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Heading to physics through a beer glass, darkly
STANFORD -- Pour a tall glass of beer and watch the bubbles stream up from the bottom. Notice that they get larger and are spaced farther apart as they rise. What's going on?
When Stanford University chemistry professor Richard Zare and postdoctoral researcher Neil Shafer asked themselves that question, it led to a whole series of investigations into the interplay among gases, liquids, solids, temperature, pressure and gravity.
"Once you begin to learn about the nature of beer bubbles, you will never again look at a glass of beer in quite the same way," they write in the October issue of Physics Today.
Their study is described by the distinguished physics journal as "serious - well, mostly serious - business."
They explained the link between beer bubbles and raindrops: Both begin as tiny clusters of molecules that grow on rough spots called "nucleation sites" - dust particles in the case of rain clouds, scratches on the glass in the case of bubbling beer. The bubbles form from carbon dioxide, which is dissolved in the beer until pressure is released with the pop of the bottlecap.
Zare and Shafer debunked an earlier theory that bubbles double in size as they rise because of a change in hydrostatic pressure. This would require a pressure difference of 2 atmospheres from the bottom to the top of the glass - a rise of nearly 30 feet. "Not even a yard of ale is that tall," Zare said.
Instead, he and Shafer have shown that the bubbles act as nucleation centers for themselves, accumulating more of the carbon dioxide dissolved in the beer. As the bubbles get bigger, their buoyancy is greater in proportion to the volume of the beer.
This is just Archimedes' Principle applied to beer: Fbubble = Vbubble (pbeer - pbubble)g. (F is the force on the bubble; V is its volume, p is density, g is the gravitational constant.)
Drag on the surface holds the bubble back from rising, but drag increases less rapidly than buoyancy, so the bigger the bubble, the faster it rises. Thus, higher bubbles race away from lower ones in the stream, spacing bubbles further apart at the top of the glass.
The fluid dynamics of this process turn out to be much more complicated than they seem, Zare said. For example, there is no simple method to predict the drag on a particle moving in a viscous medium, and when Zare and Shafer tested the two most likely theories, their observations did not match either one.
Surfactants - the slippery substances that give staying power to the head of foam at the top of the glass - affect the ascent of the bubbles. Even the bubbles' shape changes if they rise in a tall enough glass, from a sphere to an ellipse that oscillates and travels in a zigzag path.
Zare said that the two chemists' excursion into physics and fluid dynamics was purely a spare-time activity. Most of their insights into beer also would apply to other carbonated beverages such as mineral water or champagne - though a serious study of the latter might have been beyond the researchers' budgets.
"I want to point out that no federal funds were used for this research," Zare said with a smile.
"Beer-bubble dynamics (is) a rich phenomenon, worthy of study in the laboratory as well as in the pub," his article concludes. "Bottoms up!"
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