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Taking Measure

Just a Standard Blog

Minding your Peas and Carrots: Please Try This at Home

By: Ron Cowen
Zach Levine in his kitchen wearing an orange and white striped apron and chef's hat
Credit: E. Levine

Zach Levine whipping up some peas and carrots. 

NIST physicist Zachary Levine doesn’t cook that often, but when he does it can easily turn into a science experiment.

Two years ago, after he and his wife had endured a week of under-baked cookies and chicken that took forever to roast, Levine wasn’t content to simply recalibrate his oven according to the manufacturer’s directions. In attempting his own calibration, using the boiling point of water as a standard reference, Levine ended up studying the thermal physical properties of water.

More recently, Levine was back in the kitchen, boiling the contents of a frozen package of peas and carrots for dinner, when he noticed something odd: The two vegetables spontaneously parted company, with the peas generally moving to the edges of the pot while the carrots stayed put in the center. Every time Levine stirred the vegetables together — once, twice, three times, four times — they quickly separated, reverting to the same pattern in some 15 seconds.

He had to know why.

For his experiment, Levine placed a frozen mixture of peas and carrots in a 1.5-quart aluminum-bottom pot. Upon heating, the peas and carrots once again separated, although this time the peas floated to one side of the pot while the carrots sank to the bottom of the other side. Later, in the same pot, Levine observed a separation pattern much closer to the one that had originally piqued his curiosity, although the carrots now clumped in a region slightly off-center.

At first Levine thought that the phenomenon might be explained by the tea leaf paradox. In that phenomenon, tea leaves in a stirred teacup migrate to the center and bottom of the cup, even though the stirring would create an outward centrifugal force that would thrust the leaves to the cup’s outskirts. The explanation, as reported by Albert Einstein in 1926, is that the stirring creates a secondary flow, related to friction on the bottom of the teacup. This flow runs counter to and can be stronger than the centrifugal force, keeping the tea leaves centered.

But although that type of secondary flow might account for the distribution of the carrots, and might even be extended to the floating peas, that explanation had a fatal flaw: It required a spoon and did not account for the boiling of the liquid.

Peas and carrots in a pan filled with room temperature water. The peas and carrots are mixed and neither are floating.
Credit: Z. Levine/NIST
Peas and carrots, quantity 100 grams, in 500 milliliters of room temperature water in a 1.4 liter (1.5 quart) aluminum-bottom pan. The peas and carrots are mixed, and neither are floating.
Peas and carrots 256 s after initiation of heat. The peas are  oating on the lower right half of the pan while the carrots are not  oating and are in the upper left of the pan. Temperature, as measured with an optical thermometer, is approximately 70 C.
Credit: Z. Levine/NIST
Peas and carrots 256 seconds after initiation of heat. The peas are floating on the lower right half of the pan while the carrots are not floating and are in the upper left of the pan. Temperature, as measured with an optical thermometer, is approximately 70 C (158 F).
Peas and carrots 323 seconds after initiation of heat. The temperature is approximately 80 C (176 F). The peas have moved about 150 degrees clockwise while the carrots are mostly in the center. A few carrots have begun to float and are mixed with the peas.
Credit: Z. Levine/NIST
Peas and carrots 323 seconds after initiation of heat. The temperature is approximately 80 C (176 F). The peas have moved about 150 degrees clockwise while the carrots are mostly in the center. A few carrots have begun to float and are mixed with the peas.

Pondering the observations further, Levine hit upon the likely solution — a different type of process, known as Rayleigh-Bénard convection. This kind of convection, or heat-driven flow, describes what happens when a horizontal layer of water is uniformly heated from below by a source such as an oven burner. The peas and carrots, Levine hypothesized, were merely tracers of the water’s motion — an upwelling at the center of the pot, a downward flow at the sides, and an inward, center-directed flow at the bottom. (A similar type of motion occurs in a thunderstorm, which is driven by warm air that rises beneath a cloud of water vapor.) Because the carrots and peas have different densities, the two vegetables track different parts of the flow, which would account for their separation.

Aside from the separation of the vegetables, Levine observed other effects, such as the sinking-to-floating transition of the peas, then the carrots. He also found that the carrots do not move until they become hot enough to become buoyant.

While Levine doesn’t have a definitive physical model, he did perform a statistical test known as a chi-square test, which showed that after boiling, there were far fewer peas or carrots mingling with each other than expected if the two vegetables were randomly mixed. Levine reports great joy in finding a probability, or p-value (get it?), of 0.00001, indicating that the separation of peas and carrots he found was statistically significant rather than a random occurrence.

Studying the dynamics of peas and carrots in boiling water could teach students about an emerging area in physics: non-equilibrium pattern formation. If dissertations on the physics of sandpiles and ponytails and treatises on why Brazil nuts always rise to the top of a shaken can of nuts can be published in such prestigious journals as Physical Review Letters, Levine muses, why not a study of peas and carrots?

About the author

Ron Cowen

Ron Cowen has been a science writer and editor at NIST since 2016. When not working at NIST, he’s a freelance writer specializing in physics and astronomy. Last year, he authored his first book, a...

Comments

I wonder if there was any type of experiment where a tank full of several liquid densities was heated and cooled over the surface at various spots?

I don't know about that, but when I was a kid, the Franklin Institute in Philadelphia had a tube of 7 immiscible liquids which, when shaken together, would separate out into a column which looked like a parfait.

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