A study led by researchers at Princeton University has yielded insights into how liquid spreads along flexible fibers, which could allow for increased efficiency in various industrial applications. The team’s experiments show that the size of oil droplets determines whether they spread along flexible glass fibers. At the critical size (top two examples), the droplets expand into columns of liquid, but larger droplets sit immobile between the glass rods (bottom example). Image: Camille Duprat and Suzie Protière
Under a microscope, a tiny droplet slides
between two fine hairs like a roller coaster on a set of rails until—poof—it
suddenly spreads along them, a droplet no more.
That instant of change, like the popping of
soap bubble, comes so suddenly that it seems almost magical. But describing it,
and mapping out how droplets stretch into tiny columns, is a key to
understanding how liquids affect fibrous materials from air filters to human
hair. And that knowledge allows scientists to better describe why water soaks
into some materials, beads atop others and leaves others matted and clumped.
To get those answers, an international team
of researchers led by scientists at Princeton
University made a series
of close observations of how liquid spreads along flexible fibers. They were
able to construct a set of rules that govern the spreading behavior, including
some unexpected results. In a paper published in Nature, the researchers found that a key parameter was the size of
the liquid drop.
“That surprised us,” said Camille
Duprat, the paper’s lead author. “No one had thought about volume very
Duprat, a postdoctoral researcher in the Department
of Mechanical and Aerospace Engineering, said the research team was able to
determine drop sizes that maximized wetting along certain fibers, which could
allow for increased efficiency in industrial applications of liquids interacting
with fibrous materials—from cleaning oil slicks to developing microscopic
electronics. The team also discovered a critical drop size above which the drop
would not spread along the fibers, but would remain perched like a stranded
roller coaster car.
“If in any engineering problem you can
learn an optimal size above which something does not happen, you have learned
something very important about the system,” said Howard Stone, a coauthor
of the paper.
Stone, the Donald R. Dixon ’69 and
Elizabeth W. Dixon Professor in Mechanical and Aerospace Engineering, said the
team conducted a series of experiments observing how liquid spread along
different types of fibers. The plan was to make broad observations and derive a
governing theory from the experiments.
“We had a lot of results and at some
point we started having these meetings trying to understand what we had,”
he said. “We realized the way to think about it was in the way of critical
Besides Duprat and Stone, the researchers
included Alexander Beebe, a Princeton junior majoring in mechanical and
aerospace engineering, and Suzie Protière, an associate scientist at the University of Pierre
and Marie Curie in Paris.
The research at Princeton was conducted with
support from Unilever.
In the researchers’ study of natural fibers, oil applied to goose feathers shows how droplets of smaller volumes spread along the fibers and cause clumping, while larger droplets do not. The finding could prove important for cleaning waterfowl after accidental spills. Image: Camille Duprat and Suzie Protière
The researchers determined that the
critical parameters governing how drops interact with flexible fibers were the
size of the droplet, the flexibility and radii of the fibers, and the geometry
of the fiber array (such as the space and angle between pairs of fibers).
The experiment examined the behavior of a
droplet placed on a pair of flexible glass fibers that was clamped at one end
and free at the other. When the drop was placed at the clamped end of the pair,
the fibers bent inward and the drop moved toward the free end. As the drop
moved further out, the fibers bent more, and the drop accelerated and
elongated. At some point, the drop spontaneously spread and formed a liquid
column between the now-coalesced fibers.
To understand the critical drop size at
which no spreading occurred, the researchers measured the distance between the
fibers at the instant that the spreading began. They concluded that spreading
occurs when the spacing between the fibers dictates that it takes less energy
for the liquid to form a column than it does to remain as a drop. The
researchers were also able to use their observations to calculate an optimal
drop size that resulted in a maximum spread of liquid along the fibers.
The researchers said their findings could
have a wide array of applications. Waterfowls’ feathers, for example, are a
natural array of fibers that keep the birds warm and dry. When oil coats the
feathers, it disrupts the fiber arrangement by clumping the feathers. Using
goose feathers, the team found that oil droplets above a certain size did not
spread along the fibers and allowed the feather to be cleaned more easily.
Duprat said the findings could have implications for methods used to rescue
injured birds and also for dispersants applied to oil slicks after accidents.
On the other hand, items such as
aerosol-removal filters or hairsprays require total spreading along fibers for
effectiveness. The control of droplet sizes could also prove important for the
fabrication of microstructures by resulting in the optimal spread of liquid
material along pillars and similar forms, such as those found in various forms
of lithography used in micro- and nanofabrication.
“Materials react differently to
different drop sizes,” Duprat said. “You can design a material to
react to a specific drop size or you can produce a drop size to affect a