# Absorption and Dispersion of Ultrasonic Waves

## 1st Edition

**Authors:**Karl F. Herzfeld Theodore A. Litovitz

**Editors:**H. S. W. Massey Keith A. Brueckner

**eBook ISBN:**9781483275703

**Imprint:**Academic Press

**Published Date:**1st January 1959

**Page Count:**536

## Description

Absorption and Dispersion of Ultrasonic Waves focuses on the influence of ultrasonics on molecular processes in liquids and gases, including hydrodynamics, energy exchange, and chemical reactions.

The book first offers information on the Stokes-Navier equations of hydrodynamics, as well as equations of motion, viscosity, formal introduction of volume viscosity, and linearized wave equation for a nonviscous fluid. The manuscript then ponders on energy exchange between internal and external degrees of freedom as relaxation phenomenon; effect of slow energy exchange on sound propagation; different ways of evaluating the dispersion curve; and exact calculation of absorption and dispersion.

The text examines the effects of chemical reactions, thermodynamic theory of relaxation, and mixtures. The book also evaluates the absorption of high intensity sound waves, ratio of relaxation absorption to classical absorption at maximum, and gas mixtures. Discussions also focus on translational relaxation in monatomic gases, linear triatomic molecules, and results for rotational relaxation.

The manuscript is a dependable source of data for readers interested in the absorption and dispersion of ultrasonic waves.

## Table of Contents

Contents

Preface

List of Notations

Introduction

A. General Theory of Relaxation in Fluids

I. The Stokes-Navier Equations of Hydrodynamics

1. The State of the Fluid

2. The Equations of Motion

3. The Linearized Hydrodynamic Equations

4. Thermodynamic Discussion of the Compressibility

5. The Linearized Wave Equation for a Nonviscous Fluid

6. Viscosity

7. The Stokes-Navier Equation. "Classical" Sound Absorption

8. Formal Introduction of Volume Viscosity

II. General Considerations on Relaxation

9. General Discussion of Resonance and Relaxation Phenomena

10. Energy Exchange between Internal and External Degrees of Freedom as Relaxation Phenomenon

11. The Effect of Slow Energy Exchange on Sound Propagation

12. Discussion of the Dispersion Equation

13. Different Ways of Evaluating the Dispersion Curve

14. The Absorption Curve

15. Continuation of the Discussion of Absorption

16. Continuation of the Discussion of Absorption and Dispersion: Kneser's Expression. Calculation of Ceff

17. Exact Calculation of Absorption and Dispersion

18. Dependence on τ. Summary of Characteristic Times

19. Exchange of Energy and Relaxation Equation

20. General Discussion of the Case in Which More Than One Relaxation Time Exists

21. The Excitation of Different Degrees of Freedom Which Behave like a Group

of Parallel Reactions

22. Excitations of Different Degrees of Freedom Which Behave like Chemical Reactions in Series. Classical Theory

23. Excitation in Series, with Exchange with Translational Energy (Quantum Theory)

24. The Solution of the General Equations of Excitation in Series

25. Relation of Dispersion and Absorption if More Than One Relaxation Time Is Present. General Shape of the Curves

26. Mixtures

27. The Effect of Chemical Reactions

28. Discussion of Special Cases. Various Orders of the Reaction

29. Continuation of Discussion. Different Values of V and H'

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?

31. Thermodynamic Theory of Relaxation

III. Special Topics

32. Scattering

33. Absorption of High Intensity Sound Waves

B. Gases

IV. Application of the General Formulas to Gases

34. Application of Previous Equations to Ideal Gases

35. Correction for Nonideality of the Gas

36. Viscosity and Relaxation Time for Translational Energy

37. Assumption That Only Binary Collisions are Effective

38. Low Frequency Absorption. Ratio of Relaxation Absorption to Classical Absorption at Maximum

39. Gas Mixtures

40. Triple Collisions in Pure Gases and in Mixtures

41. Additional Absorption in Mixtures

V. Experimental Methods to Determine Velocity and Absorption of Ultrasonic Waves in Gases

42. Methods for Low Frequencies

43. The Ultrasonic Interferometer

44. Miscellaneous Methods

45. Aerodynamical Methods

46. Direct Methods for Measuring Absorption and Relaxation Time

VI. Experimental Results in Molecules Without Electronic Excitation

47. Translational Relaxation in Monatomic Gases

48. Methods to Determine Rotational Relaxation Time

49. Results for Rotational Relaxation

50. Oxygen, Nitrogen, Air

51. Other Diatomic Molecules

52. Linear Triatomic Molecules

53. Nonlinear Triatomic Molecules and Four Atomic Molecules

54. Large Molecules

VII. Theory of Vibrational and Rotational Energy Exchange

65. Introductory Remarks

56. The Theory of Landau and Teller (Classical)

67. Fundamental Quantum Consideration

58. Inelastic Scattering for an Exponential Interaction Potential

59. Introduction of a Better Interaction Potential

60. Tridimensional Case

61. Discussion of Scattering

62. Conclusion of the Tridimensional Calculation

63. Some Numerical Data. Effect of Molecular Frequency on Low Frequency Absorption

64. Simultaneous' Transitions in Rotational, Vibrational, and Translational Energy

65. Polyatomic Molecules. More Than One Vibrations Is Involved. Complex Collisions

66. Numerical Results for Diatomic and Linear Triatomic Molecules

67. Further Numerical Discussion of the Effect of Impurities, of Complex Collisions, and of Exact Resonance

68. Polyatomic Molecules: Methane and Chlorinated Methanes

69. Theory of Exchange of Rotational and Translational Energy

70. Energy Transfer and the Kinetics of Chemical Gas Reactions

71. Summary and Comparison of Theory and Experiment

C Liquids

VIII. General Review of Ultrasonic Absorption and Dispersion in Liquids

72. Classical Absorption

73. Absorption of Ultrasonic Waves in Liquids : The Situation in 1948. Pinkerton's Classification of Liquids

74. Developments Since 1948. Critical Review of Pinkerton's Classification

75. Velocity of Sound Waves of Ultrahigh Frequency (UHF)

IX. Experimental Methods to Determine Dispersion and Absorption of Ultrasonic Waves in Liquids

76. Methods for Low Frequencies

77. The Ultrasonic Interferometer

78. Pulse Methods

79. Mechanical Method: Radiation Pressure Measurements

80. Optical Methods

X. Review of Theories of Liquids

81. Introduction

82. Connection with Internal Pressure. Theory of Jäger

83. Heat Produced by Friction. Number of Collisions

84. Cubic Cell Model. Available Volume

85. Spherical Cell Model. "Free Volume" According to Thermodynamics

86. Spherical Cell Model. The Motion Treated as Simple Harmonic Motion

87. The Distribution Function; Calculation of η and η'

88. The Relaxation Time of the Distribution. Green's Theory

89. Brillouin's Theory of Viscosity

90. Eyring's Theory of Viscosity

91. The Theory of Bulk Viscosity by Gierer and Wirtz

92. Theory of Relaxation Time. Theory of Absolute Reaction Rates

XI. Kneser Liquids

93. Discussion of Specific Heats in Nonassociated Organic Liquids with Molecules of Moderate Size

94. A Cooperative Theory of Relaxation Time for Kneser Liquids

95. Comparison of Relaxation Time in the Gaseous and Liquid States. Thermal Relaxation as due to Interaction between a Pair of Molecules

96. Temperature Dependence of the Absorption in Kneser Liquids

97. Carbon Disulfide CS2

98. Relaxation due to Rotational Isomerism

99. Liquid Mixtures

XII. Associated Liquids and Liquids with High Viscosity

100. The Theory of Hall

101. Eucken's Theory of the Constitution of Water

102. The Effect of Pressure on Sound Absorption in Water

103. The Associated Liquids (Other than Water) and the Glassy State

104. Elastic Moduli of Liquids

105. Distribution of Relaxation Times

106. Absorption and Dispersion Measurements in Glycerol

107. Absorption and Dispersion in η-Propyl Alcohol

108. Transversal or Shear Waves in Liquids

109. Compressional Relaxation in Associated Liquids. Comparison with Shear Relaxation

110. Velocity Dispersion in Associated Liquids

111. Numerical Relationships Between the Moduli

112. The Temperature Dependence of Elastic Moduli of Liquids

113. The Origin of Volume Viscosity in Associated Liquids

114. The Relation of Ultrasonic and Dielectric Relaxation Times

115. Ultrasonic Hysteresis at High Frequencies

116. Dissociation of Dimers: Acetic and Propionic Acids

117. Mixtures Containing Associated Liquids

118. Effect of Pressure on Ultrasonic Relaxation in Liquids

Author Index

Subject Index

## Details

- No. of pages:
- 536

- Language:
- English

- Copyright:
- © Academic Press 1959

- Published:
- 1st January 1959

- Imprint:
- Academic Press

- eBook ISBN:
- 9781483275703