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January 21, 2013 • Gear Bits

Physicists Help Show Math Behind Growth of ‘Coffee Rings’


Have you ever left a cup of coffee sitting for a few hours and prior to dumping it out you notice a ring remains at the top-level of the fluid? That is the ‘coffee ring effect’, and recently physicists have helped to demonstrate the effect both theoretically and on the microscopic level.

The studies looked at particle aggregation based on Poisson and Kardar-Parisi-Zhang (KPZ) processes. KPZ is harder to study because any impurities in the experiment will impact the behavior of the system. The combined theoretical and practical study looked at a variety of particle types and shapes as drops dried and measured the way those particles aggregated at the boundary.

In practical terms, the experiment showed that when spheres and highly stretched particles are deposited, surface roughness grows at a high rate. However, when slightly stretched particles are deposited, surface roughness grows at a relatively slow rate.

Here is a cool video showing off the effect:

And here we see both theoretical simulations and the actual process in action:

If you are interested in some of the cooler math details or reading it in full you can head to the Pys. Rev. Lett. article listing. If your company or institution has a subscription (as mine does) you can check out the whole thing. The APS also has a ‘physics focus’ that looks at “Coffee Stains Test Universal Equation.”

Check it out if you can!

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