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Rivers of Sand

December 22, 2014

Scrooge McDuck, known as Uncle Scrooge to his grandnephews, Huey, Dewey, and Louie, began his cartoon existence as a miserly business magnate. Over the years, Scrooge morphed into a more lovable character, as Disney started to distance itself from cartoon stereotypes, such as the Scots being a miserly people. Today, even the stereotype of the Disney princess yearning for her husband prince is being replaced by strong-willed cartoon cuties.

One of Scrooge's favorite activities was to dive into his money pit for a swim.[1] This may have worked if his wealth was in loose, paper currency, but he was diving into metal coinage. This ill-advised activity didn't seem to injure him, proving again that cartoon physics is different from our own. Another example of this is when a character (e.g., Wile E. Coyote) walks off a cliff and is suspended in air for a few seconds before discovering what he had done.

Ebenezer Scrooge at a fireplace, from a John Leech illustration for  Charles Dickens, A Christmas Carol.

The likeness of Scrooge McDuck is copyrighted, so you'll need to visit elsewhere for his image, or see ref. 1.

Instead, here's an illustration of his eponym, Ebenezer Scrooge, sitting at a fireplace, from a John Leech illustration for Charles Dickens', "A Christmas Carol."

(Detail from "A Christmas Carol in prose," Chapman & Hall, London, 1843, British Library, accession number C.58.b.7, opposite 25, via Wikimedia Commons.)


The particles in Scrooge's money pool, the coins, are large and have quite a bit of relative friction, so they don't move easily against each other to allow entry of a duck's body. Diving into liquid water from a reasonably small height is safe, since the particles that comprise water, the water molecules, are small and glide easily against each other. The inter-molecular spacing of water molecules is about 400 picometers (pm), so we can say that the radius of a water "particle" is about 200 pm. This is 25 million times smaller than the centimeter radius of a typical coin. Strange things are known to happen in the region between these extremes, at the dimension of granular materials.

Sand is a very common granular material on the Earth, and sand illustrates some of the strange properties of granular materials. As I wrote in a previous article (Sand Dunes, February 14, 2012), piles of beach and desert sand emit sound when they avalanche from wind or human action. These singing sands in deserts emit a low frequency sound, but some dry beach sands make high frequency sound when they are walked upon. The presumed mechanism is stick-slip friction between rubbing grains, similar to the action of a violin bow rubbing against a string.[2]

The well-known Brazil nut effect is the tendency for large nuts to move to the top of a container of mixed nuts after shaking, but the phenomenon is not restricted to nuts. It will happen in any vertically shaken dry, granular mixture of large and small particles. Unlike water flow, the flow rate of sand through an hourglass is independent of the height of the sand in the upper chamber. A conical sand pile will exert the highest pressure at the base, not at its center, but in a ring at one third the radius of the base.

Brazil nut

The Brazil nut, Bertholletia excelsa. I was always interested in the seams of the shell, and the fact that the seed shape was smooth, while the shell shape was angular. (nut image, left, and seed image, right, via Wikimedia Commons.)


Rubbing things together often produces electrical charging because of the triboelectric effect. If two colors of "art sand" (as found in craft stores) are mixed in a shaker and then poured into a beaker, the different colors will segregate. Shaking will give both types of particles a positive charge as electrons are stripped away by friction, but one color will lose electrons more easily than the other. Since one color is more positively charged than the other, the repulsive force of the electrical charge will "unmix" the mixture.[3]

One granular phenomenon, discovered more than a decade ago, but still unexplained, is the "sand river" that only manifests itself for certain sands.[4-9] If you pour a steam of sand from Santa Teresa, Cuba, and just a few other places, onto a flat surface, a pile forms as expected. After that, the pile grows in an unexpected way. A river of sand forms from the apex of the conical pile, flowing to the base, and rotating around the pile to build more conical volume.[4-5]

When the pile grows larger than a certain size, the river flow becomes intermittent. Although a river still rotates around the pile, undulations form on the surface of the pile as a result of the intermittent flow. An understanding of the transition between the continuous and intermittent flow has been explained through experiment, allowing construction of a “dynamical phase diagram." The mechanical reason for the river behavior is that a build-up of sand to one side, or the other, forces the river in a certain direction, but the underlying mechanism as to why is unknown.[6-8]

Sand rivers, smooth and undulating

Photographs of a typical sand river (left), and a sand river after the point of undulation (right). The diameter of the left pile is 11 cm. The diameter of the right pile is 17 cm, and the undulations stop about 6 cm from the edge of the pile. (Fig. 2 of ref. 7, redrawn, via arXiv.)[7)]


The sand river phenomenon was noticed by physicist, Ernesto Altshuler, of the University of Havana in 1995. Altshuler's home page has more information about the phenomenon.[10] What's especially interesting about the phenomenon is that it will only happen in fresh sand. If you use the same batch of sand again and again, it stops making sand rivers.[8]

References:

  1. Ted Johansson, "Uncle Scrooge - The Daily Money Swim," YouTube Video, March 16, 2010.
  2. Vincent Gibiat, Eric Plaza and Pierre De Guibert, "Acoustic emission before avalanches in granular media," arXiv, June 20, 2009.
  3. Amit Mehrotra, Fernando J. Muzzio, and Troy Shinbrot, "Spontaneous Separation of Charged Grains," Phys. Rev. Lett., vol. 99, no. 5 (July 31, 2007), Article No. 058001.
  4. E. Altshuler, O. Ramos, A.J. Batista-Leyva, A. Rivera, and K.E. Bassler, "Sandpile formation by revolving rivers," Phys. Rev. Lett., vol. 91, no. 1 (July 3, 2003), Article No. 014501, DOI: http://dx.doi.org/10.1103/PhysRevLett.91.014501.
  5. E. Altshuler, O. Ramos, A.J. Batista-Leyva, A. Rivera, and K.E. Bassler, "Sandpile formation by revolving rivers," arXiv, June 25, 2002.
  6. E. Altshuler, R. Toussaint, E. Martinez, O. Sotolongo-Costa, J. Schmittbuhl, and K. J. Måløy, "Revolving rivers in sandpiles: from continuous to intermittent flows," Phys. Rev. E, vol. 77, no. 3 (March 17, 2008), Article No. 031305, DOI: http://dx.doi.org/10.1103/PhysRevE.77.031305.
  7. E. Altshuler, R. Toussaint, E. Martinez, O. Sotolongo-Costa, J. Schmittbuhl, and K. J. Måløy, "Revolving rivers in sandpiles: from continuous to intermittent flows," arXiv, November 6, 2007.
  8. Esther Inglis-Arkell, "How This Special Sand from Cuba Created a New Physics Phenomenon," io9, October 28, 2014.
  9. Strange phenomena in sands --revolving rivers, YouTube Video, Oct 27, 2010.
  10. Home page of Ernesto Altshuler, Professor and Director of the 'Henri Poincare' Group of Complex Systems & Superconductivity Laboratory at the University of Havana.

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