Absorption and Dispersion of Ultrasonic Waves (eBook)

Front Cover 1
Absorption and Dispersion of Ultrasonic Waves 4
Copyright Page 5
Table of Contents 8
PREFACE 6
NOTATION 12
INTRODUCTION 20
Part: A. GENERAL THEORY OF RELAXATION IN FLUIDS 42
Chapter I.The Stokes-Navier Equations of Hydrodynamics 44
1. The State of the Fluid1 44
2. The Equations of Motion 46
3. The Linearized Hydrodynamic Equations 47
4. Thermodynamic Discussion of the Compressibility 49
5. The Linearized Wave Equation for a Nonviscous Fluid 51
6. Viscosity 53
7. The Stokes-Navier Equation. "Classical" Sound Absorption 57
8. Formal Introduction of Volume Viscosity 66
Chapter II. General Considerations on Relaxation 68
9. General Discussion of Resonance and Relaxation Phenomena 68
10. Energy Exchange between Internal and External Degrees of Freedom as Relaxation Phenomenon 74
11. The Effect of Slow Energy Exchange on Sound Propagation 78
12. Discussion of the Dispersion Equation 82
13. Different Ways of Evaluating the Dispersion Curve 86
14. The Absorption Curve 89
15. Continuation of the Discussion of Absorption 91
16. Continuation of the Discussion of Absorption and Dispersion: Kneser's Expression.1 Calculation of Ceit 95
17. Exact Calculation of Absorption and Dispersion 97
18. Dependence on t. Summary of Characteristic Times 99
19. Exchange of Energy and Relaxation Equation 102
20. General Discussion of the Case in Which More Than One Relaxation Time Exists 109
21. The Excitation of Different Degrees of Freedom Which Behave like a Group of Parallel Reactions1 112
22. Excitations of Different Degrees of Freedom Which Behave like Chemical Reactions in Series. Classical Theory 124
23. Excitation in Series, with Exchange with Translational Energy (Quantum Theory) 129
24. The Solution of the General Equations of Excitation in Series 136
25. Relation of Dispersion and Absorption If More Than One Relaxation Time Is Present. General Shape of the Curves 149
26. Mixtures 155
27. The Effect of Chemical Reactions 157
28. Discussion of Special Cases. Various Orders of the Reaction 162
29. Continuation of Discussion. Different Values of V and H' 166
30. Does the "Volume Viscosity" Provide Actual Stresses, Even if the Relaxation Phenomenon is the Slow Energy Exchange with Internal Degrees of Freedom or a Chemical Reaction? 175
31. Thermodynamic Theory of Relaxation 178
Chapter III. Special Topics 190
32. Scattering 190
33. Absorption of High Intensity Sound Waves 193
Part: B GASES 202
Chapter IV. Application of the General Formulas to Gases 204
34. Application of Previous Equations to Ideal Gases 204
35. Correction for Nonideality of the Gas 207
36. Viscosity and Relaxation Time for Translational Energy 213
37. Assumption That Only Binary Collisions Are Effective (See also Sec. 26) 221
38. Low Frequency Absorption. Ratio of Relaxation Absorption to Classical Absorption at Maximum 222
39. Gas Mixtures 225
40. Triple Collisions in Pure Gases and in Mixtures 228
41. Additional Absorption in Mixtures 234
Chapter V. Experimental Methods to Determine Velocity and Absorption of Ultrasonic Waves in Gases 236
42. Methods for Low Frequencies 236
43. The Ultrasonic Interferometer 238
44. Miscellaneous Methods 243
45. Aerodynamical Methods 244
46. Direct Methods for Measuring Absorption and Relaxation Time 248
Chapter VI. Experimental Results in Molecules Without Electronic Excitation 250
47. Translational Relaxation in Monatomic Gases 250
48. Methods to Determine Rotational Relaxation Time 253
49. Results for Rotational Relaxation 255
50. Oxygen, Nitrogen, Air 260
51. Other Diatomic Molecules 263
52. Linear Triatomic Molecules 265
53. Nonlinear Triatomic Molecules and Four Atomic Molecules 272
54. Large Molecules 274
Chapter VII. Theory of Vibrational and Rotational Energy Exchange 279
55. Introductory Remarks 279
56. The Theory of Landau and Teller (Classical) 281
57. Fundamental Quantum Consideration 286
58. Inelastic Scattering for an Exponential Interaction Potential 293
59. Introduction of a Better Interaction Potential 297
60. Tridimensional Case 304
61. Discussion of Scattering 307
62. Conclusion of the Tridimensional Calculation 314
63. Some Numerical Data. Effect of Molecular Frequency on Low Frequency Absorption 319
64. Simultaneous Transitions in Rotational, Vibrational, and Translational Energy 322
65. Polyatomic Molecules. More Than One Vibration Is Involved. Complex Collisions 334
66. Numerical Results for Diatomic and Linear Triatomic Molecules 340
67. Further Numerical Discussion of the Effect of Impurities, of Complex Collisions, and of Exact Resonance 347
68. Polyatomic Molecules: Methane and Chlorinated Methanes 350
69. Theory of Exchange of Rotational and Translational Energy 355
70. Energy Transfer and the Kinetics of Chemical Gas Reactions13 361
71. Summary and Comparison of Theory and Experiment 367
Part: C LIQUIDS 370
Chapter VIII. General Review of Ultrasonic Absorption and Dispersion in Liquids1,2 372
72. Classical Absorption 372
73. Absorption of Ultrasonic Waves in Liquids: The Situation in 1948. Pinkerton's Classification of Liquids 373
74. Developments Since 1948. Critical Review of Pinkerton's Classification 378
75. Velocity of Sound Waves of Ultrahigh Frequency (UHF) 380
Chapter IX. Experimental Methods to Determine Dispersion and Absorption of Ultrasonic Waves in Liquids 384
76. Methods for Low Frequencies 384
77. The Ultrasonic Interferometer 385
78. Pulse Methods 386
79. Mechanical Method: Radiation Pressure Measurements 387
80. Optical Methods1a 388
Chapter X. Review of Theories of Liquids 390
81. Introduction 390
82. Connection with Internal Pressure. Theory of Jäger 391
83. Heat Produced by Friction. Number of Collisions 394
84. Cubic Cell Model. Available Volume 396
85. Spherical Cell Model. "Free Volume" According to Thermodynamics 398
86. Spherical Cell Model. The Motion Treated as Simple Harmonic Motion 400
87. The Distribution Function Calculation of . and .
88. The Relaxation Time of the Distribution. Green's Theory 404
89. Brillouin's Theory of Viscosity 412
90. Eyring's Theory of Viscosity 414
91. The Theory of Bulk Viscosity by Gierer and Wirtz1 417
92. Theory of Relaxation Time. Theory of Absolute Reaction Rates 419
Chapter XI. Kneser Liquids 423
93. Discussion of Specific Heats in Nonassociated Organic Liquids with Molecules of Moderate Size 423
94. A Cooperative Theory of Relaxation Time for Kneser Liquids 424
95. Comparison of Relaxation Time in the Gaseous and Liquid States. Thermal Relaxation as due to Interaction between a Pair of Molecules 425
96. Temperature Dependence of the Absorption in Kneser Liquids 430
97. Carbon Disulfide CS2 431
98. Relaxation due to Rotational Isomerism 436
99. Liquid Mixtures 444
Chapter XII. Associated Liquids and Liquids with High Viscosity 447
100. The Theory of Hall 447
101. Eucken's Theory of the Constitution of Water 451
102. The Effect of Pressure on Sound Absorption in Water 454
103. The Associated Liquids (Other than Water) and the Glassy State 458
104. Elastic Moduli of Liquids 465
105. Distribution of Relaxation Times 473
106. Absorption and Dispersion Measurements in Glycerol 476
107. Absorption and Dispersion in n-Propyl Alcohol 480
108. Transversal or Shear Waves in Liquids 485
109. Compressional Relaxation in Associated Liquids. Comparison with Shear Relaxation 494
110. Velocity Dispersion in Associated Liquids 498
111. Numerical Relationships Between the Moduli 502
112. The Temperature Dependence of Elastic Moduli of Liquids 505
113. The Origin of Volume Viscosity in Associated Liquids 509
114. The Relation of Ultrasonic and Dielectric Relaxation Times 517
115. Ultrasonic Hysteresis at High Frequencies 522
116. Dissociation of Dimers: Acetic and Propionic Acids 524
117. Mixtures Containing Associated Liquids 528
118. Effect of Pressure on Ultrasonic Relaxation in Liquids 531
AUTHOR INDEX 536
SUBJECT INDEX 543