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Title: Experiments on transport phenomena at low temperatures
Author: Chandrasekhar, B. S.
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 1952
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This thesis deals mainly with soraa investigations on the helium II film in motion. Some experiments are also described on the flow of liquid helium II through a capillary packed with jewellers rouge. A summary, chapter by chapter, of the contents of the thesis follows. Chapter 1. This contains a brief survey of the state of our experimental knowledge about the helium II film when these investigations were started. The various theories of the film that have been proposed, are very briefly reviewed, with particular regard to their physical interpretation. This survey is relevant to an understanding of the experiments that are described in the succeeding chapters of the thesis. A brief description of the oryostat and auxiliary apparatus that were used in these experiments is given. Chapter 2. The isothermal transfer of the helium II film at sub- critical ratas has been studied. The study of such transfer is of importance, for it can give information About frictional forces which may arise during the motion of the film. Sub-critical rates are produced in a manner analogous to that by which the current in a superconductor is kept below its critical value by means of a limiting series resistance, A detailed analysis of the results shows that neither the hypothesis of vanishing viscosity for Helium II, nor the mechanism of siphon flow, can account for these sub-critical rates. The concept of the aero-point diffusion of the superfluid, suggested by Mendelssohn, is shown to provide a satisfactory explanation of the results. Chapter 3. An investigation of the transfer of the helium II film at sub-critical rates, produced by the thermomechanical effect, is described. This method is more versatile than the one described in chapter 2, for a wide range of sub-critical rates can be produced vary much more simply. The apparatus consists essentially of a small glass dewar with a well-fitting lid, so that the inside of the dewar is thermally well isolated from the outside world. Flow of liquid helium II into the dewar through the film is produced by supplying heat electrically to the inside. The variation of the rate of flow with the heating rate, for different temperatures, has been studied. Some interesting results on the properties of the film follow: The flow in the film is friotionless for a wide range of sub-critioal velocities. This provides an independent and more complete oorroboratiun of the conclusions obtained In chapter 2. It is pointed out that, for these sub-critical rates in the film, the Gorter-Mellink theory of mutual friction is inapplicable. On the other hand, it seems clear that a mechanism allowing a sharp onset of the critical rate, below which the flow is frictionless, is necessary. Such a mechanism is provided by all those theories of film transfer which ultimately appeal to the principle of indeterminacy for determining the minimum excitation energy of the moving liquid. The heat of transport, Q, of the helium II film has been determined as a function of the temperature. The difference between this quantity, and H, the heat content (or enthalpy) of the bulk liquid, is pointed out. This distinction has caused some confusion in the past. It is shown that the entropy carried by the loving film is vanishingly small (the Tisza-London hypothesis), by calculating the entropy S of the bulk liquid from the relation Q = TS, and comparing it with that obtained from specific heat measurements. The heat of transport Q has been determined in the present experiments directly; it is, in essence, an isothermal, isobario determination for the film. The experiments of Kapitza on the fountain effect also give values of Q, for bulk flow in narrow channels, deduced from H.London's equation. There is close agreement between the Q's obtained by the two methods, thus supporting the interpretation, on the two-fluid model, of these phenomena. Chapter 4 Some observations are reported, which establish the conditions under which bulk liquid can "be formed from the helium II film during isothermal transfer. It had been thought previously that bulk liquid could be so formed, at any point below the highest meniscus, in a given arrangement for film transfer. The present experiments show that this is a necessary, but not a sufficient condition. The film will only form bulk liquid if it has to flow at a super-critical rate in order to remain as the film. In other words, bulk liquid is formed if the film encounters a perimeter, smaller than the limiting perimeter above the highest manisous. These considerations do not apply to the lowest point on the surface for film transfer, where bulk liquid can always be formed from the film. The experiments provide an indirect confirmation of the uniqueness of the critical rate of film transfer. Chapter 5 The transfer rates of the helium II film on a variety of surfaces have been studied, and the following results obtained: Experiments with specially polished stainless steel beakers show that the anomalous transfer rates previously observed on metal surfaces are to be associated with capillary flow in surface cracks and irregularities. If such a surface could be given a finish comparable to that of glass, the transfer rate would be the same as that on glass. A study of the transfer rates on perspex and lucite in dependence on their surface finish corroborates the hypothesis of capillary flow; it is suggested that this may also be responsible for the maximum in the curve of transfer rate versus temperature, observed in some cases. Surface flow of liquid helium just above the &gamme;-point, simulating genuine film transfer, was predicted, and actually observed in a carefully shielded 'rough' perspex beaker. This provides further evidence for the hypothesis of capillary flow. Experiments are described, which show that the increase in the transfer rates observed when the higher meniscus is near the rim of the be beaker, cannot be due to an increased thickness of the film at the rim. An alternative explanation is offered, that it is a manifestation of capillary flow, possibly coupled with the effect of a random distribution of the (microscopic) available perimeters for film transfer. The transfer rates on glass have been measured under large gravitational pressure differences, up to 15 cms. of liquid helium. It appears likely that the increased potential difference has no influence on the transfer rate, the observed increase of which can be attributed to the surface structure of the beakers used. All these experiments point indubitably to a uniquely defined critical rate of transfer of the Helium II film, independent of the nature of the substrate. Thus a complete theory of the critical rate should come out of the quantum mechanics of the helium film alone, independently of the nature of the forces between the atoms in the substrate and the helium atoms. This last factor would of course influence the thickness of the film. It thus appears that the theories of the critical rate based on considerations of zero-point energy are in the right direction. Chapter 6. The flow of helium II through a capillary tightly packed with jewellers rouge has been studied, under thermal and gravitational potential gradients. The pressure at an intermediate point in the channel is measured by the method previously used by Bowers and Mendelssohn in their experiments with smooth narrow channels. It appears that superflow in such tortuous channels is of a turbulent nature under isothermal conditions. The possibility of turbulence in superflow, thus established, has an important bearing on the interpretation of a large number of experiments on the flow in capillaries, and on experiments with oscillating discs. The thermal flow measurements show a curious inconsistency with those on gravitational flow. For a wide range of velocities, thermal flow is frictionless, while gravitational flow is dissipative; this is deduced from the behiviour of the pressure at the intermediate point in the channal. Furthermore, thermal flow shows a more or less sharp critical rate, while gravitational flow does not do so. These observations indicate that the concept of 'pressure at a point' in a superflow channel may not have the same meaning as in classical flow; it is not simply dependent on the pressures at the two ends, but requires one or more other parameters to determine it.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available