Third-year graduate student Nathaniel Goldberg is one of the latest researchers to try his hand at the floppy dish. He works in Dr. Oliver O’Reilly’s lab at the University of California Berkeley, which models all kinds of things—from plant stems to shoelaces—as slender rods, a one-dimensional mathematical construction. Maybe it’s a case of having a hammer and only seeing nails, but Goldberg can’t help but think about rods anywhere he looks. “The other day, I was looking out the window at all the palm trees and started thinking, Wow, that would be fun to model,” he says—so perhaps it was inevitable that his dinner would eventually turn into a scientific paper, recently published in Physical Review E.
Curious about why perfectly straight stands of dry spaghetti transform into a messy knot on the plate, Goldberg decided to tackle the problem as an intellectual exercise. “It was just curiosity,” he admits. “I just saw something and thought, Hey, can I model that?” A dive into the scientific literature and several head-scratchers later, he finally has his answer.
“There are really two things to look at as the spaghetti cooks,” he says. “You can think about what’s happening to a given cross-section of spaghetti, and you can think about what’s happening to the piece of spaghetti as a whole.” As Goldberg discovered, food scientists have already described the process through which a spaghetti strand absorbs water from the outside in and undergoes a chemical change called starch gelatinization—that’s when the starch molecules in the pasta start disconnecting from each other, resulting in a more gel-like texture.
What Goldberg didn’t find was a description of why the noodle changes shape as it swells, transforming from straight-line pitched against the side of the pot to a curled heap on the bottom in nine-to-eleven minutes. “People have worked on totally cooked spaghetti, and they’ve worked on uncooked spaghetti,” he says, “but no one has ever studied how spaghetti deforms as it cooks.” Take a look at the images below:
As this (real) strand of spaghetti shows, when the pasta is cooked in a tall pot it goes through three stages. The first, shown to the left, is a slight sagging, caused by the pull of gravity but resisted by the still-rigid noodle. However, as the pasta absorbs water its elasticity changes, allowing it to settle along the bottom of the pan (middle image). Finally, right as the pasta finishes cooking it curls over, as shown to the right.
According to Goldberg, these cooking stages result in a permanent—if slight—curvature in the pasta, which he was able to model mathematically, though it wasn’t easy. To begin with, the length and diameter of a noodle increase as it absorbs water, changing the strand’s moment of inertia. Water absorption also affects the elastic modulus, which is responsible for spaghetti’s change from stiff to floppy. “From a problem-solving perspective, this is a really challenging thing to formulate numerically,” Goldberg explains. He had to rely on some mathematical tricks, like expressing segments of the strand as fractions, to get a functional model:
This video shows the predictions of Goldberg’s model against an actual strand of spaghetti soaking in water. Although boiling water would have introduced too many complications—vortices caused by convection and the like—this room-temperature soaking approximates the pasta cooking process.
However, the model only worked once Goldberg introduced a term representing the strand’s ability to adjust its mechanical properties based on its ever-changing shape—and as it turns out, the equations match those of a growing plant! Mathematically speaking, the two phenomena are very similar: a rod changing its length, mass, diameter, and curvature in response to environmental conditions. “The analogy is mainly mathematical, but nevertheless there’s a connection there,” Goldberg says.
As for broader implications? “I don’t think this is some groundbreaking, profound work,” Goldberg laughs, “but it’s always good to work on problems that spark people’s curiosity. It was satisfying to me to be able to do it!” It goes to show that when you’re an engineer, dinner is never just dinner.
– Eleanor Hook
“What’s going on in this video? Our science teacher claims that the pain comes from a small electrical shock, but we believe that this is due to the absorption of light. Please help us resolve this dispute!”
(We’ve since updated this article to include the science behind vegan ice cream. To learn more about ice cream science, check out The Science of Ice Cream, Redux)
Over at Physics@Home there’s an easy recipe for homemade ice cream. But what kind of milk should you use to make ice cream? And do you really need to chill the ice cream base before making it? Why do ice cream recipes always call for salt on ice?