Does This Rheometer Make Me Look Fat?

hexpacking.png I didn’t manage to get myself scraped off onto this month’s Accretionary Wedge – oh, noes! While I am tragically subducted into the mantle, though, the rest of you can read about the many open questions currently puzzling the geoblogosphere.

Perhaps I can make it into the volcanic arc or something with a late entry about what’s making me go “hmm” this afternoon. It’s related to volcanoes, too: the behavior of glass beads suspended in a zinc iodide solution, spun between two cylinders.

The picture adorning this post is from an article by Völtz et al. in Physical Review E. They spun a suspension of tiny glass beads between two cylinders, and found that under the right conditions, the beads will arrange themselves into sheets of neat hexagons. This arrangement governs the large-scale behavior of the bead-fluid mixture.

Suspensions of perfectly spherical, neutrally buoyant particles are not found in nature, but if you want to find a dense suspension of funny-shaped, not-so-neutrally-buoyant particles, you just need to visit your nearest slush puddle, mud puddle, beach, or crystal-rich magma chamber.

What has me going hmm, though, is not the difference between real mud and glass beads. I’m going hmm about the difference between experimental setups, where you are typically working with a thin layer of fluid (in this case, the gap between cylinders was large enough for perhaps 10-30 glass beads), and the real world, where things are thick and have weird 3D structures. There are good reasons to use thin layers for experiments – it means you don’t have to worry so much about turbulence, and you can get a large region in the middle of your apparatus where conditions are nicely uniform – but I have a hard time imagining neat hexagons appearing in a big wet sandbox. Are our experiments so thin that we’re missing some important 3D structures?



Voltz C, Nitschke M, Heymann L, and Rehberg I, 2002, Thixotropy in macroscopic suspensions of spheres, Phys. Rev. E 65:5, pp. 1539-3755. DOI: 10.1103/PhysRevE.65.051402 .


  1. Lab Lemming wrote:

    Isn’t the difference between experimental design that is relevant to the natural world and that which isn’t the same as the difference between the Journal of Petrology and Physical Review E?

    I’ll try to exhume you before you get too eclogitized.

  2. Benjamin Franz wrote:

    It is infinitely large spherical cows all the way down. :)

  3. Monte Davis wrote:

    …infinitely large frictionless homogeneous spherical cows, if you please.

    But seriously: there are so many hideous complications lurking within the innocent-looking term “bulk effects” that I’m disposed to forgive those laboring over 1D, 2D, and thin-film models. Of course qualitative as well as quantitative surprises will emerge as the models get more realistic… but the track record of “start manageable and build up from there” is pretty good for a species in its infancy (geologically speaking).

  4. Maria Brumm wrote:

    No, they can’t be infinitely large cows! They need to be infinitely smaller than most of the other length scales in the problem (but infinitely larger than Brownian motion).

    Frictionless homogeneous spherical baby hummingbirds should do it.

    I don’t mean to rag on the 2D-ists – I’ve got a very nice plate rheometer downstairs that does the same thing and I fully intend to extrapolate the results to 3D systems. But it’s always good to spend a little bit of thought on the limitations of one’s experiments.

  5. Monte Davis wrote:

    Somewhere in John McPhee’s Annals of the Former World is a splendid analogy for the challenges of stratigraphy — about an ice-cream store next to a carpet warehouse, a fire that collapses/melts them together as the sprinklers drench both, and the poor SOB of an investigator who comes along the next morning to reconstruct what happened.

    As for trying to track the percolating water in real time — well, that’s just craziness, of course.

  6. Maria Brumm wrote:

    As for trying to track the percolating water in real time — well, that’s just craziness, of course.

    I think you mean crazy awesomeness.

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