ONE OF the most difficult sauces to prepare is sauce béarnaise, a warm emulsified concoction consisting primarily of dilute vinegar, wine, egg yolks and butter. For many cooks the blending of this sauce verges on alchemy. The difficulty is not only that the preparation is demanding but also that even when the preparer seemingly does everything right, the sauce can still go bad, coagulating into a repellent mess.

Two recent scientific papers have discussed how to salvage a coagulated sauce béarnaise. C. M. Perram, C. Nicolau and J. W. Perram argued in Nature that a coagulated sauce can be resurrected by adding a small amount of dilute acetic acid (vinegar) and then stirring the sauce vigorously. (The word coagulated may be incorrect. The authors probably meant to describe a reversible aggregation of the droplets of butter in the sauce true coagulation is irreversible.) The stratagem of adding an acid appears to have been known earlier; Julia Child, the popular cooking expert, has recommended adding lemon juice (citric acid) to rejuvenate the sauce.

The second paper was published in The New England Journal of Medicine by D. M. Small, a biochemist in Boston, and Michael Bernstein, a chef at a French restaurant in Rochester. They point out that the pH of the solution (the measure of its acidity or alkalinity) appears to have no effect on the temperature at which the sauce goes bad and hence that the addition of an acid to prevent coagulation is unnecessary. Instead they recommend that the sauce be briskly stirred into a clean container with a small amount of water. Some of my own cookbooks make a similar recommendation.

Which technique is correct? Does the acid level matter? Why is sauce béarnaise so hard to make? Why does it go bad? To answer these questions one must first understand the physics and the chemistry of the sauce, both of which are fairly complex and not yet fully understood in fundamental terms. Here I shall describe what I understand of the sauce in terms of emulsions and colloidal suspensions. If you pursue the subject, you can correct and expand my picture. Recipes for preparing the sauce vary slightly, differing primarily in the method of mixing in the egg yolks and of heating the sauce. I shall follow the recipe outlined as the "professional method" in The Making of a Cook, by Madeleine Kamman. (This fine cookbook actually explains some of the science involved in cooking.) Kamman's list of the ingredients for the sauce appears in the illustration at right.

The first task is to make an infusion o wine, vinegar, shallots, 1-l/2 teaspoons o tarragon, one teaspoon of chervil, three teaspoons of fresh parsley, a bay leaf, salt and white pepper. The infusion is cooked over low heat until only five teaspoons of liquid remain when you press the herbs with the back of a spoon. The egg yolks are added and the mixture is stirred with a wire whisk over low heat until it is thick. Kamman warns that if the pot is thin, a pad of asbestos or metal should be put under it to protect the mixture from hot spots and rapid heating. If the mixture is overheated at this stage, the product will amount to scrambled eggs (actually denatured egg yolk floating on an infusion of herbs.

The mixture is removed from the heat and the warm butter is dribbled into it. The butter must be added in a slow stream to facilitate the making of an emulsion. If it is added too quickly, it will separate into a layer. Once the butter is added the emulsion is drained through a coarse strainer into a warm bowl. The strainer should be sufficiently fine to remove the herbs but not the butter droplets.

After preparing the basic emulsion you make a mixture of the remaining herbs. Mix one teaspoon of tarragon and one teaspoon of chervil into a tablespoon of boiling water. Add the rest of the parsley and a good pinch of cayenne pepper. (Kamman defines a good pinch as the amount "you can pick up on the tip of a paring knife.") Everything is added to the strained sauce. The sauce is to be served warm to accompany broiled red meats, chicken, fish and even poached eggs.

The sauce can be described as a colloidal suspension of solid or semisolid particles, mostly the fat of the butter, in a liquid medium of water, acetic acid, salt and various other ingredients. Colloidal suspensions are characterized by having particles with diameters of between one micrometer and 100 micrometers. The term colloidal is usually reserved for a suspension of solid particles in a liquid, but it is also employed loosely for the sauce in spite of the semiliquid nature of the particles. The term emulsion also describes the sauce, since sauce béarnaise is a dispersion of two immiscible liquids (butterfat and water), with one of them forming droplets in the other.

Regardless of terminology, the stability of the sauce depends on the correct interplay of the forces holding the particles or droplets in suspension. A failure of the sauce to turn out right arises because the delicate balance of those forces can be broken by variations in the ingredients or by careless overheating of the sauce. Both papers agree that attractive forces operate to aggregate the suspended particles or droplets, but they disagree on the nature of the repulsive forces countering the attraction. Each paper may be partly correct.

According to Perram, Nicolau and Perram the colloidal particles are micelles (electrically charged aggregates of large molecules) consisting of phospholipids, fats, proteins, cholesterol and several long-chain fatty acids. The particles are hydrophobic, so that they do not bond to water, and globular. (These descriptions may not reflect the usual terminology employed for colloids. The contention of these authors that the particles are lyophobic, that is, do not bond to the liquid medium, is an important concept to question later on.) The authors do not consider the possible role of the wine in the sauce, instead regarding the liquid medium as consisting of water, acetic acid, sodium chloride and dissolved molecules from the herbs. For the sake of simplicity I shall disregard both the wine and the herbs. Although these ingredients may be important to the science of the sauce, most of the interesting features of emulsions and colloidal suspensions can be displayed without them.

Perram, Nicolau and Perram think the key to the stability of the sauce lies in two electrical interactions of the colloidal particles, a repulsive Coulomb force and an attractive van der Waals force. The van der Waals force is a relatively weak one attributable primarily to the attraction between electric dipoles in two neighboring colloidal particles. Consider an electrically neutral molecule. If the centers of positive and negative charge in the molecule coincide, the molecule would display no external electric field. If the centers are separated, they constitute an electric dipole. An external electric field would arise even though the molecule itself is electrically neutral. Two such neighboring molecules can arrange themselves so that their electric dipoles attract each other, creating an attractive force between the molecules.

A molecule can have an electric dipole for three possible reasons. First, the charge distribution may be such that a dipole is always present. Second, a non-spherical molecule may have a dipole induced by a neighboring molecule that has a dipole. Third, quantum-mechanical fluctuations in the charge distributions may give rise to induced dipoles in two neighboring molecules.

The molecules of a colloidal particle will tend to align themselves so that they give the particle a net dipole. Hence neighboring colloidal particles will be attracted to one another by the van der Waals force between them. Specialists in colloids often call this force a dispersion force. I find the term misleading, since the force is attractive.

The van der Waals forces between the particles in sauce béarnaise are relatively weak and so do not come into play unless the particles are quite close. With a microscope one sees that the particles are normally close enough for this force to be important. If the sauce is kept cool, the colloidal particles are unlikely to touch one another with a frequency that would allow the van der Waals forces to make them coalesce into pools of butter. The sauce is heated during its preparation, however, and is served warm. The thermal motion of the molecules of the sauce sets the colloidal particles in Brownian motion. A warm sauce is likelier to coalesce because the Brownian motion makes collisions between particles more frequent.

The authors of the two papers differ primarily in their description of what prevents coalescence. Perram, Nicolau and Perram contend that a second electric interaction between neighboring particles counters the van der Waals force. Adhering to the surface of each particle is a layer of charge derived from the ionized molecules fixed to the droplet or from ions collected out of the liquid. These authors believe the colloidal particles in the sauce have a negative surface charge. Outside the surface is more negative charge, but its concentration decreases with distance. In the fluid layer adjacent to the surface is a positive charge distributed so that the net electric potential is increased from its value on the surface of the particle to the value of the liquid at a distance from the surface. This arrangement of charges is called a diffuse double layer because of the intermixing of opposite charges. When two colloidal particles attempt to collide (because of the thermal motion and the van der Waals force), repulsion develops as their atmospheres of charge begin to overlap. The nature of the repulsion is the same as that of any electrostatic (or Coulomb) repulsion between charges of the same sign. The particles can aggregate only if the repulsion cannot prevent them from touching.

When warm (not overheated) sauce béarnaise fails, the reason may be an insufficient surface charge on the colloidal particles. With less surface charge the diffuse double layer is less charged and the particles can collide and adhere. Perram, Nicolau and Perram maintain that the negative charge on the butter droplets is due to the adsorption of ionized acetic acid provided by the vinegar. This argument is open to question, since the volatile acetic acid may be partly lost as the infusion is heated before the egg yolks are added.

Although the role ascribed to the attractive van der Waals force is likely to be correct, the one ascribed to the acetic acid may be wrong. Another way to view the sauce is as an emulsion of butterfat and water, which become emulsified because of an ingredient of the egg yolk. Whereas the acetic acid is responsible for the stability of the lyophobic suspension of micelles in Perram, Nicolau and Perram's model, it is the yolk to which I shall now turn as the source of the stabilization in a lyophilic suspension that involves bonding between the particles and the water.

Unfortunately no one overall explanation of emulsions is available, but the major theories are grouped into two classes. One set of theories emphasizes the geometrical arrangement of the molecules on the surface of the droplets and the strength of the film of molecules at the interface of the two liquids. The other set, which is quite similar to the theories involving true colloidal suspensions, argues for an electric interaction between the particles. The connection between these two approaches to emulsions is hazy. The stability of sauce béarnaise may involve components of both theories. I think the difference between the two papers on the sauce reflects this difference in the theoretical explanations of emulsions.

To create the emulsion of water and butterfat in the sauce one adds egg yolks to provide the emulsifying agent for the two immiscible liquids. Generally such emulsifying agents have two purposes. One purpose is to lower the surface tension at the interface of the two liquids so that droplets of one of them can form. The other is to stabilize the droplets, preventing them from aggregating and coalescing and thereby separating into layers. In an emulsion of oil and water the molecules of the emulsifying agent will usually have on one end a lipophilic group, which is attracted to the butterfat. Normally the other end has a polar group, which is attracted to the water. (A polar molecule has its negative charge permanently separated from its positive charge. Because water is polar a molecule of water and another polar molecule can orient themselves so that they electrically attract each other.) In the sauce the butter droplets are covered with the emulsifying agent lecithin, which is provided by the lipoproteins in the egg yolks. The lecithin orients itself to present its polar end, called livetin, to the water and its lipophilic end to the butterfat droplet. In the conventional terminology of colloidal suspensions this arrangement is termed lyophilic because the particles (droplets) bind the liquid medium (in this case water) to their surface.

The layer of water molecules surrounding each droplet helps to prevent it from coalescing with other droplets. Although the water molecules are held in place by an electric interaction between polar molecules, this preventive effect is not due to the electric interactions between colliding particles I described above. In that instance the two particles were repelled from each other because of the electrostatic repulsion between the diffuse double layers on each particle. This time the preventive effect comes from the strength of the film of water molecules held in place on the drops, preventing the drops from touching and coalescing.

If the lecithin carried a charge, it could also create a diffuse double layer around each particle. Presumably two colliding particles would then be kept from coalescing by the electrostatic repulsion from their diffuse double layers and by the protective coating of bound water molecules. Small and Bernstein point out that lecithin is uncharged in a medium with a pH of 6, which is the pH of sauce béarnaise. Without a charge it would appear that the lecithin from the egg yolk protects the sauce against aggregation because of the layer of water it binds rather than because of an electrostatic repulsion.

An example of an emulsion involving an electrostatic interaction is oil and water emulsified with soap. A molecule of soap on the surface of an oil droplet orients itself so that its lipophilic component is toward the oil and its polar component, which is a negatively charged carboxyl group, is toward the water. Part of the strength of the emulsion may lie in the strength of the film of water molecules held in place around the oil droplet. Part is also due to the particular arrangement of charge at the surface. The negative carboxyl group, which is fixed to the surface of the droplet, attracts positive ions (such as potassium in a potassium soap) that lie in the liquid layer just outside the surface. The double layer of negative and positive charges therefore provides an electric repulsion between two colliding drops, and in this way it prevents them from coalescing.

Mayonnaise is another common emulsion (although the medium is semisolid rather than liquid), consisting of vegetable oils in dilute vinegar or lemon juice. Its emulsifying agents are egg yolks, extra lecithin and other additives. Mayonnaise is an oil-in-water emulsion. So is sauce béarnaise, although Small and Bernstein describe it more adequately as an oil-and-air-in-water emulsion because of the air whipped into the mixture to lighten the sauce.

Recipes for sauce béarnaise have traditionally called for the use of fresh eggs. Although this requirement may be partly based on personal preference, it could have some basis in the aging of the emulsifying molecules. If a yolk is to function well as an emulsifying agent in an oil-in-water emulsion, it must have a fairly high ratio of lecithin to cholesterol. Whereas the lecithin serves as an emulsifying agent for oil-in-water emulsions, cholesterol is an emulsifying agent for the opposite, a water-in-oil emulsion. When an egg is stored for any length of time, its lecithin apparently breaks down but its cholesterol does not. The ratio of the two is therefore reduced and the yolk does not serve as well in oil in-water emulsions such as sauce béarnaise and mayonnaise.

Two types of aggregation can be seen in sauce béarnaise. If the aggregation is reversible, it is called flocculation. If it is irreversible, it is called coagulation. The physical differences between the two are not well understood, and I am not certain that coagulation in the sauce involves anything more than the denaturing of the proteins from the egg yolks.

Small and Bernstein tested the temperatures at which the sauce will flocculate and coagulate. When they prepared a sauce with water instead of vinegar, the sauce flocculated at about 70 degrees Celsius (158 degrees Fahrenheit) and appeared to coagulate at temperatures between 70 and 80 degrees C. On coagulation the cooked egg floated to the surface. When the investigators tested a sauce prepared with the normal amount of vinegar, flocculation developed at about the same temperature, but coagulation was not observed even at 90 degrees.

Since the addition of vinegar did not alter the temperature of flocculation, Small and Bernstein concluded that the vinegar plays no role in preventing flocculation at lower temperatures. This conclusion could be wrong, however, if one argues (as is done in theories of colloidal suspensions) that when the sauce is heated, the impact of molecules on a particle eliminates the net charge on its surface, thereby compressing its diffuse double layer and making flocculation more likely. Hence one expects about the same temperature for flocculation regardless of the role of acetic acid at temperatures below the flocculation temperature.

The thickness of the diffuse double layer surrounding the particles depends on the inverse of the square root of the concentration of ions in the electrolyte (an ionic solution). If the ion concentration is increased, the layer is compressed. At first flocculation would seem to be likelier, but the situation is probably not that simple. If an electrolyte is added to a lyophobic colloidal suspension (one that does not involve binding the liquid), one of three things can happen: (1) more charge can be adsorbed onto the surface of the particles, thereby increasing the surface charge and thickening the diffuse layer; (2) the electrolyte can neutralize the particles, eliminating the diffuse layer and thus causing flocculation, and (3) the added electrolyte can change the sign of the charge adhering to the particles, re-creating a diffuse double layer but with interchanged positive and negative charges.

Generally positive colloidal particles in lyophobic suspensions are neutralized by alkalis. If the colloidal particles are negative, they should be neutralized by the addition of acids. I do not know if this general rule holds for the sauce.

Electrolytes that release multivalent ions (ions with more than a single unit of charge) can have much stronger effects than those releasing univalent ions. For example, the bivalent ions released by Epsom salt (magnesium sulfate) should have a stronger effect than the univalent ions released by table salt (sodium chloride). If colloidal particles are negatively charged, they should be readily neutralized and then flocculated by multivalent positive ions released by the added electrolyte.

For some reason the negative ions released by the electrolyte play a minor role. With positively charged colloidal particles the effect is the opposite. The multivalent negative ions should readily neutralize the particles and so cause flocculation. For some equally mysterious reason the positive ions released by the electrolyte also play only a minor role. All the possible conditions of lyophobic suspensions come under what is called the Schulze-Hardy rule, which has three parts. First, flocculation of the particles is caused by ions opposite in electric charge from the charge of the particles. Second, the ions with charges of the same sign as that of the particles participate little. Third, the ability of an electrolyte to neutralize the particles and so flocculate the suspension increases dramatically with the valence of the ions it releases. Because of the Schulze-Hardy rule ingredients that release multivalent ions should be avoided in recipes for sauce béarnaise.

At the risk of discouraging you with the complexity of the sauce, let me cautiously point out that the suspension may not be lyophobic at all, in which case all the above arguments would not be applicable. If the particles are charged and the mechanism that prevents them from flocculating is the diffuse double layer, the arguments are valid. If the particles are uncharged and the antiflocculation property stems from the layer of bound water, the arguments are not valid.

In a lyophilic suspension the addition of an electrolyte can have results that are much different from those in a lyophobic suspension. Salts may lead to flocculation, but only if they are added in relatively large concentrations, perhaps so large that this possibility is meaningless where sauce béarnaise is concerned. In nearly all lyophilic suspensions it is the negative ions released by the added electrolyte that figure in flocculation. The Schulze-Hardy rule therefore does not apply, and no significant difference in the flocculation of the suspension results from the valence of the ions that are released. When one compiles a list of the ability of certain salts to flocculate a lyophilic suspension, however, one finds that sulfates generally work better than chlorides, a fact I tested with my own sauce.

Before I try to resolve some of the arguments about sauce béarnaise let me summarize the ways the sauce can fail. It may be that not enough egg yolk or water is added or that the butter is put in too fast. The effect in each instance is to prevent the full emulsification of the mixture. The sauce can be carelessly overheated to the point of flocculation, which can be remedied, or coagulation, which cannot. The vaporization of the acetic acid during the initial heating of the infusion could diminish it as a source of the negative charge required by the colloidal particles later on. The interfacial film of water molecules protecting the particles may somehow be broken. Finally, the ions in the liquid may neutralize the particles.

How might a flocculated sauce be remedied? Perram, Nicolau and Perram (along with Julia Child) suggest beating in additional acid. Small and Bernstein and some of my cookbooks imply that additional acid has no effect and instead recommend beating in water. Which technique is correct? I think either one may work, but the best choice is likely to be governed by the flavor of the resulting sauce.

If one adds vinegar or lemon juice, some of the acid molecules can be adsorbed onto the particles, as Perram, Nicolau and Perram believe. If the particles already have a surface charge, this addition of charge will thicken the diffuse double layer. If little acid remains from the original infusion, the addition of charge to the particles will help to create the double layer. The whisking by the cook breaks up the flocculation, and the diffuse double layers then aid in preventing or delaying reflocculation. (Of course, if the cook were to rely entirely on the acid for protection against reflocculation, the sauce would be much too acid for serving at table.)

Adding water to the sauce, either as tap water or as a component of vinegar or lemon juice, can have several possible effects. If the particles in the sauce are preventing flocculation by means of their surface charge, the medium may neutralize the particles and initiate flocculation. The addition of water decreases the ion concentration of the medium. Once the sauce is whisked and the flocculation is undone the medium will not neutralize the particles as fast, and reflocculation will be prevented or at least delayed.

A second effect from the addition of water may be that it and the whisking redissolve the flocculated particles. This result would be important if the sauce were primarily a lyophilic suspension that depended on the egg yolk for its protection against flocculation. The additional water may also be required if the ratio of water to butter is too low for adequate emulsification. Regardless of what the water does, an excess of it will certainly make the sauce too runny.

If the flocculation is due to insufficient yolk in the sauce, the best remedy is to whisk in more yolk. The step would also add water, since much of the yolk is water. If too much yolk is added, however, the sauce will lose its lightness and will sit heavily in the belly of the diner.

Which remedy is best? Any of the remedies will probably work in general, although some of them may not work in special cases and each one will lead to an unacceptable sauce if it is overdone. Since preparing the sauce involves rather inexact measurements of ingredients that can vary considerably in their composition, I cannot be more definite about what is responsible for the stability of the sauce or about which remedy is best every time. I cannot even say with certainty that the sauce is either a lyophobic or a lyophilic suspension or whether its stability is due to electric repulsions between diffuse layers or to protective coatings of bound water. In short, the preparation of sauce béarnaise remains more an art than a science.

My experiments with sauce béarnaise followed Kamman's basic procedure but did not include the herbs and (except for my first trial) the wine. The sauce was prepared on my electric stove (with asbestos pads on the burners) and with my usual kitchen utensils. The first trial was a mess because as soon as I added the butter the sauce flocculated heavily and rapidly. I followed Child's standing directive for decisive action in the face' of a cooking disaster and immediately poured the sauce into two bowls. I vigorously whisked additional vinegar into one and soon had a smooth, unflocculated sauce. To the other I added a small amount of water and again was rewarded with a smooth sauce. Why did the first batch go bad? Because I had unwisely added the butter when the temperature of the infusion was slightly above 60 degrees C.

In my second attempt I kept the temperature of the melted butter and the infusion below 60 degrees. The wine and the salt were eliminated and the egg content was reduced so that the infusion' consisted of only one egg yolk and five teaspoons of warm water. The resulting sauce was smooth, displaying no flocculation.

Some of the other trials I ran are summarized in the chart on the preceding page. Drawing on a "mother batch" of butter and water, I added vinegar, lemon juice, sodium chloride, Epsom salt, water, egg whites and egg yolks. The salts were included to check the possibility that they induced flocculation of the suspension, presumably by neutralizing the colloidal particles. To a portion of the mother batch I first added just enough vinegar to prevent the sauce from flocculating within five minutes after whisking. Then I added a salt, whisked the sauce and added more of the salt. Flocculation eventually resulted. I could see no difference between the salts in causing flocculation, notwithstanding the Schulze-Hardy prediction that the bivalent ions released by Epsom salt should promote flocculation more strongly in a lyophobic suspension. The fact that salt can lead to flocculation may be one reason unsalted butter is required in the recipe for the sauce. (Flavor must also be a factor.)

When I added egg yolk to the mixture of butter and water, the emulsification was much more difficult than it was when I followed the standard procedure of putting the yolk in before the butter. Vigorous whisking usually yielded a good sauce even with this reversal of procedure. To flocculate the sauce with salt required a relatively large amount of salt and resulted in a slurry that had a high viscosity. This result is called "salting out" and comes about because the salt competes with the lyophilic particles for the water in the mixture. Again the results with the two types of salt seemed to be approximately the same, although the sulfate should have led to flocculation more readily than the chloride did.

In another experiment I tested the effects of adding lemon juice and egg whites to the sauce. Lemon juice had the same rejuvenating effect as vinegar when the sauce was flocculated. The addition of a small amount of egg white helped to stabilize the sauce but made it look more like a gel than a table-ready mixture.

To summarize, a flocculated sauce béarnaise can be emulsified and held in a stable suspension if one vigorously whisks in either water or acid or if one includes additional egg yolks. The salt concentration may play a role in making the sauce unstable against the aggregation of the suspended butter droplets but probably only if the sauce depends on the electric repulsion between the particles for its stability.

If you would like to investigate sauce béarnaise further, much can be done. I was impressed by how little quantitative control I had over the experiments. For example, the eggs were nonuniform and all measurements were unnervingly imprecise for a physicist. A thorough quantitative, controlled experiment is needed. The comparison of the two salts should be investigated further. The role of the herbs and the wine needs to be clarified. Perhaps they are just for flavor. Finally, the question of whether the eggs need to be fresh could be pursued. All the experiments should monitor the state of the sauce for a reasonable period of time, because a stabilized sauce should remain stable for at least 30 minutes. I should be particularly pleased if someone could prove that my dual model of the sauce is incorrect and that the sauce is always either lyophilic or lyophobic. If the experiments make you tire of sauce béarnaise, you can turn to hollandaise sauce, another warm emulsified mixture, and start over with all my questions.

Bibliography

A SHORT TEXTBOOK OF COLLOID CHEMISTRY. B. Jirgensons and M. E. Straumanis. Macmillan Company, 1962.

EGG PROTEINS. William J. Stadelman in Food Colloids, edited by Horace D. Graham. The Avi Publishing Company, Inc., 1977.

A MATRIARCHAL SOCIETY (SAUCES). Madeleine Kamman in The Making of a Cook. Atheneum Publishers, 1977.

INTERPARTICLE FORCES IN MULTIPHASE COLLOID SYSTEMS: THE RESURRECTION OF COAGULATED SAUCE BÉARNAISE. C. M. Perram, C. Nicolau and J. W. Perram in Nature, Vol.270, No. 5638, pages 572-573; December 15, 1977.

DOCTOR IN THE KITCHEN: EXPERIMENTS ON SAUCE BÉARNAISE. D. M. Small and Michael Bernstein in The New England Journal of Medicine, Vol. 300, No. 14, pages 801-802. April 5,1979.

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