Science of Building Sandcastles Mysteriously Explained for 150 Years by the “Kelvin Equation” Is Finally Understood

Giant Sand Castle

Water vapor from ambient air will spontaneously condense inside porous materials or between touching surfaces. But with the liquid layer being only a few molecules thick this ubiquitous and important phenomenon has lacked understanding, until now.

Researchers at The University of Manchester led by Nobel Laureate Andre Geim — who, with Kostya Novoselov, was awarded the Nobel Prize for Physics 10 years ago this month — have made artificial capillaries small enough for water vapor to condense inside them under normal, ambient conditions.

The Manchester study is entitled ‘Capillary condensation under atomic-scale confinement’ and will be published in Nature. The research provides a solution for the century-and-half-old puzzle of why capillary condensation, a fundamentally microscopic phenomenon involving a few molecular layers of water, can be described reasonably well using macroscopic equations and macroscopic characteristics of bulk water. Is it a coincidence or a hidden law of nature?

Capillary condensation, a textbook phenomenon, is omnipresent in the world around us, and such important properties as friction, adhesion, stiction, lubrication, and corrosion are strongly affected by capillary condensation. This phenomenon is important in many technological processes used by microelectronics, pharmaceutical, food, and other industries — and even sandcastles could not be built by children if not for capillary condensation.

Scientifically, the phenomenon is often described by the 150-year-old Kelvin equation that has proven to be remarkably accurate even for capillaries as small as 10 nanometers, a thousandth of human hair’s width. Still, for condensation to occur under normal humidity of say 30% to 50%, capillaries should be much smaller, of about 1 nm in size. This is comparable with the diameter of water molecules (about 0.3 nm), so that only a couple of molecular layers of water can fit inside those pores responsible for common condensation effects.

The macroscopic Kelvin equation could not be justified for describing properties involving the molecular scale and, in fact, the equation has little sense at this scale. For example, it is impossible to define the curvature of a water meniscus, which enters the equation, if the meniscus is only a couple of molecules wide. Accordingly, the Kelvin equation has been used as a poor-man’s approach, for the lack of a proper description. The scientific progress has been hindered by many experimental problems and, in particular, by surface roughness that makes it difficult to make and study capillaries with sizes at the required molecular scale.

To create such capillaries, the Manchester researchers painstakingly assembled atomically flat crystals of mica and graphite. They put two such crystals on top of each other with narrow strips of graphene, another atomically thin and flat crystal, being placed in between. The strips acted as spacers and could be of different thickness. This trilayer assembly allowed capillaries of various heights. Some of them were only one atom high, the smallest possible capillaries, and could accommodate just one layer of water molecules.

The Manchester experiments have shown that the Kelvin equation can describe capillary condensation even in the smallest capillaries, at least qualitatively. This is not only surprising but contradicts general expectations as water changes its properties at this scale and its structure becomes distinctly discrete and layered.

“This came as a big surprise. I expected a complete breakdown of conventional physics,” said Dr. Qian Yang, the lead author of the Nature report. “The old equation turned out to work well. A bit disappointing but also exciting to finally solve the century-old mystery.

“So we can relax, all those numerous condensation effects and related properties are now backed by hard evidence rather than a hunch that ‘it seems to work so therefore it should be OK to use the equation’.”

The Manchester researchers argue that the found agreement, although qualitative, is also fortuitous. Pressures involved in capillary condensation under ambient humidity exceed 1,000 bars, more than that at the bottom of the deepest ocean. Such pressures cause capillaries to adjust their sizes by a fraction of angstrom, which is sufficient to snugly accommodate only an integer number of molecular layers inside. These microscopic adjustments suppress commensurability effects, allowing the Kelvin equation to hold well.

“Good theory often works beyond its applicability limits,” said Geim.

“Lord Kelvin was a remarkable scientist, making many discoveries but even he would surely be surprised to find that his theory — originally considering millimeter-sized tubes — holds even at the one-atom scale. In fact, in his seminal paper Kelvin commented about exactly this impossibility.

“So, our work has proved him both right and wrong, at the same time.”

Lord Kelvin

Sir William Thomson, later Lord Kelvin (1824-1907), first referenced his famous equation in an article entitled ‘On the equilibrium of vapour at a curved surface of liquid’ published in 1871 in the Philosophical Magazine. Kelvin’s significant contributions to science have included a major role in the development of the second law of thermodynamics; the absolute temperature scale (measured in kelvins); the dynamical theory of heat; the mathematical analysis of electricity and magnetism, including the basic ideas for the electromagnetic theory of light; plus fundamental work in hydrodynamics.

Reference: “Capillary condensation under atomic-scale confinement” by Qian Yang, P. Z. Sun, L. Fumagalli, Y. V. Stebunov, S. J. Haigh, Z. W. Zhou, I. V. Grigorieva, F. C. Wang and A. K. Geim, 9 December 2020, Nature.
DOI: 10.1038/s41586-020-2978-1

3 Comments on "Science of Building Sandcastles Mysteriously Explained for 150 Years by the “Kelvin Equation” Is Finally Understood"

  1. kamir bouchareb st | December 13, 2020 at 3:24 am | Reply

    very good

  2. Sekar Vedaraman | January 27, 2021 at 10:36 am | Reply

    Extremely interesting and exciting Science.

    Kudos to Lord Kelvin.

    Let us extend this finding to the current Problem Humanity Faces. Covid -19.

    The Blood Flow in the circulatory systems of Humans and mammalian creatures involves blodd flowing through such capillaries in the blood circulatory system , where the same Science would work.

    The Stealth Bomber( C-19) impacts practically all organs in the Human Body and finally also attachs the Carrier (BLOOD) on which it piggybacks to reach these organs and make them
    non-functional. Then it attacks the carrier as well , making it more viscous and impossible to enable flow through the capillaries in the Human/Mammalian circulatory system. Probably, in the treatment of Covid-19 the doctors are prescribing Blood – Thinners as part of the treatment.

    Fits in with the fact that the 104 year old Italian Grandma we saw, who was being wheeled out after recovery from the C-19 Infection and when asked by a reporter what she did right to recover , she answered I ensured that I stayed well-hydrated. Probably kept the blood flowing and kept her alive till the immune system nullifed the Infection.

    Conclusions drawn and opinions expressed are personal and not binding on anyone or be construed as medical advise. These ideas needs to be verified and proved by researchers and Scientists.

  3. Sekar Vedaraman | January 28, 2021 at 2:25 pm | Reply

    Further to the above comment an additional comment for consideration.

    Gets even more interesting when you think about it for some more time from a medical advancement pont of View.

    Capillaries are an integral part of ALL the Six Systems in the Human Body, as well as the mammalian ecosystems. Though humanity has a very great deal of information and knowledge about these cappilaries , the critical nature of the same in the functioning of the Human and Mammalian Body is very poorly understood. TILL NOW.

    This Post will focus on the Digestive System and the Central Nervous Sysytem (CNS) and the role of the Circulatory system in the same.

    The Cells require energy to function optimally. The source of energy is the food we consume , which gets converted into energy by known mechanisms. The blood is the supplier of all such energy and the same is regulated by the Circulatory System.

    The Common element which becomes evident on a close observation of the travels of the C-19 Virus which piggy backs on the back of Blood and travels through the human and mammalian ecosystem and its ability to infect practically every organ in the body are the capillaries present in practically every one of these systems INCLUDING the Central Nervous System.

    I was wondering how the C-19 was able to infect the Controller (Brain) and penetrate the Blood-brain Barrier. The answer is obvious . Capillaries . Hope this insight will be helpful to Medical Researchers and Scentists in banishing ALL Dieseaes caused as a result of Cells going Awry.

    Going back to the Sandcastles we all love to builld in the Sands on the pristine and sometimes highly polluted beaches across the globe. I remember one of my favourtie haunts on the week-ends when I was in New Jersey was Sandy Hook in New Jersey.

    I have watched this scene paly out many times . The Little tykes would build sandcastles and the big bullies would come and kick it down. Especially when the parents had gone for a dip. Well, the reason I am sharing this is because ALL Scientific and Human progress, is built on the many many contributors to Knowledge who have preceded us. We clamber on their shoulders and add one more brick to the same wealth of knowledge —in our own small way.

    The balance between the right of the inventors to benefit from the new knowledge created and to benefit from the same is sacrosanct (vide monopoly rights to exploit the same – Patents) AND needs to be protected BUT balanced with the PUBLIC Good and the right of humanity and all of Gods creation to exist. This is the lesson that the C-19 virus has taught me personally.

    Another lesson we should have learnt long ago after New York State and California State fiasco with chemicals (both have been discussed endlessy in the Media) experience with POLLUTION of the Earth and its consequences on Human Health —- is still not learnt or understood by most of the people across the globe including the USA. High time the wanton pollution of the Planet is stopped. By the way the Pollution of the atmosphere and the environment in the developing world impacts the people in residing anywhere on the planet. Last I heard , I dont think that WIND, Water of other elements whic constitute the components of Mother Nature required a Visa to flow across borders!

    For survival of humanity , many events impact all of us and are global in nature needs to be addressed with Global Co-operation andaddressing ROOT Causes of potential catostrophes. Cannot be done by a single nation.

    VIEWS and Opinions Expressed are perosnal and not binding on Anyone.

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