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Beer bubble math

12:50pm, June 10, 2011
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The rate of change of bubble volume. If this quantity is positive, the bubble will grow; if it’s negative, it will shrink.

A constant that depends on the temperature and the specific gas in the foam. (The foam on top of a glass of Guinness lasts unusually long because Guinness uses nitrogen in addition to carbon dioxide in its beer. K is smaller for nitrogen, so the bubbles change size more slowly.)

The sum of the lengths of the edges of the surfaces where the bubble intersects other bubbles. For an isolated bubble, E is 0; for a big bubble surrounded by many little bubbles, it is large.

Any plane one can imagine that cuts through the bubble.

The shape made by the intersection of plane P with the bubble.

The Euler characteristic of the shape P ∩ B.

The symbol for integrating over planes, which allows you to essentially add up the Euler characteristics of every possible way you might slice the bubble.

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