Mechanics-based model for the cooking-induced deformation of spaghetti

In this article, we propose a minimal model for the cooking-induced deformation of spaghetti and related food products. Our approach has parallels to the use of rod theories for the mechanics of slender bodies undergoing growth and is inspired by a wealth of experimental data from the food science literature. We use our model to investigate the cooking of a single strand of spaghetti confined to a pot and reproduce a curious three-stage deformation sequence that arises in the cooking process.

Figure 1

Three stages of the cooking process. The black bar in the upper left corner of each image is 1 cm in length. These images of an experiment have been color corrected for clarity. A video of the experiment is included in the Supplemental Material for this paper [4]. (a) Stage 1: sagging, (b) Stage 2: settling, and (c) Stage 3: curling.

Figure 2

The effect of hydration on a typical spaghetti strand's cross section.

Figure 3

Images of the deformed rod at each of the three stages of the simulated process: (a) sagging, (b) settling, and (c) curling. The points $s=0,s={\gamma }_1,s={\gamma }_2$, and $s=L$ are highlighted. The images in this figure should be compared to the experimental results shown in Fig. 1.

Figure 4

Evolution of the height $y\left(L\right)$ of the right endpoint of a spaghetti noodle according to the model (solid curve) and experiment (dashed curve). The inset images show typical shapes predicted by the model during each stage of the deformation. Asterisks are used to distinguish the points $s={\gamma }_1$ and $s={\gamma }_2$. A video comparing the experiment to the simulation can be found in the Supplemental Material accompanying this paper [4].

Figure 5

Experimental length strain versus time at $20{}^{\circ }\mathrm{C}$ as reported by Del Nobile and Massera [27]. A fit based on a logistic curve is superimposed on the data.

Figure 6

Left: experimental time-aspect ratio relationship at $20{}^{\circ }\mathrm{C}$ according to Del Nobile and Massera [27] with a superimposed two-term exponential fit. Right: diameter $d$ as a function of time as calculated from the two-term exponential fit in combination with the logistic curve fit for $\mathrm{\Delta }L$ in Fig. 5.

Figure 7

Left: mass increase versus time as reported by Del Nobile and Massera [27] with our own square-root fit superimposed. Right: linear density as a function of time as computed from using the square-root fit with $m_0=0.1702\mathrm{g}$ in combination with Fig. 5 with $L_0=4.71\mathrm{cm}$.