A large drop can grow by swallowing up the smaller drops at its edge. Credit: MPI for Dynamics and Self-Organisation |
Fine
dew drops on spider webs, blades of grass, and even insects can lend
them breathtaking beauty. And, examining them very closely, one
recognizes that the drops themselves form astonishingly regular and
aesthetic patterns. For the first time, scientists at the Max Planck
Institute for Dynamics and Self-Organisation in Göttingen have now
comprehensively investigated what laws these drops obey when they
originate and grow in size. Elaborate computer simulations and
experiments show that in particular the beginning of this growth phase
proceeds differently than previously thought: the smallest droplets grow
notably faster compared to their larger siblings. This new knowledge is
especially important for irrigation technology and refrigeration.
When
moisture impinges upon a cooler surface, the following series of events
takes place; individual water molecules first coalesce into tiny
droplets, being only a few micrometers in size. While these grow,
smaller ones constantly repopulate the spaces between them, and can
coalesce with their larger siblings over time. Up to now, researchers
have assumed that the distribution of droplet sizes followed a power
law. This states that irrespective of whether the early, middle or late
growth phase is involved, the majority of droplets are small, and the
larger the droplets are, the fewer of them are present. These kinds of
power laws describe numerous distributions in nature and in technology,
for example the size of craters on the moon, the frequency distribution
of chemical elements in the earth’s crust, and of words in texts.
However,
the newest results of the Göttingen-based scientists show that one and
the same law does not aptly describe the entire growth phrase of the
droplets. Their behavior does not follow the precepts of scaling
theory, especially at the beginning of their growth—the early childhood
of the droplets, so to speak.
“No
doubt, there are many more small drops than large ones, just as
previously predicted. Still, significantly fewer small droplets are
observed than expected,” says Jürgen Vollmer, the scientist at the
Max-Planck Institute for Dynamics and Self-Organisation leading the
study, while describing the results. The researchers explain this by the
fact that the small drops grow out of their childhood more rapidly than
required by scaling theory. In addition, during the final growth phase,
the droplet growth speed had to be augmented.
To
detect these features, precise observation is required. Jürgen Vollmer
and Björn Hof, who also conducts research at the Max Planck Institute in
Göttingen, practise the art of “drop counting” with their team in two
ways: experimentally and in computer simulations.
“The
basic setup of the experiment is reminiscent of a pot of boiling water
with a lid,” says Tobias Lapp, who carried out the majority of the
experiments. In the experiment, water is heated under carefully
controlled conditions in a container that is sealed with transparent
cover. A camera that is mounted above the cover takes a snapshot image
of the droplet pattern six times per second. The images are then
evaluated with a specially developed computer program. “To evaluate each
image, each drop must be identified and assigned to a specific size
category,” says Lapp.
The
other leg of the study is numerical simulation. “How moisture condenses
on a surface can be very well modeled using a computer,” explains
Vollmer.
Current thinking predicts fewer large drops and many small drops in a typical collection of droplets. A closer look would reveal that there are fewer small drops than the previous theory would lead to expect. Credit: MPI for Dynamics and Self-Organisation |
In
the simulations water impinges uniformly on a surface and initially
forms tiny droplets that gradually grow due to the on-going
precipitation of water. Frequently there are cascading collisions in
which several smaller droplets merge into a larger one. “To trace the
growth process exactly, we have to account for young, tiny drops just
the same as for the significantly older, larger ones,” says Johannes
Blaschke in explanation of the method’s difficulty. Blaschke developed
and carried out the simulations as part of his master’s thesis. In
addition, it was necessary to average over several hundred simulations.
“This sort of numerical effort had not been undertaken by anyone else in
this field until now.”
The
pay-off for the sophisticated droplet counting: the researchers could
identify a significant kink in the early growth, as well as corrections
to the growth speed in the very late phase. “The power law thus no
longer holds,” summarizes Vollmer, adding: “In the experiments there are
more exceptions than instances that go by the old rules.”
To
explain the new results, droplet growth must be observed very
carefully. There are fundamentally three mechanisms by which an existing
droplet can increase in size: two drops which are more or less equal in
size can coalesce, a small droplet can grow until its edge touches the
edge of a significantly larger one and thus be swallowed up, or the
droplets can grow via precipitation. In the beginning, small droplets
are still widely separated and therefore collect the precipitate
especially efficiently. The water that lands in their vicinity migrates
over the surface toward them, which speeds up their growth. Near the end
of the growth process, there are already so many drops nearby that the
neighbors absorb these “indirect hits”. In contrast, the especially
large drops hardly meet any others which are larger, and so there are
none to swallow them up—consequentially, their growth slows.
The
researchers’ results could benefit technical applications that are
based on the special properties of drops. Since droplets can absorb heat
effectively, they are especially needed in refrigeration and air
conditioning to name a few. An improved understanding of the processes
by which they develop can facilitate energy-saving methods and foster
mildew-free homes. Furthermore, modern efficient irrigation methods also
depend on creating droplets of specific sizes. Hence, in-depth
knowledge of the features of droplet growth could be of assistance there
as well.
Source: Max Planck Institute