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Physics for breakfast
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When physicist Sidney Nagel sits down to breakfast each morning, he's also doing research-on disordered, nonlinear phenomena. His observations could be a manufacturer's meal ticket.


IMAGE:  Physics for breakfastBreakfast is a messy meal. It involves sticky stuff that drips, like honey or syrup, intended for pancakes but destined for your elbow, gritty granules of sugar that cascade off your quivering spoon, and hot caffeinated liquids that slosh, spill, and stain. Don't blame yourself. Breakfast food, we now know, does not behave properly. Coffee and a roll, hash browns, over-easy eggs, sausage, and a side of toast: these are nonlinear and disordered phenomena, appearing in macroscopic systems far from equilibrium.

Fortunately, Sidney Nagel, the Stein Frieler distinguished service professor of physics, studies nonlinear and disordered phenomena in macroscopic systems far from equilibrium-which is tech talk for the scrambled, agglomerated, unpredictable world we can see and smell and swallow. For ten years Nagel and his students and colleagues have been meditating on the mechanics of this messy morning meal and have begun to unravel the problematic physics of breakfast: why syrups drip, granules avalanche, and coffee forms distinctive stains. Most recently, they have explained-but not corrected-the inequities caused by Brazil nuts.

"These are not just toy problems to hone our skills," says Nagel. "They present significant questions that are tremendously difficult to understand on their own." All of his findings, he adds, "surprise me. In no case has nature arranged things in the ways one might have expected."

Modern physics is usually done at the extremes, asking questions about the imponderably small or the unimaginably vast. Nagel wants to grasp the mysteries that lurk in the ponderable, the imaginable, the pourable, spillable, and edible.

IMAGE:  Physics for breakfast

"How can we maintain that we are inquisitive about the world," he asks, "and yet remain unmoved by the omnipresent occurrences that disturb our daily existence?" These daily disturbances are so ubiquitous that they dominate a wide variety of industrial applications, he insists, from how particles pass through pipes to how paint dries. As it turns out, most of the unanticipated answers to his previously unasked questions have practical applications that go well beyond the breakfast table. Many technological dilemmas, he says, could be solved if only we "knew more about the physics staring at us each morning."


Drip
Trickle
Slosh
Crunch


Drip
Part of the problem is your sweet tooth. The sweeter the breakfast syrup, the stickier-and messier. Around 1990 Nagel began investigating the flow and fissioning of fluids, or what happens when you pour some water and then stop. As the flow slows, the fluid separates into drops, but in ways that are "much more exciting" than his preconceived ideas. High-speed photographs have revealed a series of unanticipated geometric shapes just before and after the "snapoff" point.

Honey and syrup, however, are far more viscous than water; they flow slower and appear tenaciously unwilling to let go. The more sugar the fluid contains, the longer the connecting neck from source to drop. Viscous liquids, Nagel has discovered, produce a series of necks, each smaller and thinner than the last as they slowly stretch. Indeed, Nagel notes, in an observation that may change how ink-jet printers work or how industrial coatings are applied, "We believe that this neck-forming-neck cascade goes on ad infinitum until breakup."

No wonder it gets everywhere.



IMAGE:  Physics for breakfastTrickle
Granular materials, like sugar, oats, or coffee grounds, also behave in "dangerous, obstinate, and unpredictable ways," says Nagel. Grain silos, for example, are prone to collapse because of the unpredictable pressures created by flowing particles. Closer to home, the pyramid of sugar on a teaspoon may seem stable at first, but the slightest tremor on the trip from sugar bowl to coffee cup can trigger a quiet avalanche. The problem is not tenacity but density. For the simplest example, perfectly round particles, density-how tightly the particles pack together-can vary by as much as 15 percent, depending on how the grains settle into place. Packed grains are fairly stable, but the slightest trembling enables the grains near the surface to unpack and dilate slightly-allowing them to flow, off the spoon and onto the table. Where they bounce is another matter.

If this distresses you, don't take a powder. Pharmaceutical companies face the same difficulties transporting substances that sometimes flow like water and other times jam like cement. "It is surprisingly difficult," admits Nagel, "to produce a uniform mixture of powders which have different sizes, shapes, or surface properties."



Slosh
Coffee also behaves in ways that mock intuition, not so much when guzzled as when spilled. Spills, it has long been observed, are thickest at the center, but the stains concentrate at the edge. A thorough investigator, Nagel has shown that this phenomenon occurs with almost any beverage, with or without caffeine, on most hard surfaces, even when dried upside down (in case you slosh something-such as paint-on your ceiling). In the process, he realized that the key was the pattern not of the spill but of evaporation, which occurs more rapidly at the periphery, where slightly more surface is exposed. As the water evaporates, it deposits dissolved coffee particles underneath. Then the remaining fluid flows out from the center to the edge, where it evaporates, forming a neat outline of a messy spill.



Crunch
Science marches on. In the November 15 issue of Nature, Nagel and colleagues pointed out flaws in previous attempts to understand the "Brazil-nut effect," or why the first person to open a box of muesli gets all the big pieces and the last helping contains only crumbled oats. Theorists since the 1930s have blamed smaller grains for slipping into the spaces created beneath larger particles. Others claim that everything rises when shaken but only the smaller bits find room to descend. The Chicago physicists suggested that we can no longer simply blame the little guys; the problem is far too complex.

Not only must grains, nuts, and fruit be considered, Nagel and his colleagues suggest, but also the air between particles. "Our results," they conclude, "indicate an intricate interplay between vibration-induced convection and fluidization, drag by interstitial air, and intruder motion." In other words, both the smaller particles and the air between particles act like fluids, so variations of air pressure within the box alter how the nuts "float." Despite this discovery, no one has yet developed a pressurized cereal box.

IMAGE:  Physics for breakfast

So pull out a napkin and wipe up the morning mess-the syrup, the sugar, the stains. Then crush the napkin, compress it. Squeeze as hard as you can.

 

It's still 75 percent air. Nagel knows why.



Contributing editor John Easton, AM'77, most recently wrote "Consuming Interests" (August/01).




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