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Go with the Flow

July 8, 2019

There's a scientific myth that window glass is a liquid, not a solid. The "proof" of this is that windows made during the American colonial period are thicker at the bottom than at the top, as if the liquid glass has flowed downwards over the centuries. Windows of the much older stained glass windows in medieval churches are thicker at the bottom as well.

The stained glass rose window of the Notre Dame cathedral

One of the stained glass rose windows of the Notre Dame cathedral in Paris during better days.

A fire on April 15, 2019, destroyed most of this church, but the three rose windows dating to the 13th century were undamaged.

The glass pieces in such windows are held together by lead channels. Lead melts at ​621.43 °F (327.46 °C), and a hot wood fire can burn at 1000 °F (538 °C)

(Wikimedia Commons image by Rijinatwiki.)

All this makes a good story, since today's glass window panes are exceedingly flat. Their flatness arises from the process of manufacture, the float glass technique in which the soda-lime glass is floated on a bath of molten tin. This process was perfected in the mid-20th century, but from the mid-19th century glass was flattened between hot rollers and then polished. Before that time, glass was blown into large cylinders by traditional glassworking techniques, then cut and flattened. This gave an uneven cross-section, and workers would instinctively mount panes with the thicker end at the bottom.

Solid glass does not flow, but it is unlike most other solids, which are built from small crystallites. Glass is a non-crystalline, amorphous solid. Other glassy materials exist beyond the transparent window glass commonly known. These include Amorphous metals, many of which have useful magnetic properties, and a glassy form of carbon, an extremely useful material. A distinguishing characteristic of glasses is the glass-transition temperature below which atomic movement nearly stops. However, at temperatures just below the glass-transition temperature the atoms will arrange themselves into a crystal structure, but far below that the amorphous glassy structure is locked into place.

A 2013 study of fossil amber by chemical engineers at Texas Tech University (Lubbock, Texas) reaffirmed the conjecture that glass does not flow at room temperature over long periods of time.[1] This research looked at the stress relaxation of a 20-million-year-old specimen of Dominican amber at temperatures just above room temperature to its glass transition temperature. It was found that the atoms of this glass behaved as would be expected of a solid locked into place below the glass transition temperature and kept near room temperature for such an extended period of time.[1]

As is confirmed by everyone's experience with liquids from water to honey, some materials flow faster than others, and the rate of flow is temperature-dependent. As I wrote in an earlier article (Rheometry, November 3, 2011) scientists quantify flow rate with instruments called rheometers, and the science of flow is called rheology.

As early as the 5th century BC, the Greek philosopher, Heraclitus of Ephesus, observed that "everything flows" (παντα ρει). The Roman philosopher, Lucretius (c. 99 BC - c. 55 BC), wrote about rheology in his book, De Rerum Natura (On the Nature of Things).[2-3]

Lucretius, De Rerum Natura (On the Nature of Things), Book II, ll. 391-397.

Lucretius wrote about rheology in his De Rerum Natura (On the Nature of Things), Book II, ll. 391-397.[2] The above excerpt reads in English translation as,"We see how quickly through a colander the wines will flow; how, on the other hand, the sluggish olive oil delays: no doubt, because 'tis wrought of elements more large, or else more crook'd and intertangled. Thus it comes that the primordials cannot be so suddenly sundered one from other, and seep, one through each several hole of anything."[3] (Created using Inkscape. Click for larger image.)

Isaac Newton (1642-1727), proposed a theory of viscosity, the resistance to flow, in his Principia, where he writes, [4-5]
"Resistentiam, quae oritur ex defectu lubricitatis partium Fluidi, caeteris paribus, proportionalem esse velocitati, qua partes Fluidi separantur ab invicem."

"The resistance which arises from the lack of slipperiness of the parts of the liquid, other things being equal, is proportional to the velocity with which the parts of the liquid are separated from one another."

Viscosity is the scientific term for Newton's "lack of slipperiness."

University of Queensland Pitch Drop Experiment

The flow of a very high viscosity material, pitch, is illustrated in the University of Queensland Pitch Drop Experiment.

Hot pitch was poured into a funnel having a sealed end, where it was allowed to set for several years. The sealed end was broken, and the high viscosity pitch was allowed to flow into a beaker.

From 1930 until 2000, only eight drops of pitch flowed into the beaker, illustrating a viscosity that's about 230 billion times that of water at room temperature.

(Wikimedia Commons image, modified.)

In these cases of flow, the materials are actually flowing through another medium, air, that we've ignored. Air does not appear to have any affect, since the density of air, about a milligram per cubic centimeter is more than three orders of magnitude less than that of these materials; so, it's as if these flows are in vacuum. However, when a dense fluid flows onto a fluid that's slightly less dense, such as water onto oil, the shape of the interface between the fluids distorts over time. Lobes of one liquid poke into the other in what's known as a Rayleigh–Taylor instability, named after John William Strutt, the 3rd Baron Rayleigh (1842-1919) and Geoffrey Ingram Taylor (1886-1975).

There's a simple scientific explanation for the Rayleigh–Taylor instability. In nature, a system tends to arrange itself to minimize energy. When lobes of one fluid interpenetrate another and a volume of a heavier fluid is pushed downwards and an equal volume of a lighter fluid is pushed upwards, the potential energy of the system is reduced since these fluid masses are affected by gravity. As Rayleigh found, the energy is further reduced as this interface disturbance grows under the influence of gravity, and Taylor generalized the action to accelerations other than just gravitational acceleration.

A team of mechanical engineers at Lehigh University (Bethlehem, Pennsylvania), led by Arindam Banerjee, an associate professor at Lehigh's Department of mechanical engineering and mechanics, have investigated the dynamics of fluids and other materials as they exhibit Rayleigh-Taylor instability under extreme accelerations.[6-7] Since things happen on a short timescale, not much is known about these conditions.[7]

The Lehigh team perfected their measurement apparatus, a vane-spindle rheometer, over the course of several years.[6-7] Their research involved the incompressible Rayleigh-Taylor instability in elastic-plastic materials. Says Banerjee,
"There has been an ongoing debate in the scientific community about whether instability growth is a function of the initial conditions or a more local catastrophic process... Our experiments confirm the former conclusion: that interface growth is strongly dependent on the choice of initial conditions, such as amplitude and wavelength."[7]

The motivation for these studies is the understanding of two-fluid mixing at conditions relevant to those in inertial confinement fusion.[7] Inertial confinement fusion is the fusion of hydrogen isotopes contained inside centimeter-sized metal spheres. These are excited by high-powered lasers that compress the hydrogen gas to bring its temperature up to several million kelvin to potentially cause fusion.[7] This process happens in just nanoseconds, and the concept is that the melted metal compresses the gas. However, the mixing of the molten metal and gas creates a premature explosion.[7]

In the Lehigh experiments, mayonnaise is used as an elastic-plastic material whose properties are much like that of the molten metal.[6-7] Wave-like perturbations were formed on the mayonnaise before acceleration, and a high-speed camera (500 frames/second) imaged the growth of the perturbations.[6-7]

Perturbation growth

Growth of the interface perturbation with time. (Lehigh University image by Arindam Banerjee)

It was found that the perturbations increased exponentially with time after instability, and three-dimensional interfaces were found to be more stable.[6] In these, and also two-dimensional instability, a decrease in initial amplitude led to a more stable interface in which a higher acceleration was needed to generate the instability.[6-7] Aside from the implications to inertial confinement fusion, these findings are applicable also to geophysics, astrophysics, and industrial processes such as explosion welding.[7] This research was funded by the Department of Energy, Los Alamos National Laboratory and the National Science Foundation.[7]


  1. Jing Zhao, Sindee L. Simon, and Gregory B. McKenna, "Using 20-million-year-old amber to test the super-Arrhenius behaviour of glass-forming systems," Nature Communications, vol. 4, Article no. 1783, April 30, 2013, https://doi.org/10.1038/ncomms2809. This is an open access article with a PDF file available here.
  2. TITI LVCRETI CARI DE RERVM NATVRA LIBER SECVNDVS, Book II, ll. 391-397, Latin Text, via The Latin Library.com.
  3. Lucretius, "On the Nature of Things," Translated by William Ellery Leonard, Book II, ll. 391-397, via Classics.MIT.edu.
  4. Roger I. Tanner and Kenneth Walters, "Rheology: an historical perspective," Elsevier, 1998, 255 pages.
  5. I.S. Newton, "Philosophiae Naturalis Principia Mathematica," 1st Ed., 1687, Bk 2, Sect. IX, Latin text via Project Gutenberg.
  6. Rinosh Polavarapu, Pamela Roach, and Arindam Banerjee, "Rayleigh-Taylor-instability experiments with elastic-plastic materials," Phys. Rev. E, vol. 99, no. 5 (May 8, 2019), Article no. 053104, Rinosh Polavarapu, Pamela Roach, and Arindam Banerjee, "Rayleigh-Taylor-instability experiments with elastic-plastic materials," Phys. Rev. E, vol. 99, no. 5 (May 8, 2019), Article no. 053104.
  7. Lori Friedman, "Behold the Mayo: Researchers Reveal 'Instability Threshold' of Elastic-Plastic Material Using Hellmann's Real Mayonnaise," Lehigh University Press Release, May 8, 2019.

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