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Granular Capillarity

June 19, 2017

There are assembly toys for children, such as Lego, but the first construction materials used by children are typically snow and mud. Although much of the world is devoid of snow, even in the local cold season, every child has access to mud. Nearly 10,000 years ago, our ancestors didn't just play with mud, they used mud as adobe to build their houses. The major constituents of adobe, which make about 85% of this material, are silt and sand, both granular materials.

Figure caption

Chefs in training.

Portion of an 1873 oil on canvas painting entitled, "Mud Pies," by Ludwig Knaus (1829–1910).

This painting now resides at the Walters Art Museum, Baltimore, Maryland.

(Via Wikimedia Commons.)


An understanding of granular materials is good for more than making better mud pies and adobe houses. Pharmaceutical powders are made into tablets, and granular materials such as seeds, grains, flour, and cement must be stored and transported. The physics of granular materials has become a popular topic in the last few decades, with more than 3,000 physics papers having the word, "granular," in the abstract posted on arXiv from 2000 to the present.

A few prominent Physicists have investigated the properties of granular materials over the centuries. Faraday (1791-1867), while notable for his work on electricity and magnetism, also discovered the convective instability of powder to vertical motion in a vibrated container. Reynolds (1842-1912) discovered dilatancy, the tendency for compacted granular material to expand in volume when it is sheared.[1-2]

As anyone who has needed to pour powder through a funnel has noticed, jamming is the most annoying feature of granular materials. Jamming occurs because the particles are prevented from flowing past each other since they are held in place by chains of force that lock them against the sides of the funnel. As shown in the figure, the weight of an individual particle is carried by many, but not all, of the underlying particles.

Figure caption

Force chain of stress in a planar granular medium consisting of US nickel coins in a frame of eight inch width.

This is the stress distributed from one of the topmost coins.

(Illustration by the author, via Wikimedia Commons.)


Granular materials exhibit quite a number of unusual properties, the most interesting of which is possibly the Brazil nut effect, the tendency for large nuts to move to the top of a container of mixed nuts after shaking. This phenomenon, of course, extends beyond mixed nuts in their can, and it happens in any vertically-shaken, dry, granular mixture of large and small particles.[3]

Simulation of the Brazil nut effect

Screenshots of a simulation of the Brazil nut effect. Vibration in the vertical direction causes the large object to rise in a sea of smaller objects. (Used with permission from the Granular Dynamics Update Web Site of Prof. Derek C. Richardson of the University of Maryland - College Park. For further information, see ref. 3)]


Another granular phenomenon that I described in an earlier article (Sand Dunes, February 14, 2012) is singing sand, the loud sound made when desert sand dunes avalanche or slump as a result of wind action or human trespass. Desert singing sands produce low frequency sound, but some dry beach sands are known to make high frequency sound when they're walked upon. There is no precise understanding of the mechanism for this, but the sound might arise from a stick-slip friction between rubbing grains.[4]

A granular material effect that's simply produced in the laboratory is the segregation of granular mixtures of different materials as they are poured. This effect, which arises from the combination of friction and triboelectricity, can be observed in a mixture of two different colors of "art sand," found in craft stores, when they are mixed in a shaker and then poured.[5]

Shaking causes electrons to be stripped away from the particles by friction, with some of the charge being lost to the mixing container.[5] The material difference between the particles allows an excess charge to develop on one of the materials, so pouring from the charged container results in a different repulsive force for the materials that causes "unmixing" of the mixture.[5]

One other granular phenomenon, granular capillarity, is the topic of a recent paper in Physical Review Letters.[6-8] Granular capillarity is the ascent of particles in a narrow tube when it's inserted into a bed of vibrating granular material, just as a liquid will rise in a thin tube. This study was a particle-based simulation by physicists from the University of Shanghai for Science and Technology (Shanghai, China), the Friedrich-Alexander-Universität Erlangen-Nürnberg (Erlangen, Germany), and the University of Cologne (Cologne, Germany). It's interesting to note that one of Einstein's first published papers was about capillarity.[9]

Liquid capillarity is caused by the attractive forces between the liquid and the tube wall, and it allows sponges to absorb water and the lifting water to the tops of trees. If a tube is dipped into a granular material, nothing will happen. However, if the tube is shaken, the granular material will rise in it. The mystery is why this would happen, since there's not enough attraction between the granular particles and the tube wall to counteract gravity. Also, the attraction between the molecules in the liquid hold the liquid together while it rises in the tube, but no such force keeps the granular material together.[8] A vibration of just a few particle diameters at a few hertz will result in granular capillarity.[8]

Granular capillarity

Ascent of particles into a tube by granular capillarity. The granular material rises to a terminal vertical level. (University of Cologne image by Fengxian Fan, Eric Parteli, and Thorsten Pöschel.)


Through use of discrete element method numerical simulations, the research team showed that granular capillarity is caused by convection of the granular material in the container.[6-8] In their simulations, they considered a rectangular container that was partially filled with spherical particles about 0.6 millimeter in diameter. A cylindrical tube of 8 millimeter diameter was inserted into the particles.[7] The calculations considered the trajectory of every particle, including the ones outside the tube. This allowed tracking of the velocity and trajectory of all particles.[8]

Vibrating the tube up and down in the simulation caused the particles to rise about 5 centimeter. When the container walls were made frictionless, the particles did not rise at all, indicating that convective motion, as in the Brazil nut effect, was the mechanism for the capillarity.[7] This convective motion causes lateral transport of the particles, and this leads to an upward pressure on the base of the granular column, causing the column to rise.[8]

The speed and height of the granular material's rise in the tube was found to depend on the tube diameter. The terminal height was found to be inversely related to the tube diameter for large ratios of the tube to particle diameter.[7] This inverse functionality is the same found in liquid capillarity.[8] At tube diameters just a few times larger than the particle diameter, linear behavior is observed.[6] The results hold whether the tube or the container is shaken, and this effect might have industrial applications.[8]

References:

  1. Heinrich Jaeger, "An Introduction to Granular Physics," James Franck Institute, University of Chicago Web Site.
  2. Heinrich M. Jaeger, Sidney R. Nagel, and Robert P. Behringer, "The Physics of Granular Materials," Physics Today, vol. 49, no. 4( April. 1996). pp. 32-38, doi: http://dx.doi.org/10.1063/1.881494. A PDF file can be found here.
  3. Soko Matsumura, Derek C. Richardson, Patrick Michel, Stephen R. Schwartz, and Ronald-Louis Ballouz, "The Brazil nut effect and its application to asteroids," Mon. Not. R. Astron. Soc., vol. 443, no. 4 (October 1, 2014), pp. 3368-3380. A PDF file is available here, and also at arXiv.
  4. Vincent Gibiat, Eric Plaza and Pierre De Guibert, "Acoustic emission before avalanches in granular media," arXiv, June 20, 2009.
  5. Amit Mehrotra, Fernando J. Muzzio, and Troy Shinbrot, "Spontaneous Separation of Charged Grains," Phys. Rev. Lett., vol. 99, no. 5 (August 3, 2007), Document no. 058001, DOI:https://doi.org/10.1103/PhysRevLett.99.058001.
  6. Fengxian Fan, Eric J. R. Parteli, and Thorsten Pöschel, "Origin of Granular Capillarity Revealed by Particle-Based Simulations," Phys. Rev. Lett., vol. 118, no. 21 (May 23, 2017), Document no. 218001, DOI:https://doi.org/10.1103/PhysRevLett.118.218001.
  7. Michael Schirber, " Synopsis: Capillary Effect in Grains Explained, Physics, May 23, 2017.
  8. Physicists Discover Mechanism Behind Granular Capillary Effect, University of Cologne Press Release, May 24, 2017. Press Release in German.
  9. Albert Einstein, "Folgerungen aus den Capillaritätserscheinungen," Annalen der Physik, vol. 309, no. 3 (1901), pp. 513-523.

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