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Physicists Explore Math Behind Tetris-like Growth of Coffee Rings

Posted on January 19, 2013

University of Pennsylvania physicists are exploring the math behind the Tetris-like growth of coffee rings. The physicists discovered that different particles make smoother or rougher deposition profiles at the drop edge depending on their shape. They also found the growth profiles involved in coffee rings test mathematical concepts that could also be relevant in industrial coating applications. The physicists say in a press release that they are examining two different mathematical processes involved with coffee ring growth. They include "Poisson" and "Kardar-Parisi-Zhang (KPZ)" processes.

• The physicists say that in a Poisson process, a tall stack is just as likely to be next to a short stack as another tall stack. Poisson processes result in a very rough surface because there are large changes in surface height from one column to the next.
• Blocks are stickier in KPZ processes. The physicists explain that when these stickier blocks fall into a column, they don't always fall all the way to the bottom and can stick to adjacent columns at their highest point. KPZ processes result in smoother growth surfaces because it is easier for short columns to catch up to their tall neighbors.