THE SOUND OF WATER BEING boiled for coffee or tea is so familiar to me that I hardly notice it. Yet I can always tell by the sound when the water is at full boil and ready for pouring. Interpreting the details of what takes place in the container requires a good deal more attention and is actually quite difficult. Nevertheless, much of the thermodynamics is now understood. It reveals that more is going on than meets the eye or ear.

Much of my discussion of this phenomenon is drawn from A Heat Transfer Textbook, by John H. Lienhard of the University of Houston. A useful adjunct to the discussion is a graph relating the heat flux (the rate per unit of area at which heat is transferred to the water) to the difference in temperature between he pan (mainly the bottom of it) and the bulk of the water. The temperature of the bottom of the pan goes above the temperature of the water and gives rise to convection in the water and eventually to evaporation.

I supposed such a graph would show a simple curve indicating that the amount of energy transferred to the water increases with the temperature of the pan. Instead the curve rises to a peak, falls rapidly and then rises again. At the lower temperatures the heat flux does increase with the temperature, but just beyond the peak the flux drops radically.

The temperature of the water and of the bottom of the pan is often measured with respect to the normal boiling temperature of the water at the existing pressure. The result is known as the saturation temperature. Water at the boiling temperature is said to be saturated. When water is heated above the saturation temperature but does not change in phase from a liquid to a gas, it is said to be superheated. In the accompanying graph [Figure 2] the temperature scale records the difference between I the temperature of the bottom of the container and the saturation temperature of the water.

One might think that in the early heating stages the water layer just above the heated surface would quickly reach saturation temperature. In such a case it would form bubbles of vapor. Convection, however, keeps the water temperature below the saturation temperature. The heat that is added decreases the density of the water, forcing it to move upward because of its buoyancy. The cooler water descends to the bottom and is heated.

The heat transferred to the water is thus carried to the top by convection. At the top the water can change its state. If the heat flux is low enough, this type of transfer continues until all the water vaporizes off the top surface.

With a larger heat flux the boiling process soon reaches the stage called nucleate boiling. At first isolated bubbles form on the bottom of the pan. If the source of heat is more powerful than a kitchen stove, the water reaches another stage: freshly formed vapor bubbles from many sites merge into columns, jets and slugs of vapor that rise to the top and escape. In both stages of nucleate boiling the formation of vapor bubbles increases the transfer of heat away from the heated surface.

If you boil fresh water on a stove, two types of bubble appear in the first stage of nucleate boiling. One is a vapor bubble. The other is a bubble formed out of the air dissolved in fresh water. As the water is heated the air is driven out of solution and into bubbles that form at isolated places on the bottom.

The two types of bubble are easily distinguished by what they do. An air bubble remains stable on the bottom until it

breaks loose and rises. Vapor bubbles, which are blurry, form and collapse and then re-form from 30 to 60 times per second. Even if they break loose from the bottom and start to rise, they collapse in the cooler water above them. (This stage is termed subcooled boiling because only the bottom layer of water is saturated or superheated.) Water that has been heated previously, either on the stove or in the hot-water system of the building, does not develop air bubbles because most of the air has been eliminated.

In the early stage of nucleate boiling isolated vapor bubbles also begin to appear at certain places on the bottom. These places are nucleating sites. They generate many bubbles, but each one collapses soon after it forms or as it begins rising into the cooler water above. With a continued heat flux the water well above the heated surface eventually gets hot enough for the bubbles to be able to rise farther. If they reach the surface, they burst and release their vapor.

Much of the vaporization in a bubble takes place during the ascent through he superheated liquid. One might suppose most of the heat transferred from he bottom of the pan would go into he formation of bubbles there. Instead most of it goes into the water touching he bottom, either in the regions between the sites of bubble formation or in he inflow of water at one of those sites after a bubble has collapsed or has been released.

At the higher temperatures of nucleate boiling the bubble sites on the bottom of the pan are much more numerous. The bubbles almost immediately merge into columns, jets and slugs of vapor that linger just above the sites of formation. In this phase of boiling the heat is transferred to the water at a high rate. Bubbles form and leave the bottom so rapidly that gushes of cooler water are carried to the bottom to be heated.

The rapid drop in flux is reached at somewhat higher temperature. This stage is termed the transition boiling regime. It is dangerous in industrial cooling systems if the heat continues to be delivered to the container; heat transfer to the water suddenly declines. The increased temperature can damage the container. Hence the transition boiling regime is also called burnout or the boiling crisis.

In the transition boiling regime an increase in the temperature of the container actually leads to a suppression of the mount of heat carried away by the water. The cause is vapor that develops over the bottom of the container. Heat is transferred slower through vapor than it is through water. The higher the temperature of the container, the more extensive the vapor and the poorer the transfer of heat.

At the very-high-temperature stage of boiling the heat flux rises again as the temperature increases. In this stage, termed film boiling, a constant layer of vapor lies over the bottom of the container. Although the heat flux is poor at first because of the vapor, the high temperature eventually drives the heat through the layer.

Water boiled on a kitchen stove does not, however, reach these high-temperature phases. Nevertheless, all the characteristics of boiling can be observed up to the region of isolated bubbles. Lienhard suggests the following experiments. Put a pan of cold tap water on a stove burner turned to its highest intensity. After a while you will see some of the circulation that results when heated water leaves the bottom of the pan and rises toward the top. The circulation is visible because the differences of density created in the water by the heating give rise to variations in the index of refraction of the water, distorting the paths of the light rays reflected from the bottom.

Air bubbles soon appear on the bottom, probably over the hotter places. On my electric stove the coils heat from the outside inward. I can tell when the inner coils begin to heat by watching the distribution of air bubbles. In order to achieve a more uniform heating I insert a piece of aluminum (a quarter of an inch thick and slightly wider than the pan) between the coils and the pan. A thicker piece would work better.

Soon after the air bubbles appear the r pan begins to "sing." The sound marks the rapid creation, oscillation and collapse of vapor bubbles on the bottom. When a bubble collapses, it makes a sharp ping or click. (Air bubbles do not emit sound because they do not collapse.) As the water continues to heat up, more of the vapor bubbles give their note of collapse and the pan makes quite a racket. I know from experience, however, that the noise does not mean the water is hot enough for coffee or tea.

The noise gradually abates as more of the vapor bubbles survive their ascent through the cooler water and reach the top. There they burst with a small splash. The burbling that now results is the sign the water is ready, being at full rolling boil.

Lienhard says the bubble motions can be observed more closely with a stroboscope. Heat the water in a Pyrex beaker. (Ordinary glass may shatter from the heat.) Set the stroboscope to flash at a frequency of from six to 10 hertz. Put a piece of tissue paper or frosted glass in front of the stroboscope to diffuse the light. With the room lights off you can slow the bubble motions on the bottom of the container.

The generation of bubbles starts in the tiny pits and short cracks on the bottom of a container. Although the bottom of a metal pan may appear to be smooth, it is covered with such small irregularities. Some of them trap air when water is first poured into the pan. Surface tension then prevents the water from entering them. The tiny pockets of trapped air serve as the nucleating sites for the air and vapor bubbles that develop as the water is heated. A vapor bubble grows at a nucleating site as superheated water vaporizes into the air in the pit.

Theoretically there is an equilibrium at the radius of the bubble. At that point the vapor pressure in the bubble matches the external pressure from the overlying water and the surface tension of the water at the interface between the bubble and the water. Usually, however, the bubble is unstable in the sense that if any perturbation makes the radius smaller, the surface tension overwhelms the internal vapor pressure, causing the bubble to collapse. If something makes the radius larger, the liquid at the interface vaporizes into the bubble, causing the bubble to grow.

The theoretical value for the radius of a stable bubble depends in part on the temperature of the surrounding water. At first the water is not much superheated. The stable radius is large, with the result that the growth of bubbles is rare since most of the nucleating sites are occupied by small bubbles. As the temperature of the water increases, the value for the stable radius decreases. The formation and the growth of bubbles become likelier.

When the temperature of the water increases, the heat flux into the water also increases at least in the stage of isolated bubbles. The increased influx of heat does not go directly into the bubbles. Rather the bubbles act as tiny pumps that continuously bring cooler water in contact with the heated surface of the pan.

Suppose the water is not hot enough to allow a bubble to escape toward the top. The bubble, situated over a nucleating site, has a radius larger than the radius for a stable bubble. Therefore it grows as water vaporizes into it. The bubble's growth, however, pushes its top surface up into cooler water. There vapor condenses even as water continues to vaporize at the heated surface. The top of the bubble begins to collapse and then the entire bubble collapses. The collapse drives a tiny circulation, with the superheated water at the bottom of the bubble springing up and the cooler water at the top dropping down. The cooler water is then heated. This circulation increases the rate at which heat is transferred to the water.

Later in the heating process the vapor bubbles break free of the heated surface. As a bubble grows over its nucleating site it absorbs heat from the surrounding superheated liquid. When the bubble escapes, it entrains in its wake cooler water from higher above the heated surface. That circulation of cooler water. enhances the heat flux into the water. The heat flux is further enhanced because in this later stage of nucleate boiling more nucleating sites are active.

The actual rate of heat transfer to the water in nucleate boiling depends in part on the nature of the heated surface. A bubble tending to form at a nucleating site has a radius partly determined by the size of the pit at the site. Large pits or pits with flat bottoms, however, are relatively ineffective in bubble nucleation. The smaller the pit, the smaller the bubble that tends to form over it. Particularly small pits, however, probably have no role in the initial onset of bubble generation. The bubbles that form in small pits are smaller than the radius for stability and therefore tend to collapse. As the water temperature near the heated surface increases, the radius for a stable bubble decreases and the smaller pits become more active.

In general the heat flux at a particular temperature is greater for a pan with a rough inside bottom surface than it is for one with a smooth, polished surface. I experimented with one of my steel pans heated by a piece of aluminum on an electric stove. The bottom of the pan had been scratched by years of service and scouring. When I heated fresh, cool tap water, air bubbles collected near the perimeter of the pan, apparently because the outside bottom surface made the best contact with the aluminum in that area.

I could clearly see the network of old scratches on the inside surface, but the air bubbles did not reflect that pattern. Instead they were spread out rather uniformly, as were the vapor bubbles. Apparently the old visible scratches were too large to take part in the formation of bubbles.

As the pan heated further, the formation of bubbles extended inward toward the center. Once the vapor bubbles near the perimeter began to form rapidly, however, the activity nearer the center diminished and eventually disappeared. Why did it? Surely the piece of aluminum was then hotter than ever. I believe this oddity was due to the rapid heat flux in the ring at the perimeter. Bubble nucleation began in that ring. Once the vapor bubbles were able to break free the heat flux in the ring was significantly higher than the heat flux toward the center. The ring drained enough heat from the underlying piece of aluminum to make the water nearer the center of the pan unable to superheat sufficiently to continue bubble nucleation.

I emptied the pan and reheated it briefly to dry the inside. Then I made scratches in three areas near the perimeter. In one area I stroked twice with a ball of steel wool. In another I made two hard scratches with the tip of a steel screw. Next to them I made a double scratch with the pointed tip of an aluminum rod. Then I refilled the pan with cool tap water and heated it.

The generation of bubbles in the region stroked with steel wool was the same as it was in the unaltered regions near the perimeter. The screw scratches were also seemingly ineffective in nucleating bubbles. Although bubbles appeared nearby, they seemed to be unrelated to the scratches. The shallower scratches made by the aluminum rod gave rise to lots of bubbles, first of air and then of vapor.

I could not see well after the water began a rolling boil, and so I occasionally picked up the pan to reduce the boiling. Although bubble generation elsewhere disappeared almost immediately, at the scratches from the aluminum rod they continued for 20 or 30 seconds. I cannot believe the scratches from the rod were in fact nucleating bubbles; they were too large. It is more likely that the rod skipped a little as I scratched the surface, gouging small pits in the scratch that served as nucleating sites.

The mechanics of bubble growth in a surface irregularity can be modeled by considering a conical pit in the heating surface. Initially the air trapped in the pit is covered by an upwardly curved water surface at the top of the pit. The gas is at the same temperature as the surrounding water. The pressure inside the gas pocket is higher than the surrounding pressure from the liquid because it must also counter the inward force from the surface tension at the gas-water interface. The radius of curvature of the interface is determined by the ratio of the surface tension of the water and the difference between the two pressures.

The bubble growth begins as the water layer adjacent to the heated surface becomes superheated. Water at the interface evaporates into the gas in the pit, expanding its volume. The radius of curvature increases and the inward force due to the surface tension decreases. (Something similar happens as you blow up a spherical balloon. Initially the balloon has a small radius of curvature and the inward forces opposing expansion are large. When the radius of curvature is larger, those forces are smaller and it is easier to blow up the balloon further.)

Since the inward force on the gas pocket is smaller, the pressure difference between the inside of the pocket and the surrounding water is reduced. The reduced pressure persists as evaporation into the pocket brings the gas-water interface up to the lip of the pit. Additional evaporation of water and expansion of the pocket push the interface upward farther, but the bubble still does not leave the lip.

The bubble now reaches a critical point. Its upward expansion decreases the radius of curvature of the interface, thereby increasing the inward force due to surface tension. At the critical point the interface is at its smallest radius of curvature, and correspondingly the inward force from surface tension is at its strongest. At that stage the difference between the pressure inside the bubble and the pressure of the surrounding liquid is at its greatest.

Either one of two things can happen now. If the surrounding water is sufficiently superheated, evaporation continues at the interface. The bubble grows larger as the interface moves away from the lip of the pit. The radius of curvature increases, decreasing the inward force due to surface tension. The bubble continues to grow and may eventually detach from the heated surface,; leaving behind a pocket of vapor that can serve as a nucleating agent for the next bubble.

Alternatively, the surrounding water may not be superheated enough to force vapor into the bubble poised at the lip of the pit. The bubble stops growing, at least until the water temperature is increased by additional heat influx. Just how superheated the water must be to drive a bubble through the critical point in its growth depends partly on the size of the pit. A bubble in a relatively large pit (say 10 micrometers in diameter) may not require much superheating to continue through its critical stage. A bubble in a small pit (say one micrometer in diameter) reaches its critical stage with a smaller radius of curvature and thus a higher internal pressure. The surrounding water must be heated even more to push the bubble through the critical stage. That is why the smaller rough spots on the heated surface participate in the nucleation of bubbles later than the larger spots.

My argument, however, ignores the fact that many of the rough spots are not conical. It also ignores the possibility that a pit may not trap any air. As water is poured into a pan a sheet of liquid advances over the pits. Whether or not the water completely fills a pit depends on two factors: the geometry of the pit and the angle of contact between the advancing sheet of water and the metal. The contact angle is governed by the surface tension of the water at the air metal interface. If the angle is larger than the angle of the conical pit, the water reaches the far side of the pit before it reaches the bottom. It therefore traps air in the pit to serve as a nucleating site. Otherwise the pit is entirely cleared of air by the advancing water and cannot function as a nucleating site.

Although the stage of boiling marking the change from the formation of slugs and columns to the burnout phase of the transitional regime cannot be achieved on a kitchen stove, the physics underlying the change is curious. Why should boiling rather suddenly switch from its greatest rate of heat transfer to a rate so low that it endangers the container? The peak transfer rate is achieved only because of the successful creation of bubbles on the heated surface. The bubbles' upward motion after they detach continuously stirs cooler water down onto the heated surface, preventing it from rapidly increasing in temperature to a catastrophic point. As the boiling process approaches the stage of peak heat transfer a network of bubbles emerges on the heated surface. They detach quickly and ascend in columns or slugs. Gushes of cooler water descend.

The columns of ascending vapor form a pattern over the heated surface. The condition in which a lighter fluid (a vapor layer) underlies a heavier fluid (water) is referred to as a Rayleigh-Taylor instability. It forces the ascending columns of vapor into an approximately geometric pattern. The heat is still transferred effectively through the water in this stage, but as the bottom surface is heated further the ascending vapor columns must move faster in order to maintain the boiling regime. Eventually they move so fast that their vertical surfaces break down into waves in what is called the Helmholtz instability. Thereafter the transfer is less effective and the boiling process quickly reaches burnout as the heat influx at the bottom surface overloads the ability of the system to convey vapor to the top surface.

Water is not the only liquid heated or boiled in the kitchen. I have often had the dismaying experience of overheating a thick sauce. In haste I turn up the heat too much. Then I conclude that since the top surface is still cool, the bottom surface must be almost as cool. Suddenly huge bubbles gurgle to the top surface and splash sauce all over the top of the stove.

Jeffrey C. May of the Cambridge School in Weston, Mass., recently communicated with me about this common kitchen error. He shows that my mistake is in ignoring the viscosity of the fluid. In the early stage of heating water the normal convection of the liquid successfully conveys heat away from the bottom surface to the top, where the water can evaporate. In a viscous sauce the convection is ineffective. The sauce super-heats at the bottom surface until large bubbles are generated. The top surface a P may still be cool. The bubbles suddenly break free from the bottom surface and rise to the top, where they burst vigorously.

In cooking pasta I have long followed two rules for boiling the water. The first is to heat an amount of water that is about three times the volume of the pasta. The reason is that with a smaller amount of water the nucleate boiling would be halted when the pasta was dropped into the pan and the transfer of heat would be limited to convection. The top of the water would cool, leaving the pasta in lukewarm water and complicating the cook's timing. When the pan contains the proper amount of water, the addition of the pasta scarcely affects the boiling process.

I have never been certain of the logic behind the second rule I follow. All recipes for pasta say to add salt. Surely the salt is for seasoning, but why should it be added to the pasta instead of to the sauce? It is asserted in explanation that the salt raises the boiling temperature of the water so that the pasta cooks faster. There is some truth to the assertion, because any solvent (here water) containing a nonvolatile solute (here salt) has a higher boiling point than the pure solvent.

In a rolling boil the vapor pressure from the water must match the ambient pressure on the water. When the water is unsaturated, the vapor pressure is lower than the ambient pressure. If a solute such as salt is added to the water, the vapor pressure of the water is reduced. The reason is that the presence of the salt (the ions of sodium and chloride) at the top surface makes the escape of water molecules from the surface less likely. When the solution of water and salt reaches what would have been the boiling temperature of pure water, the vapor pressure is still less than it would PS have been without the salt. The temperature increases further until finally the vapor pressure matches the ambient pressure. Then the solution boils.

Does the addition of salt speed the cooking of pasta? I added half a teaspoon of salt at a time to two quarts of boiling water. Although I doubled the amount of two teaspoons called for in a standard recipe, the water temperature rose by less than a degree. One must conclude that the salt serves only as a seasoning.

Bibliography

BOILING. G. Leppert and C. C. Pitts in Advances in Heat Transfer: Vol. 1, edited by Thomas F. Irvine, Jr., and | James P. Hartnett. Academic Press, 1964.

HEAT TRANSFER IN BOILING AND OTHER PHASE-CHANGE CONFIGURATIONS. John H. Lienhard in A Heat Transfer Textbook. Prentice-Hall, Inc., 1981.

The Society for Amateur Scientists (SAS) is a nonprofit research and educational organization dedicated to helping people enrich their lives by following their passion to take part in scientific adventures of all kinds.