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An experiment with Mayonnaise
Fermi Questions
Surface volume-density

An extended quote from
The Curious Cook : more kitchen science and lore
by Harold McGee, 1990
from Chapter 8, Mayonnaise: Doing More with Lecithin

Mayonnaise: Doing More with Lecithin

Mayonnaise is a remarkable sauce in two obvious ways: it's produced without the application of heat, and it forms the base of many variations that can be served with a wide range of cold dishes. This "beautiful shining golden ointment." as Elizabeth David has called it, is made by emulsifying a quantity of oil in raw egg yolks [emphasis added, to frame context]. Lemon juice or vinegar, salt and pepper, and sometimes mustard provide the basic seasoning, but mayonnaise can be imbued with many different flavors depending on the dish it's meant to accompany, which might be [...]

While mayonnaise is a wonderfully adaptable sauce, many recipes for it are rather rigid and forbidding, with their intimations of a runny mess if you barely exceed the yolk's capacity for oil. [... ... ...]

The possibility of alternative recipes suggested itself one day when I did a simple experiment to determine the maximum amount of oil that a single egg yolk could emulsify. I had been surprised to find that the small amount of emulsifying material in butter was sufficient to stabilize a beurre blanc unaided. The egg yolk is much richer in these materials, so I wondered whether its emulsifying power hadn't been somewhat underestimated.

Somewhat indeed! Most recipes for mayonnaise peg the limit at about 3/4 cup oil per U.S. Large yolk, and recommend that novices stay well below that. The figure I came up with for that same ordinary yolk was on the order of 100 cups. Something more than 6 gallons of oil! Of course, I didn't just add the oil straight, gallon by gallon; that would have been a waste of oil and work. After adding a certain amount of inexpensive soybean oil, I took a small portion -- around a teaspoon -- of the mixture and then added more oil to just that portion. I repeated this subdivision several times more, periodically adding water to prevent the emulsion from breaking solely on account of crowding. When all the additions and multiplications were done (if a portion containing one-tenth of the yolk absorbs 1 tablespoon oil, then the whole yolk would have absorbed 10), that astonishing figure emerged: 1 yolk, 100 cups of oil. It seemed impossible, so I did the whole experiment again from scratch. There were some differences, but the result was of the same order of magnitude. There can be no doubt that the egg yolk is a prodigious emulsifier.

I then sat down with a pocket calculator and a few numbers from chemistry books and found that this experimental result could easily have been predicted. By weight, and egg yolk is 50% water, 16% protein, and 33% fats and related substances. Of the last, about two-thirds is fat proper, while 5% is cholesterol and a whopping 28% is phospholipids, the potent family of emulsifiers to which lecithin belongs. A single large yolk contains 2 grams of phospholipid and 3 grams of protein (by comparison, a tablespoon of butter contains 0.02 grams of phospholipid and 0.1 grams protein).

The properties of phospholipids have been studied form many years, especially once they were discovered to be the main structural material of the membranes of living cells. It's known that the "head" of the lecithin molecule, the part that projects from the surface of an oil droplet and protects it from other droplets, takes up a surface area of about 100 square angstroms, or 1.6 × 10-15 square inches. Now we make a couple of approximations. First, that all 2 grams of the egg phospholipid are lecithin (the true figure is 1.5 grams, but the other phospholipids are chemically very similar). Second, that the average molecular weight of egg yolk lecithin is 825 grams per mole (a mole is defined as 6 × 1023 molecules). The number of phospholipid molecules in a single yolk is then

2 grams / 825 grams/mole) × (6 × 1023 molecules/mole)
or about 1.5 × 1021 molecules (1.5 times 10 raised to the 21st power, or 15 followed by 20 zeros, or 1,500 billion billion). So the total droplet surface area protected is that number of molecules times 100 square angstroms. It comes out to 1,850 square yards, or nearly a third of the proverbial football field. From roughly 1 tablespoon of egg yolk.

That may seem impossibly large. But two considerations make it sound more reasonable. First, although the area taken up by one molecule is infinitesimal, we're dealing with a tremendous number of molecules. And in essence they're being spread into an infinitesimally thin layer, just one molecule thick. Pull a piece of any material that thin and it will extend over a very large area. In fact, one of the earliest such experiments was done by Benjamin Franklin, and it gives graphic support to our calculations. Franklin's inspiration was his observation, in itself not original, that when a cook tosses greasy water overboard during a sea voyage, the ship's wake is smoothed (hence the phrase "pouring oil on troubled waters"). And as we now know, because oil can't mix with water and is also less dense, it will spread on water into a surface film one molecule thick (if the area of the water is large enough). One windy day around 1770 at a pond in Clapham, near London, as Franklin later wrote,

I fetched out a Cruet of Oil, and dropt a little of it on the Water. I saw it spread itself with surprising Swiftness upon the Surface. ... I then went to the Windward Side, where [the waves] began to form; and there the Oil tho' not more than a Tea Spoonful produced an instant Calm, over a Space several yards square, which spread amazingly, and extended itself gradually till it reached the Lee Side, making all that Quarter of the Pond, perhaps half and Acre, as smooth as a Looking Glass.
Half an acre is about 2,400 square yards; and the eighteenth-century teaspoon held about half as much as a modern one. Franklin's simple experiment demonstrates quite vividly that our calculations are in the right ballpark.

So our egg yolk has about 1,850 square yards of emulsifying power. The question now is, What volume of oil does that droplet surface area correspond to? The answer depends on the droplet size; the smaller the droplets, the more of them there are in a given volume and the greater their total surface area. From various studies it seems that a droplet diameter of 10 micrometers, or about 4 ten-thousandths of and inch, is about average for mayonnaise. Now brace yourself. With that figure, it turns out that when you beat 1 tablespoon of oil into mayonnaise, you break up that single dollop of liquid into 30 billion individual droplets with a collective surface area of about 8 square yards. The phospholipids in a single egg yolk should therefore be able to coat some 7 trillion droplets produced from 230 tablespoons -- 15 cups -- of oil.

Let's stop for a moment to contemplate these numbers. Say you begin with an unbroken mass of 3/4 cup oil and 1 egg yolk. After a few minutes and some exercise of the wrist, you have a mound of some 300 billion oil droplets. These days, astronomers estimate that there are about 100 billion stars in the main body of our galaxy, the Milky Way, which like all spiral galaxies, appears to have been stirred around once or twice. In the past cheesemaking has served as a metaphor for Creation; perhaps saucemaking deserves a look. [...]

Back to our calculated capacity of 15 cups oil per yolk. That's not quite in the 100-cup neighborhood I entered when I tested an actual yolk, but it's some 20 times the limit cited in most cookbooks. Our calculation also ignores the contribution that the egg proteins and cholesterol certainly make to coating the oil droplets, so it's a conservative figure. The bottom line for the cook is this: When you're making a mayonnaise, the last thing you have to worry about is exceeding the emulsifying capacity of the yolk. In most recipes there's a huge safety factor built in. So don't take the dire warnings in recipes too seriously. Still, there is one reason not to stray too far from the standard proportion of 1/2 to 1 cup oil per egg yolk. If you have only 1 yolk but need 2 cups of sauce, the yolk can certainly emulsify 2 cups of oil. The problem, as we'll see in a moment, is that in order to keep the sauce from separating, you would have to supplement the volume of the yolk with water; and water thins the sauce out. The real virtue of the usual proportions is that they produce a thick, weighty, dignified mayonnaise.

To the experimentally minded cook, the 15-cup and 100-cup figures suggest the possibility of developing a very different mayonnaise recipe, one that contains a fraction of the usual amount of egg yolk. Because the yolk contributes an eggy note to the traditional mayonnaise, perhaps such a recipe would produce a lighter flavor, in which the oil and seasonings would be more prominent. To find out, I embarked on a new round of experiments.

From pages 116-121. This quote was hand typed, and thus is likely to contain typos.

On Food and Cooking : the science and lore of the kitchen
is Harold McGee's earlier book. I greatly enjoyed it, it is well thought of, and I should probably add it to the Resources list.


The Inquisitive Cook A newspaper column. "Understanding what ingredients do and how they work together takes the mystery out of cooking. When people know what's happening as a cake rises, a sauce thickens or a steak grills, they become more confident in the kitchen. And that leads to increased success and the freedom to be creative."
Amazon.com page for On Food and Cooking (1997 paperback edition).

A View from the Back of the Envelope
Comments encouraged. - Mitchell N Charity <mcharity@lcs.mit.edu>

My thanks to Alan Bawden for pointing out this chapter.

 2003-Feb-03  Fixed a link.
 1997.Aug.12  Created.
 Add On Food to Resources and/or Deep understanding.
 Add SI units in [brackets],
  thus both simplifying and illustrating their simplicity.
 Comment on his nice scientific method,
  and on where it might have been even better.
 Amazon link to Curious Cook.
 On Food and Cooking paragraph needs more context.
 Crossref to Weisskopf's article?  to m^2/m^3 ?
 Crossref to sphere.  
 Need illustration for folks without the lipid membrane image?