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Droplet Formation on Fibers

August 6, 2015

There are so many James Bond films that it's not hard to find a reference in one of them to a specific science or technology topic. This article is about droplets on fibers; and, yes, there's a Bond film about that. The film is You Only Live Twice (1967, Lewis Gilbert, Director).[1]

In the film, Bond, played by Sean Connery goes undercover as a Japanese fisherman, assisted by a Japanese secret agent, Aki, played by Akiko Wakabayashi. In his typical fashion, screenwriter, Roald Dahl, has Aki killed by an assassin who drips poison, intended for Bond, down a thread and into her mouth. Bond gets his revenge by shooting the assassin.

Spider web with dew drops at sunrise.

Even when anchored to these web threads, the surface tension of the water keeps the drops in a spherical shape.

(Photo by Luc Viatour, lucnix.be, via Wikimedia Commons.)

I once collaborated with a team of chemists on a project to coat wires with a unique ceramic precursor. So, how difficult could this be? Our first approach was to run the wire through a vat of the mixture, expecting a nice coating with thickness determined by how fast the wire was pulled. Instead of a uniform layer on the wire, we got a bumpy mess. This was a consequence of a phenomenon called the Plateau–Rayleigh instability.

The Plateau–Rayleigh instability is a special case of Rayleigh–Taylor instability, one of the scientific legacies of Lord Rayleigh (1842-1919). Rayleigh and William Ramsay (1852-1916) were awarded the 1904 Nobel Prize in Chemistry for the discovery of argon. Among physicists, Rayleigh is best known for Rayleigh scattering, the optical phenomenon that causes the blue color of the sky.

John William Strutt, 3rd Baron Rayleigh (1842-1919).

An 1899 color lithograph by F. T. Dalton entitled, "Argon," from an issue of Vanity Fair.

(Illustration from Wellcome Images, a website operated by Wellcome Trust, a global charitable foundation based in the United Kingdom, via Wikimedia Commons.)

The Rayleigh–Taylor instability occurs at the interface between a dense, and a less-dense, fluid when the lighter fluid is forced to infiltrate the heavier fluid by an applied pressure, or through gravity. One of its physical manifestations is the "fingers" that form when a dense fluid is placed above a less-dense fluid. An example of this instability when lighter and denser paints are combined can be seen in the references.[2-3]

The Plateau–Rayleigh instability arises from the principle that liquids will minimize their surface area. That's why droplets are nearly spherical, since that's the way to package the largest volume in the smallest area. one example of Plateau–Rayleigh instability is the breaking of a continuous stream of water from a faucet into a stream of droplets. This effect has enabled high speed inkjet printing, where vibrations from a piezoelectric transducer will break a continuous ink stream into regularly-spaced droplets.

Scientists from Saarland University (Saarbrücken, Germany), McMaster University (Hamilton, Ontario, Canada), PSL Research University (Paris, France), and the Max Planck Institute for Dynamics and Self-Organization (MPIDS, Göttingen, Germany), have investigated the Plateau–Rayleigh instability in liquid layers on fibers.[4-5] By observing lacquer films on glass fibers, the research team was able to see how the liquid flows along the fiber as a function of the fiber coating.[5]

Plateau–Rayleigh instability of liquid coatings on fibers

Two examples of the Plateau–Rayleigh instability of liquids on fibers.

(Photos by H. Haefner, S. Haefner, and A.G. Jacobs of Saarland University.)

Unlike the instability is a free stream of liquid, the instability for liquid layers on fibers requires consideration of the interface between the fiber and the liquid.[4] The research team looked at the hydrodynamics for slip and no-slip conditions at the interface.[4] Says Oliver Bäumchen from the Max Planck Institute for Dynamics and Self-Organization,

"The contact between the liquid and the fiber is indeed very important... If the liquid slips on the fiber surface, the droplet formation is much faster than in the case of just flow along the fiber".[5]

In experiments with bare and Teflon-coated fibers, the liquid film moved rather slowly and droplet formation took longer on the uncoated fibers than on coated fibers. This is because the liquid film was able to slip on the Teflon coating.[5] The wavelength of the undulations caused by the instability was not sensitive to the solid–liquid interface.[4] The wavelength of the fastest growing mode was found to be a linear function of the initial radius of the fiber plus coating, as shown in the figure.[4]

Linear dependence of wavelength with coated fiber radius.

(Fig. 2 of ref. 4, licensed under a Creative Commons license.)[4)]

Although there was no difference in the geometry of droplet separation between the coated and uncoated fibers, there was an increased growth rate in the formation of the droplets for the coated fibers.[4] This feature is technologically important to applications, such as harvesting water from fog using fiber nets.[5] I wrote about harvesting water from the air in a previous article (Fog Water Harvesting, December 2, 2010). This technology is important for arid regions of the world, such as Chile's Atacama Desert.

Conversely, having homogeneous and stable liquid films on fibers is also important, as my example of wire coating shows. In this case, you would tune your system to avoid droplet formation. As Karin Jacobs of Saarland University explains, "The surface energy of the liquid, its viscosity, the thickness of the liquid film, as well as the diameter of the fiber, play an important role."[5]

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