Dispersed systems make it possible to get a lot from a little.
IN MAKING FLANS ONE OFTEN SEEKS, for economic or dietary reasons, to limit the proportion of egg or increase the proportion of water. How far can one go in this direction? Much farther, certainly, than traditional cuisine has yet gone. Let’s begin by analyzing two related cases: making mayonnaise from a single egg yolk and making meringue from a single egg white.
Cookbooks often say that one egg yolk is enough to yield a large bowl of mayonnaise. But in fact the physical chemistry of mayonnaise makes it possible, as we have already seen, to obtain liters of sauce from a single yolk: The quantity of tensioactive molecules in an egg yolk (proteins and phospholipids, equal to about 5 grams) is sufficient to cover a football field with a monomolecular layer; and when these molecules cover oil droplets whose radius in on the order of a micrometer (a millionth of a millimeter), as in the case of mayonnaise, they suffice to stabilize several liters of sauce.
We have also seen that classic mayonnaises break because they do not have enough water to sustain the dispersion of oil droplets. Verifying this claim experimentally is a simple matter, but it means wasting a lot of oil. Instead try making a large bowl of mayonnaise using only a single drop of egg yolk (the source of the tensioactive material) dissolved in a teaspoon of water (or vinegar if you want to taste the result).
A Cubic Meter of Foam
A stiffly whipped egg white is essentially the same thing, only the oil in mayonnaise (which is insoluble in water) has been replaced by air (also largely water insoluble), and the tensioactive molecules that isolate the air are now proteins, which make up 10% of the egg white. The result is no longer an emulsion but a foam. And so our question remains essentially the same: How much meringue can be obtained from a single egg white?
Here again, calculating orders of magnitude is simple. One begins by estimating the number of protein molecules in the egg white. Then one determines the total surface that can be occupied by these proteins and the number of air bubbles that can be covered by these proteins. Multiplying this number by the volume of a bubble, one obtains the maximum volume of meringue that can be made from a single white: several liters, indeed several cubic meters, depending on what assumptions you make about the size of the bubbles and the type of protein coating.
Why, then, does one generally wind up with only a small cubic decimeter of foam? There’s no shortage of air, so the problem must once again be a lack of water. If you add some water to an egg white and whisk you will find that the volume of the foam increases, and if you keep on beating the mixture vigorously you will eventually end up with several liters of meringue. This version is less stable than the classic preparation, however. The stability of a foam depends on the viscosity of the liquid (which is reduced by the addition of water) and the size of the bubbles (which determines the action of capillary forces between the bubbles).
Extreme Flan
The fact that emulsions and foams are both dispersed systems suggests that other such systems found in cooking may display the same behavior. Consider what happens in the case of a quiche. First one lines a baking pan with dough and fills it with cubes of bacon and a mixture of eggs and milk. Yet the cook who skimps on eggs (perhaps because they cost more than the milk) sometimes ends up adding so much milk that the quiche remains liquid after cooking. Because milk is mostly water, the question now becomes: How much water can we add to an egg and still obtain the equivalent of a flan?
Let’s suppose that the proteins responsible for coagulation are spherical. In the course of coagulating they can be assembled either in a compact fashion, so that no water is trapped between them; or next to one another along the edges of a very large cube that encloses a maximum amount of water; or along the edges of a network that, for the sake of simplicity, may be assumed to be cubic.
In the first case, the volume of water enclosed is zero. In the second case, a simple calculation shows that the volume would be impossibly large, on the order of several cubic meters. Let us therefore consider an intermediate case, based on observation of a fried egg using an atomic resolution microscope. This time, an order-of-magnitude calculation leads to a volume of flan—what physical chemists call a gel—equal to a liter.
To check this calculation experimentally, take an egg and add to it an equal volume of water, and then heat the mixture. Having successfully obtained a flan by this method, repeat the experiment while progressively increasing the quantity of water: twice the original volume, three times, and so on. You will discover that almost three-quarters of a liter of water can be made to “gelatinize” with a single egg—the same order of magnitude predicted by the calculation.
The number of different types of dispersed systems is huge. So far we have explored a liquid dispersed in a liquid, a gas dispersed in a liquid, and a solid dispersed in a liquid. But other combinations remain to be investigated.