Discussion point 3: Modern theories of boiling

In the traditional theory of boiling in physics and physical chemistry, the boundary between the liquid state and the gas state is sharply defined as the line on which the vapor pressure (function of temperature) reaches the level of the external pressure. This is as shown in a typical phase diagram on the right. The assumption of the sharpness of the liquid-gas boundary theoretically precludes the variability of boiling point under fixed external pressure; this means that there is no obvious way of accommodating the observed variations within the traditional physical theory.

In modern treatises on boiling in mechanical and chemical engineering, we do not find the standard thermodynamic phase diagrams. Instead, the engineer’s paradigmatic representation of boiling is the “boiling curve”, which plots the rate of heat transfer against the degree of the “surface superheat” or the "excess temperature". The figure on the left shows a typical boiling curve, taken from Incropera and DeWitt (1996), p. 540. (Click on the picture to see a larger version with readable text.) The boiling curve shows a couple of important things about the incommensurability between the physicist’s and the engineer’s understanding of boiling. The main independent variable in the engineering discourse is how much the temperature of the heating element exceeds the "normal" boiling point. I assume that the water in immediate contact with the heating element (what De Luc called the "first layer" of water) is also heated beyond the normal boiling point. By how much, we cannot really say -- it would be extemely difficult to measure such a thing and, presumably, the engineers are more interested in variables that they can measure and control, like the temperature of the heating element. Therefore, in the best modern theory of boiling we have, the temperature of the water itself has no role to play!

And if we do assume that there is some degree of superheating in the first layer of water, and seek to say something about the effect of that superheating, we find that there is no theory that can be applied easily. The question cannot even be articulated in the standard physics discourse, because the theory there is based on the idealized assumption that superheating never occurs.

The other main thing to note about the engineer’s boiling curve is that the main dependent variable is the rate of heat transfer. These engineers are mainly interested in boiling as a method of carrying heat away from hot places to colder places (one can easily imagine the consequences of not understanding this correctly, in trying to keep a nuclear reactor from overheating, for example). In that context, the temperature of the liquid water, especially well above the first layer, is distinctly of secondary interest, and is freely admitted to be quite variable depending of the situation.

The engineering treatises on heat transfer give a detailed classification of boiling behavior, largely determined by the degree of surface superheat and the configuration of the boiling setup. A great deal of experimental work is also going on. See, for example, Incropera and DeWitt (1996), Hewitt et al. (1997), and Kandlikar (1999).

Particularly pertinent for current purposes is the modern theory of nucleation (bubble-formation), which gives excellent and detailed explanations of the effect of vessel-surface quality on boiling behavior (shown in Experiment 2 and Experiment 4). Surface tension emerges as the basic reason why water is prone to superheating. In order for boiling to take place, vapour bubbles need to form within the body of the water, and grow sufficiently to be visible as they come up through the water. Now, the basic condition for a bubble to sustain itself is that the vapour pressure should match (or exceed) the extrernal pressure. (This is as specified in the pressure-balance theory of boiling from the 19th century.) However, there is a complication here becausse the water molecules which form the surface of the bubble attract each other. This attraction manifests itself in the form of surface tension, which tends to close up the bubble. Therefore an additional force of vapour is required to sustain the bubble, which means the water temperature has to be higher than the boiling point indicated by the simple pressure-balance theory.

Standard theory says that the additional pressure created by surface tension is inversely proportional to the radius of the bubble (see Hewitt et al. 1999, 91). In other words, the additional pressure to be overcome becomes infinite when the radius is 0, which means that it would be impossible to grow a vapour bubble if there weren't a finite-sized space to begin with. This is why the precise quality of the solid surface becomes so important for the facilitation of boiling. If the surface has micro-pores and it is sufficiently water-repellent, then there would be pockets of vacuum or trapped air that can serve as the site of bubble-formation (nucleation). This is why bubbles only arise from specific places in ordinary boiling situations, especially as the water gets more and more de-gassed with the progress of boiling (see the video footage of Experiment 1). The figure on the right is Incropera and DeWitt's (1996, 547) illustration of nucleation sites.

Some other questions arising from my experiments are more difficult, and they are not satisfactorily resolved by an elementary knowledge of the modern engineering theory of boiling that I have so far acquired. First, it is difficult to understand the role of dissolved air in facilitating boiling; this may require some detailed molecular modelling, which the engineering theory does not provide. Second, the lowering of the boiling temperature below the thermodynamically defined boiling point is difficult to understand. The only explanation I can currently offer is that the "first layer" of water in those situations must be heated well beyond the normal boiling point although the main body of the water is much cooler, and that the bubbles rise to the surface before they have enough time to be collapsed in coming through the cooler water.

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