we’re taking about, the combination of surface tension in the wine combined with temperature variation in various locations in the glass results in droplets being formed on the side of the glass when it’s swirled. Here’s more info from Wikipedia, the pasta colander of all knowledge:

“A liquid with a high surface tension pulls with more force on the surrounding liquid compared to one with low surface tension. This gradient of surface tension will cause the liquid to flow away from regions of lower surface tension. The gradient itself can be caused by varying concentration in the liquid or by temperature variation.”

I want to add my two cents at this point. In regards to wine, the concentration just mentioned is related to the dry extract (amount of particles in solution) along with the levels of alcohol, glycerin, and residual sugar (if present). Thus a wine with higher levels of alcohol, glycerin, and dry extract—or the presence of residual sugar—will result in thicker, slower moving tears. On the flip side, a wine with lower levels of dry extract, alcohol, and glycerin, and the lack of residual sugar, will make for thinner, more quickly moving legs/tears in the glass.

Two additions to the menu: first, for the effect to be properly observed, the wine glasses have to be cleaned and polished. Otherwise, all bets are off. Second, the legs and tears in a glass of wine do not in any way reflect quality. In other words, there is no such thing as good legs or bad legs in wine.

In the end, the liquid universe will always fascinate. I’m thrilled that the centuries-old Leonardo’s paradox may finally have been solved. I’m sure da Vinci would be pleased to know. In fact, he’d probably celebrate the occasion with a glass of beer or sparkling wine. I only wish I could join him.