A mystery of fluid physics first noticed by da Vinci has puzzled scientists for centuries, and we now have an answer.
By Becky Ferreira
for Vice
January 18, 2023 -- 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
centuries, nobody has offered a satisfying explanation for this weird periodic
deviation in the motion of some bubbles through water, which has been
called “Leonardo’s paradox.”
Now,
a pair of scientists think they may have finally solved the longstanding riddle
by developing new simulations that match high-precision measurements of the
effect, according to a study published on Tuesday in Proceedings
of the National Academy of Sciences.
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.
Rising air bubbles in water are influenced by a host of intersecting
forces—such as fluid viscosity, surface friction, and any surrounding
contaminants—that contort the shapes of the bubbles and shift the dynamics of
the water flowing around them.
What
da Vinci noted, and other scientists have since confirmed, is that air bubbles
with a spherical radius that is much smaller than a millimeter tend to follow a
straightforward upward path through water, whereas larger bubbles develop a
wobble that results in periodic spiral or zigzag trajectories.
Herrada
and Eggers used the Navier–Stokes equations, which are a mathematical framework
for describing the motion of viscous fluids, to simulate the complex interplay
between the air bubbles and their watery medium. The team were able to pinpoint
the spherical radius that triggers this tilt—0.926 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. 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 on a periodic cycle.
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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