On the Superfluidity of Liquid Helium-II1

P. L. Kapitsa

I reported to the Academy of Sciences of the USSR on the superfluidity of liquid helium two and a half years ago[^2]. Since then, continuing to work in this field, we have obtained new results which, from our point of view, are of scientific interest and make it possible to illuminate these interesting phenomena more fully. But before speaking about these new phenomena, allow me to remind you, at least in general outline, of the content of my preceding report, which some of you may not have heard. Otherwise, I fear, our new works, which are a continuation of the earlier ones, will not be sufficiently clear.

The study of liquid helium and its properties belongs to the field of the physics of the lowest temperatures. This is one of those fields of physics in which one seeks to study natural phenomena under extreme conditions. The Vice-President of the Academy of Sciences of the USSR, Academician A. A. Baikov, in his introductory report at this session, I think quite correctly pointed out that we may expect the greatest successes, truly major changes in technology, when we pass to extreme conditions. This applies to an even greater degree to science. We may most readily expect the discovery of new and interesting phenomena when we study nature under the most extreme conditions admissible for it, as, for example, in exceptionally strong magnetic fields, high pressures, high electric voltages, etc., and also in the region of deep cold, approaching absolute zero. Here too we may hope to discover new phenomena, such properties of nature as, under ordinary conditions, either elude observation or simply do not occur at all. In this respect the region of temperatures near absolute zero is especially interesting. The work of the last decade has confirmed this with complete obviousness.

Allow me to remind you what absolute zero of the temperature scale is. The latest determination of absolute zero is −273.13°C. It is known that we shall never be able to reach absolute zero itself. The usual school definition of absolute zero says that it is the temperature at which the thermal motion of matter ceases. But this is definitely inaccurate. From the modern point of view, based on quantum theory, the existence of motion at absolute zero is admitted. The energy of this motion is quite definite and is that minimal—

molecular motion which, in the given substance, can exist. I shall give a simple example. If you heat a substance strongly, then the electrons of the atoms, which move around the atomic nucleus in definite orbits, will, under the influence of thermal motions, be torn away, fly off; what is called dissociation will occur. When the substance is cooled, the motion of the atoms slows down, the electrons begin again to revolve in their orbits, and down to absolute zero itself they retain their motion. But, besides the motion of electrons in the orbits of each atom separately, there is also a whole series of combined motions in a solid body which, from the modern point of view, must persist down to the very lowest temperatures. Owing to this so-called degeneration of motion, in this region of temperatures completely new phenomena may appear which we cannot observe at ordinary temperatures. One of such interesting phenomena, which has already become widely known, was discovered more than 30 years ago by Kamerlingh Onnes—this is the phenomenon of superconductivity. It consists in the fact that at very low temperatures an electric current is able to flow through certain conductors without resistance, without the production of heat. Experiment shows that if a current is induced in a closed superconductor by induction, it flows, without giving off heat and without decreasing, for as long as the experimenter has been able to observe it. Another of the phenomena that can be detected only at very low temperatures is the superfluidity found by us 5 years ago in liquid helium.

Studies of this and other phenomena near absolute zero are carried out by means of liquid helium itself as a refrigerant. Liquid helium is the only known substance which, even at the lowest temperatures, down to thousandths of a degree from absolute zero, remains liquid at normal pressure and does not pass into the solid state. It can be converted into a solid only under pressure, beginning at 25 atm.

Liquid helium by itself is an extremely interesting object for study.

Helium liquefies at a temperature of 4.8° abs. and forms a light, transparent liquid weighing 7–8 times less than water. Because of its not very large heat capacity, liquid helium during an experiment has to be kept, with good thermal insulation, in a vacuum Dewar vessel, further surrounded by another similar vessel containing liquid air. Experimentation with liquid helium presents considerable technical difficulties. This explains why, to this day, only in a few low-temperature laboratories in all countries is liquid helium obtained in sufficient quantities.

If the temperature of liquid helium is lowered from its liquefaction point (4.8° abs.), then, when we reach a temperature of 2.19° abs., it undergoes changes, and it is customary to say that helium-I passes into helium-II. This temperature is called the λ-point. In its initial state, liquid helium usually boils continuously owing to the slightest access of heat, which is difficult to avoid even with the best

thermal insulation. Below the λ-point helium suddenly stops boiling; its surface becomes smooth; this is connected with a change in a number of physical properties of liquid helium. The new state of liquid helium was first discovered by Keesom-Onnes, began to be studied by Keesom, and proved to be extremely curious.

Keesom² found that helium-II acquires in this state a large thermal conductivity. Its thermal conductivity, studied in capillaries, proved to be many times greater, for example, than that of copper or silver—the most heat-conducting metals. Keesom therefore called liquid helium-II a super-thermally-conducting substance. I repeated Keesom’s experiment under somewhat altered conditions and as a result obtained an even greater thermal conductivity.

An attempt to illuminate the experimental data on the basis of modern views of thermal conductivity revealed a deep contradiction between theory and experiment. I shall not enter into a detailed description of the rather complex theoretical conceptions of thermal conductivity, as they are given mainly by Debye. The physical picture of thermal conductivity may be imagined as follows: a rise in the temperature of some body at some point increases the average velocity of the vibrational motion of the molecules of the substance; at the same time a process of equalization begins at once: the “hotter,” i.e. more excited, molecules act upon their neighbors and set them in motion. This process of successive equalization of velocities will spread farther and farther from the heated place, i.e. there will take place the process of propagation of heat, which we call thermal conductivity. A more detailed analysis, carried out on the basis of these views of thermal conductivity, shows that for every body in nature there is a limiting amount of heat per unit time which can be conducted through it. It turned out that such a large thermal conductivity as was experimentally found in our latest experiments in liquid helium-II cannot be explained with the aid of these views. We may seek a way out of this contradiction either by abandoning the fundamental views on the mechanism of thermal conductivity which have become firmly established in science, or else we must recognize that the phenomenon of thermal conductivity in helium-II owes its origin to some other mechanism.

As is known, heat can be transmitted not only by means of the mechanism described, as it is propagated in solids and as, it was assumed, it is propagated in liquid helium in narrow capillaries. Heat can also be transmitted in liquid and gaseous bodies by means of so-called convection currents. For example, convection currents in air are well known to each of you; you have felt them more than once when you held your hand above a warm radiator. The same hand feels no heat at all if it is held at the same distance from the radiator but below it, since here there are no ascending currents of heated air which carry heat upward by convection. If the intense transfer of heat in liquid helium cannot be explained from the point of view of the ordinary mechanism of thermal conductivity, then it seemed to me that perhaps what takes place here is precisely convective transfer of heat. For

to do this one must suppose that in liquid helium II there arise with extreme ease liquid currents, to which the extraordinarily great capacity of helium II to carry heat is due. Calculations showed that the intensity with which heat was transmitted in liquid helium could be realized only by such convection currents, which must flow in this liquid with unusual ease. Therefore, by analogy with superconductivity, I assumed that helium II at ultralow temperatures is an extremely fluid liquid, i.e. a liquid which has no viscosity. It remained to verify this by experiment.

To observe a small viscosity, and moreover at a low temperature, proved to be a difficult experimental task. It was necessary to find a special method for measuring it. When the necessary method had been found and developed, the observation itself did not take much time and showed that the viscosity of liquid helium is indeed vanishingly small[^3]. According to our latest measurements it is no more than \(10^{-11}\) poise. If the viscosity of ordinary water at room temperature is \(0.01\) poise, then liquid helium proved to be a liquid more than a billion times more fluid than water. Such a fluid medium is very difficult to imagine, and yet the number just cited signifies the limit not of the viscosity, but only of the sensitivity of our measurements. We do not yet have a more sensitive method. Therefore I suggested that there is every reason to consider that liquid helium has no viscosity; I called it superfluid. At first this met with many objections. Experimental errors were sought in my experiments—in the method, in the measurements, and so forth. The discovery of superfluidity in liquid helium was thus discussed from all sides, and now, I think, the existence of the superfluid state in helium II may be regarded as recognized.

When this phenomenon was first formulated, it seemed to us that the superfluidity of helium II was quite sufficient to explain the great thermal conductivity observed in liquid helium in accordance with the picture of the existence of convection currents that I have just sketched for you. But the matter turned out to be much more interesting and more complicated than we thought at first.

An account of how our views on this question developed further presents certain difficulties. The audience is large and varied, and in these questions we ourselves have not yet resolved a number of contradictions. Nevertheless I shall try to tell you what contradictions we encountered, how our views changed, and how the ideas gradually took shape among us—ideas that would seem utterly fantastic if they were set forth without connection with real experiments.

If one takes the standpoint of our usual mechanical conceptions, which quite exhaustively describe the behavior of ordinary substances under ordinary conditions, it turns out that superfluid helium, as experiment shows, cannot carry heat as intensively as is required by the measurement of convection currents. We encounter the difficulty of finding a mechanism that could cause the necessary rapid flow of helium during convection. In the ordinary mechanism of heat transfer by convection we

are due to the motion of the medium: the more heated liquid or gas becomes somewhat less dense, and therefore tends upward, as though floating up in a denser medium, while the colder, denser parts move downward, “sink.” Mixing occurs, and it is obvious that the cause producing the motion is the force of gravity. But calculation shows that this force in helium-II is insufficient to produce such a high thermal conductivity as was observed in the experiment. This made the phenomenon once again incomprehensible. Some other, new mechanisms had to be sought to explain it. As a result of a number of experiments, it was finally possible to arrive at an entirely new mechanism of motion of liquid helium-II.

It turned out that, under the influence of a temperature difference, very strong currents arise in liquid helium-II, somewhat resembling convective ones. Under the action of a temperature difference the liquid begins to move, but this motion is of an entirely special kind, specific to liquid helium-II, unknown in any other liquid and under any other conditions. Before trying to explain the essence of this motion, let us become acquainted with its features. Let us see what it looks like in experiment. I shall not describe the technical details of this experiment, since this was done by me in my previous communication. You may form an idea of its main features from the diagram shown in Fig. 1.

A small flask 1 is immersed in superfluid helium-II. In the wide part of this small flask a heating coil 2 is placed, and the small flask is open

Fig. 1                Fig. 2

on one side 3. When current is supplied to the heater 2, near the neck 3 of the small flask there is found a continuous stream of helium flowing out of it. This stream can be detected and even measured by means of a light vane if it is suspended at the neck. The stream presses upon it and deflects it.

A somewhat more effective and instructive modification of this experiment for demonstration purposes was filmed (one of the frames of which is reproduced in Fig. 2). The arrangement of the instrument filmed in operation ...

is shown in Fig. 3. The glass “spider” consists of a “bulb” 2, provided with several outlet tubes bent to one side. Thus, this whole construction reproduces the well-known “Segner wheel” (only in appearance, of course; on examining it, it is easy to see that the “spider” has no through flow for the liquid). The bulb is placed on the point of a needle 1. The whole “spider” is immersed in liquid helium. The helium contained in the bulb can be heated by means of a beam of light through lens 3. This beam of light, falling on the blackened part inside the bulb, plays the role of the heater which, in the previous experiment, was the spiral. From the tubes—the “legs” of the spider—just as from the neck of the bulb in the preceding experiment, upon heating the middle vessel there occurs a continuous outflow of jets. Under the pressure of the outflowing jets, the whole “spider” rotates, which is visible on the screen.

Fig. 3

Filming this experiment is difficult. Liquid helium is completely transparent, and the refractive index in it of a light ray is such that it is very difficult to see it through glass. It is also not easy to carry out the experiment under conditions of the general bright illumination that is necessary for filming. Therefore considerable skill on the part of the cameramen of the Moscow newsreel studio was required in order to make this filming.

Let us return again to Fig. 1. Now I shall draw your attention to the greatest paradox of this experiment. If we observe all the time the liquid flowing out of the bulb and, at the same time, no cavity forms in the bulb, this means that liquid must also all the time flow into the bulb. How, then, does the liquid get into the bulb? It cannot flow out without getting in there. The walls of the bulb are double; the spaces between them are evacuated, and it is obvious that the liquid cannot pass through them. By means of a small wing placed in the most various positions at the neck, it was in no way possible to detect the existence of a reverse flow. Therefore at first we decided that there must exist a flow along a very thin layer at the walls themselves (then it could not be detected by the small wing). But in further experiments this hypothesis proved insufficient. I began to change the conditions of the experiment: instead of a bulb with a wide mouth I used very narrow slits. The idea of these experiments was, as far as possible, to occupy the entire cross-section of the slit with a reverse wall flow and thus to try to change the character of the observed phenomena. The slit in these experiments was made very precisely from carefully (optically) polished surfaces and had a width down to 0.14 μ, i.e. of the order of ten-

hundredths of a millimeter. But no changes in the character of the phenomena were found.

Thus the phenomenon became ever more mysterious.

Before telling how it is now explained, I want to mention a few more experiments.

First of all, allow me to dwell on the concept of the reversibility of thermal phenomena. This concept was first established more than a hundred years ago by Carnot; it provides an extremely important link between the possibilities of the conversion of work into heat and back again. In thermodynamics, reversible phenomena are taken to mean theoretical processes in which heat is converted into work and, conversely, work into heat, with no dissipation of heat occurring. Completely reversible processes do not in fact exist in nature, but they can be approached very closely. The transformation of heat into the motion of helium, which we observe, for example, in our “spider” in Figs. 2 and 3, had first of all to be studied from this point of view. If the temperature difference between the helium in the bulb and the outside helium causes the motion of the helium, and if this phenomenon is reversible, then theoretically the converse phenomenon must also exist: under forced motion of the helium a temperature difference must also appear. If these phenomena are reversible, they must be connected with one another by definite quantitative relations.

In the experiment with slits it was possible to show that, with a pressure drop forcing liquid helium to flow through a slit, a temperature difference does indeed arise. It proved possible to measure quantitatively all the necessary quantities and to show that all these phenomena in liquid helium II do in fact proceed thermodynamically reversibly. If one recalls at the same time that helium II is superfluid, and that therefore during its flow there are no frictional losses, it is not hard to see that the mechanism of the temperature flow of helium works with a good efficiency. Thus, for example, our rotating “spider” in Figs. 2 and 3 is a machine with a good efficiency. Of course, such a mechanism can have no practical application, and it is hard to expect that it will ever obtain one.

But it should be noted here that this astonishing thermodynamic property of helium II, which opens up an entirely new path for the direct conversion of heat reversibly into mechanical work, has nothing similar in the phenomena of nature known to us up to now.

The reversibility of thermomechanical—or, more precisely, thermodynamic—phenomena in liquid helium appears to us to be an extremely important circumstance for the further study of phenomena at low temperatures as well. Suppose that we have a capillary 1 (Fig. 4) with two vessels at different levels. Between its ends we create a pressure difference. This we can do by placing vessel 2 at the end of the capillary higher than vessel 3

Fig. 4

at its other end. Then, as a result of the special properties of helium and the reversibility of the process, a temperature difference \(\Delta T\) arises at the ends of the capillary in vessels 2 and 3. In the lower reservoir 3, helium-II will become colder.

Thus, we have a method for lowering the temperature of helium-II, which consists in forcing helium-II to flow under pressure. Of course, Fig. 4 is only a schematic illustration of this principle; in reality the experiment is, naturally, more complicated.

But since this phenomenon remains reversible down to the very lowest temperatures, it becomes possible to draw very interesting practical conclusions. If helium is forced, by a pump or by some other means, through narrow capillary slits into some volume, the temperature in this volume will be noticeably lowered. Repeating this operation several times, we obtain a priori a method for lowering the temperature as far as desired; and thus a way opens for us to approach absolute zero as closely as desired. This conclusion is of great importance for the experimenter, since until now there has not existed any method, even a theoretical one, for approaching absolute zero arbitrarily closely. The most effective up to now has been the magnetic method (based on the demagnetization of paramagnetic salts, connected with their cooling), which had its limits both theoretically and practically. This path, first indicated by Langevin and later developed by Debye and Giauque, made it possible to reach temperatures of the order of \(1/100\) of a degree above absolute zero. But this magnetic method has theoretical limits for obtaining low temperatures, due to the interaction of the magnetic moments of the atoms of the salts being cooled. Meanwhile, we still see no reason why, by means of the described method of the flow of liquid helium-II, one cannot approach absolute zero as closely as desired, using these special properties of liquid helium-II as a refrigerating agent.

Just on the eve of the war we began, in our work, to develop this method and carried out several successful experiments in this direction. By this method I managed to obtain a lowering of the temperature by \(0.4^\circ\). But after the evacuation to Kazan it was impossible to restore work with helium. Now we intend to continue these experiments. Of course, obtaining temperatures in the immediate vicinity of absolute zero by the new method is technically no easy task, and it is difficult to count on its success at once. There are many technical difficulties here, and success depends in many respects on the skill and ingenuity of the experimenter. But all these possible difficulties do not mean that there exist any fundamental prohibitions against approaching absolute zero.

But let us now pass to a theoretical explanation of the mechanism of the phenomenon of the outflow of liquid helium from a vessel when it is heated (Fig. 1). As I have already said, at first I explained the phenomenon of the filling of a vessel with helium by the flow of helium in the opposite direction in a thin layer. I also assumed that the energy state of helium-II in this thin layer differs from the energy state of free helium-II, and,

Thus it was possible to explain the apparently high thermal conductivity of helium. It was also possible to estimate approximately the possible thickness of this layer, so that the velocity of the helium flow in it would not assume an excessively large value. Later, as I have said, in my experiments I tried to determine the thickness of this layer experimentally. To do this I forced helium to flow in a very thin layer. Gradually I reached a helium-layer thickness of 0.00014 mm, but the experiment showed that the character of all the phenomena was preserved. Thus this explanation had to be reconsidered, and this led to entirely new views on the nature of hydrodynamic phenomena in helium-II. The first outlines of these ideas were expressed by Tisza,^4 but their scientific development, their theoretical substantiation, and the creation of a hydrodynamic theory of the phenomenon belong to our scientist L. Landau.^5

I shall try to give the most general picture of these views. According to this theory, the counterflow which I tried to explain by the flow of helium in one energy state along the wall and of another inside the bulb is replaced by a counterflow of helium occurring within itself.

The explanation of this phenomenon given by Landau is as follows.

Liquid helium is, as it were, a mixture of two liquids. These two components of liquid helium are in two different quantum states. Owing to this, he showed that oppositely directed currents of one and the same liquid can exist simultaneously; these are what we observe in the neck of the vessel in Fig. 1.

If this theoretical proposition were not so fully supported by experimental evidence, it would sound like an idea that is very difficult to recognize as reasonable.

Landau’s theory gives a good description of the physical essence of those two states in which helium can exist simultaneously at temperatures below the λ-point. As I have already said, if helium, after liquefaction, is further cooled, it remains in the state of an ordinary liquid down to 2.19° abs., i.e. to the λ-point. Then, according to Landau’s theory, helium in a new state appears in this liquid as a kind of admixture. This new state is characterized, from the thermodynamic point of view, by zero entropy, and physically it has no viscosity. This helium is liquid helium-II in the state in which it would all be at absolute zero. But at any other temperature, simultaneously with this state, there exists, as it were, helium mixed with it and in the normal state. As the temperature is lowered, the concentration of helium in the normal state decreases and, conversely, the superfluid state of helium begins to predominate. Only at absolute zero should all the helium, according to the theory, pass into the superfluid state. This picture is sufficient for describing the phenomena observed by us. For example, the phenomenon observed in the experiment with the overflow of helium from the bulb, shown in Fig. 1, is explained as follows. Since helium in the superfluid state experiences no friction either against the walls or against the helium in the normal state, the stream flowing through the capillary,

does not create a friction reaction and can, as it were, imperceptibly fill the vessel. On the contrary, helium in the normal state flows out of the vessel with friction, and its flow is an ordinary liquid flow, long since studied by hydrodynamics. This normal flow is what is caught by the little wing placed in front of the mouth of the tube in Fig. 1, whereas the counterflow of helium in the superfluid state cannot be detected by ordinary methods.

On the basis of this same picture one can also explain the high thermal conductivity of helium II. As is evident, helium enters the vessel in the state of zero entropy, and helium returns in the normal state. To transform helium from one state into the other, a considerable quantity of heat must be expended. Such a process is a peculiar kind of convection and creates the impression of a high thermal conductivity of helium II.

All these phenomena, whose explanation requires us to imagine complex interactions between two different states of one and the same liquid in one and the same volume, fit only with difficulty into our customary framework even of physical thinking. In order to try to facilitate, at least somewhat, a superficial perception of this complex picture of the mechanism of the thermal conductivity of helium II, I shall permit myself to resort to an analogy with the counterflows of dressed and undressed people who circulate along the passageway in a theater cloakroom. The dressed will represent normal helium atoms that have received near the heater (“in the cloakroom”) the energy they need, while the undressed are the superfluid atoms of helium. Unfortunately, the analogy is more than incomplete, since helium atoms in the state of zero entropy pass by their fellows in the normal state without any interaction, whereas those who have not received their coats cannot possibly move through the crowd without strong friction.

On the basis of this picture one can explain why, when helium II flows through a narrow opening or a slit, a temperature difference appears. Since helium in the superfluid state flows more easily, without friction, through a small opening than helium in the normal state, a kind of filtration results. After the flow, the concentration of superfluid helium increases, and this corresponds to such a concentration of it as presupposes a lower temperature.

Between the theory developed by L. Landau and experiment there exists, on the basic questions, not only qualitative but also quantitative agreement. But there are also phenomena that are not covered by the theory. Their clarification is a matter for the future. The theory indicates certain phenomena—such as the existence of two velocities of sound—which have not yet been observed in liquid helium. The theory also does not take account of critical velocities, which are in fact observed. But it seems to me that in its main points the theory has come very close to the essence of the explanation of this remarkable phenomenon and constitutes an exceptionally valuable contribution to the study of this phenomenon. Work on the further elucidation of these phenomena is of great interest.

Now that we are again in Moscow, thanks to the remarkable successes of our Red Army and the heroism of its fighters, we can continue our scientific work on liquid helium, interrupted two and a half years ago by the invasion of the German barbarians.

References

1. P. L. Kapitsa, “The Problem of Liquid Helium,” report delivered at the general meeting of the Academy of Sciences of the USSR on December 23, 1940, Vestnik Akad. nauk SSSR, No. 2–3, 1941.
2. W. H. Keesom, miss Keesom, Physica, 3, 359, 1936.
3. P. L. Kapitsa, DAN SSSR, 18, 88, 1937; ZhETF, 11, issue 1, 1941.
4. L. W. Tisza, Nature, 141, 913, 1938; C. R., 207, 1035, 1938.
5. L. D. Landau, Journ. Physics USSR, 5, 71, 1941.

1. Report at the general meeting of the Academy of Sciences of the USSR in Moscow, September 27, 1943. ↩