The following is an article from The Annals of Improbable Research.
by W. M. J. GreCJI, K. L. Westra, K. Robbie, and M. J. Brett
Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta
With the ever-increasing demands of urban life, individuals are ever less able to find time for their fundamental daily tasks. One of the most time consuming activities undertaken during an average day is the preparation of meals: breakfast, lunch, and supper. Our society has increasingly demanded for meals that are quick to prepare, yet nutritious. As a result, we now have dishes such as instant rice, microwave dinners, and minute noodles and soups.
In this article, we present a novel addition to the "fast food" lineup. Dubbed "Nanopasta" for its small size and phenomenally rapid cooking time, this new variety of pasta can be produced with the aid of a thin film deposition technology known as glancing angle deposition1 (GLAD).
Nanopasta is made by evaporating Durum wheat in a vacuum. The vapor is then directed at glancing incidence toward a rotating substrate. The schematic in Figure 1 illustrates this process, which is also currently used for other materials.2 Once Nanopasta has been deposited on the substrate, it may be harvested by a special etching process. Figure 2a shows a scanning electron microscope image of one shape, called Nano-fusilli. The photo illustrates the nanometer size scale of Nanopasta. Figure 2b shows an image of a Nano-fusilli film immediately after deposition but before the etch harvesting process. The substrate shown in the image is a silicon wafer.
Theoretical Background-AI Dente's Ratio
Theory indicates that the most efficient way to cook dry pasta is to immerse it water that is at the boiling point. Depending on the variety and shape of pasta being prepared, the cooking process may require a relatively short or long period of time.
Experiments have shown that the degree to which a given type of pasta has been cooked -or equivalently, its tenderness- is a function of the amount of boiling water absorbed during the cooking process. The greater the mass of absorbed water, the more tender the pasta will be.
Figure 2. Scanning electronic microscope images of a variety of Nanopasta known as Nano-fusilli. Note the scale bars in the lower right comers of each image. (left) An image of individual Nano-fusilli noodles, taken after the harvesting process. (right) A film of Nano-fusilli deposited onto a silicon wafer substrate, shown as it appears prior to etch harvesting.
There exists an ideal ratio of absorbed water mass to dry pasta mass, hereafter referred to as AI Dente's ratio3. As any textbook can tell you, the value is 1:2. Any type of noodle, independent of shape, having such relative proportions of water and dry pasta mass is assumed to be properly cooked.
The cooking time required for a given pasta to attain AI Dente's ratio is strongly dependent upon its geometry, especially its surface area per unit mass. Consider a cylindrically shaped pasta, such as the spaghetti shown in Figure 3a. The surface area per unit mass of this solid shape can be calculated using elementary mathematics. Now consider a second cylindrically shaped pasta, specifically the Nano-capelli in Figure 3b, such that the cross-sectional diameter is much smaller than that of Nano-spaghetti. Performing the same calculations as before, one finds that the surface area per unit mass of Nano-capelli is much larger than that of Nano-spaghetti. (This relationship is of course true of macropasta, too.)
Figure 3. Samples of pasta shapes in this experiment (left) spaghetti, (right) capelli.
The larger the surface area per unit mass of a given Nanopasta, the greater the amount of boiling water which is able to surround the Nanopasta at any given time. Greater interaction enables more rapid cooking. Thus the cooking time, t, of a given pasta is inversely proportional to the pasta’s surface area per unit mass, denoted δ. The functional dependence of these two variables can be written as follows.
t, = Kδ"
where: t. = cooking time (s)
δ = surface area per unit mass (cm2/g)
K, α = fitting parameters
Once the constants K and α are determined, it is easy to calculate the cooking time of any Nano-pasta with a known surface area per unit mass. The validity of this model is supported by the fact that the cooking time asymptotically approaches zero as δ grows large. No physically impossible results, such as negative cooking times, are implied by this model.
The Nanopasta Experiment
Currently, in our research laboratory it is time-consuming to manufacture macroscopic quantities (i.e. grams) of Nanopasta through the GLAD process. Thus, a direct study of Nanopasta will always be difficult until someone has developed the proper manufacturing equipment.
As an alternative, we have performed experiments to evaluate the cooking times of several types of macroscopic pasta, including varieties such as spaghetti, fettucine, capelli, macaroni, and fusilli. A curve can be fitted to the data gathered from these experiments, giving the values of the constants K and α. The cooking time of Nanopasta can then be derived by extrapolation.
We considered many methods for evaluating the tenderness and cooking times of macroscopic pasta,4 but the majority proved to be overly complex or lacking in accuracy. Therefore, we exploited the fundamental principles of pasta theory to generate a series of simple, reliable experiments to measure pasta tenderness and cooking time.
First, we experimentally determined the value of Al Dente's ratio. Approximately 50 grams of uncooked fusilli (chosen arbitrarily) was boiled until the desired tenderness was reached. The cooked sample was then weighed to find the mass of water which the pasta had absorbed. From these measurements, AI Dente's ratio for cooked pasta was found to be 1.2 grams water per gram of pasta.
Figure 4. Surface area to mass ratios and experimentally determined cooking times of various pastas.
Second, 50 gram samples of the five different pasta shapes listed above were boiled for a period of 15 minutes each. Samples were taken at regular intervals and weighed to find the mass of water absorbed. For each sample, we evaluated the ratio of absorbed water to pasta mass, and compared it to Al Dente's ratio. Extrapolating the data obtained, it was possible to find the cooking time required for each pasta.
Figure 4 shows both the surface area-to-mass ratios and the experimentally calculated cooking times of each macroscopic pasta shape. The same ratio was calculated for the sample of Nano-fusilli shown in Figure 2a, and appears at the bottom of the table.
The extremely small size scale of Nanopasta makes its surface area to mass ratio many orders of magnitude larger than that of macroscopic pasta. Figure 5 contains a plot of the data in Figure 4. As predicted by theory, the surface area to mass ratio δ and the cooking time t were found to have an inverse relationship. The fitting parameters K and α were experimentally found to have values of 2.5s 104 and 1.4 respectively.
From the equation of the curve, the cooking time of the Nano-fusilli shown in Figure 2a) was calculated to be approximately microseconds. It should be noted that the fine structure of Nanopasta can be specifically tailored by the GLAD deposition technology, making a large range of cooking times possible.
Figure 5. Cooking time tc versus surface area to mass ratio s. The versatility of the GLAD deposition technology makes a wide regime of Nanopasta cooking times possible.
Let's sum up our findings.
We analyzed several shapes of macroscopic pasta to experimentally evaluate the cooking time of
Nanopasta. The particular sample of Nano-fusilli studied in this article was found to have a cooking time of 30 μs. An effort to produce other varieties of Nanopasta, such as Nano-spaghetti and Nano-lasagne, is currently underway.
The development of Nanopasta represents a significant step forward in the drive to produce nutritious meals which do not require a great deal of preparation time. People will now be able to spend less time cooking, and will be free to devote more time to pursuing their careers, social interests, and family lives.
A side benefit of Nanopasta's incredibly short cooking time is that household electricity consumption should decrease dramatically. Consumers who use electricity solely for cooking can expect a millionfold decrease in their monthly bills.
A Colorful Future
In addition to serving as a healthy source of nourishment, Nanopasta has also exhibited several other interesting properties, including surprising optical activity leading to brightly colored food that has no artificial color additives. These and other properties are currently under investigation.
(Image credit: Shuhrataxmedov)
1. "Sculptured thin films and glancing angle deposition: Growth mechanics and applications", K. Robbie, M. J. Brett, Journal of Vacuum Science Technology, vol. 15, 1997, pp. 1460-5.
2. "Chiral sculptured thin films", K. Robbie, M. J. Brett, A. Lakhtakia, Nature, vol. 386, December 19/26, 1996.
3. Named after AI Dente, renowned pasta theoretician.
4. The authors originally considered throwing partially cooked pasta against a wall, and using the corresponding "sticking coefficient" as a means to evaluate its tenderness. However, we found that this coefficient was strongly dependent upon the physical properties of the wall in question. As such, it would be unreliable.
This article is republished with permission from the January-February 2000 issue of the Annals of Improbable Research.
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