《LIQUID HELIUM》

CHAPTER 1Introduction1

1.1.The liquefaction of helium1

1.2.The λ-transition2

1.3.Super-fluidity and the two-fluid theory3

1.4.The liquid helium film6

1.5.Thermal effects9

1.6.Second sound14

1.7.Helium three17

CHAPTER 2Equilibrium Properties19

2.1.The phase diagram19

2.2.Energy relations near o°K.21

2.3.Theories of the structure of the liquid near o°K.24

2.4.χ -ray and neutron diffraction experiments28

2.5.Some basic thermodynamic quantities32

2.5.1.The specific heat32

2.5.2.The latent heat of vaporization35

2.5.3.The density,coefficient of expansion and equation of state36

2.5.4.The dielectric constant and the refractive index38

2.5.5.The surface tension40

2.6.The nature of the λ-transition41

2.6.1.The Ehrenfest relations41

2.6.2.Fluctuations near the λ-point48

CHAPTER 3Theories52

3.1.Bose-Einstein condensation52

3.1.1.Bose-Einstein condensation in an ideal gas52

3.1.2.Bose-Einstein condensation in a liquid56

3.2.Landau’s theory58

3.2.1.Phonons and rotons58

3.2.2.The thermodynamic functions62

3.2.3.The density of the normal component,Pn66

3.3.The nature of the elementary excitations70

3.3.1.Quan-tum hydrodynamics70

3.3.2.Feynman’s theories73

3.3.3.Quantum hydrodynamics and the excitation curve80

3.4.The quantum mechanical many body problem82

CHtAPTER 4The New Thermohydrodynamics87

4.1.The need for a new hydrodynamics87

4.2.Superfluidity88

4.2.1.Isothermal flow through narrow channels88

4.2.2.The flow of the films91

4.2.3.Flow through fine pores94

4.2.4.Bulk liquid95

4.3.Thermal effects97

4.3.1.The mechanocaloric effect97

4.3.2.The thermomechanical effect99

4.3.3.Theory100

4.4.The thermo-hydrodynamical equations102

4.5.The viscosity of the normal component,ηn104

4.5.1.Experimental determination of ηn104

4.5.2.The Landau-Khalatnikov theory of ηn106

4.6.Theories of superfluidity111

4.6.1.The nature of superfluidity111

4.6.2.Interaction of the superfluid compo-nent and the walls112

4.6.3.Quantized vortex lines114

4.6.4.Liquid in a rotating cylindrical vessel117

CHAPTER 5First and Second Sound123

5.1.The two types of wave propagation123

5.1.1.The two wave velocities123

5.1.2.Irreversibleeffects and attenuation125

5.2.Firstsound128

5.2.1.The velocity of first sound128

5.2.2.The attenuation of first sound near the λ-point131

5.2.3.The attenuation of first sound below 2°K.136

5.3.Second sound141

5.3.1.The nature of second sound141

5.3.2.The velocity of second sound148

5.3.3.The attenuation of second sound155

5.3.4.Large amplitude effects and shock waves157

5.3.5.The Pitot tube,the Rayleigh disk and the radiation balance161

5.4.The thermo-hydrodynamical equations163

CHAPTER 6Further Aspects of the Thermohydrodynamics164

6.1.Second sound in uniformly rotating liquid164

6.1.1.The experi-ments and their interpretation in terms of vortex lines164

6.1.2.Calcula-tion of the magnitude of the extra attenuation168

6.2.The breakdown of superfluidity171

6.3.Mutual friction172

6.3.1.The thermo-mechanical effect172

6.3.2.Thermal conduction174

6.3.3.Flow through narrow channels177

6.4.Mutual friction and vorticity181

6.4.1.Second sound in a heat current181

6.4.2.Transient effects185

6.5.Further investigations of non-linear dissipative processes188

6.5.1.Gravitational flow through wide capillaries188

6.5.2.The rotating cylinder viscometer190

6.5.3.Accelerating systems192

6.6.Critical velocities198

6.7.The Kapitza boundary effect201

CHAPTER 7Helium Films205

7.1.Introduction205

7.2.Experimental difficulties206

7.3.Measure-ments of the thickness of the saturated film208

7.4.Unsaturated films211

7.5.The flow of the saturated film214

7.6.The flow of unsaturated films219

7.7.Theories of the formation of the film224

CHIAPTER 8Helium Three230

8.1.Introduction230

8.2.Some basic properties231

8.3.The entropy and specific heat234

8.4.Magnetic properties237

8.5.Trans-port properties239

8.6.Theories of liquid He3241

8.6.1.de Boer’s modified law of corresponding states241

8.6.2.The ideal Fermi-Dirac gas244

8.6.3.The Fermi liquid245

8.6.4.Transport properties and zero sound248

8.6.5.Cell models and other theories250

8.7.The melting curve252

CHAPTER 9He3-He4 Mixtures256

9.1.Thermodynamic properties256

9.1.1.The theory of ideal solutions256

9.1.2.The vapour pressure and distribution coefficient258

9.1.3.Departures from ideality262

9.2.Theories of He3-He4 mixtures267

9.3.Variation of the λ-temperature with concentration272

9.4.The thermohydrodynamics of He3-He4 mixtures275

9.4.1.Non-participation of He3 in superfluid flow275

9.4.2.The thermohydro-dynamical equations279

9.4.3.Heat conduction in He3-He4 mixtures281

9.5.Second sound in He3-He4 mixtures284

9.6.Normal density,Pn,and viscosity,ηn288

9.7.Methods of concentrating He3-He4 mixtures291

9.8.Ions in liquid helium292

REFERENCES294

INDEX309