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.

Contenu

Contents

Preface

List of Notations

Introduction

A. General Theory of Relaxation in Fluids

I. The Stokes-Navier Equations of Hydrodynamics

The State of the Fluid
The Equations of Motion
The Linearized Hydrodynamic Equations
Thermodynamic Discussion of the Compressibility
The Linearized Wave Equation for a Nonviscous Fluid
Viscosity
The Stokes-Navier Equation. "Classical" Sound Absorption
Formal Introduction of Volume Viscosity
II. General Considerations on Relaxation
General Discussion of Resonance and Relaxation Phenomena
Energy Exchange between Internal and External Degrees of Freedom as Relaxation Phenomenon
The Effect of Slow Energy Exchange on Sound Propagation
Discussion of the Dispersion Equation
Different Ways of Evaluating the Dispersion Curve
The Absorption Curve
Continuation of the Discussion of Absorption
Continuation of the Discussion of Absorption and Dispersion: Kneser's Expression. Calculation of Ceff
Exact Calculation of Absorption and Dispersion
Dependence on t. Summary of Characteristic Times
Exchange of Energy and Relaxation Equation
General Discussion of the Case in Which More Than One Relaxation Time Exists
The Excitation of Different Degrees of Freedom Which Behave like a Group
of Parallel Reactions
Excitations of Different Degrees of Freedom Which Behave like Chemical Reactions in Series. Classical Theory
Excitation in Series, with Exchange with Translational Energy (Quantum Theory)
The Solution of the General Equations of Excitation in Series
Relation of Dispersion and Absorption if More Than One Relaxation Time Is Present. General Shape of the Curves
Mixtures
The Effect of Chemical Reactions
Discussion of Special Cases. Various Orders of the Reaction
Continuation of Discussion. Different Values of V and H'
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?
Thermodynamic Theory of Relaxation
III. Special Topics
Scattering
Absorption of High Intensity Sound Waves

B. Gases

IV. Application of the General Formulas to Gases

Application of Previous Equations to Ideal Gases
Correction for Nonideality of the Gas
Viscosity and Relaxation Time for Translational Energy
Assumption That Only Binary Collisions are Effective
Low Frequency Absorption. Ratio of Relaxation Absorption to Classical Absorption at Maximum
Gas Mixtures
Triple Collisions in Pure Gases and in Mixtures
Additional Absorption in Mixtures
V. Experimental Methods to Determine Velocity and Absorption of Ultrasonic Waves in Gases
Methods for Low Frequencies
The Ultrasonic Interferometer
Miscellaneous Methods
Aerodynamical Methods
Direct Methods for Measuring Absorption and Relaxation Time
VI. Experimental Results in Molecules Without Electronic Excitation
Translational Relaxation in Monatomic Gases
Methods to Determine Rotational Relaxation Time
Results for Rotational Relaxation
Oxygen, Nitrogen, Air
Other Diatomic Molecules
Linear Triatomic Molecules
Nonlinear Triatomic Molecules and Four Atomic Molecules
Large Molecules
VII. Theory of Vibrational and Rotational Energy Exchange
Introductory Remarks
The Theory of Landau and Teller (Classical)
Fundamental Quantum Consideration
Inelastic Scattering for an Exponential Interaction Potential
Introduction of a Better Interaction Potential
Tridimensional Case
Discussion of Scattering
Conclusion of the Tridimensional Calculation
Some Numerical Data. Effect of Molecular Frequency on Low Frequency Absorption
Simultaneous' Transitions in Rotational, Vibrational, and Translational Energy
Polyatomic Molecules. More Than One Vibrations Is Involved. Complex Collisions
Numerical Results for Diatomic and Linear Triatomic Molecules
Further Numerical Discussion of the Effect of Impurities, of Complex Collisions, and of Exact Resonance
Polyatomic Molecules: Methane and Chlorinated Methanes
Theory of Exchange of Rotational and Translational Energy
Energy Transfer and the Kinetics of Chemical Gas Reactions
Summary and Comparison of Theory and Experiment

C Liquids

VIII. General Review of Ultrasonic Absorption and Dispersion in Liquids

Classical Absorption
Absorption of Ultrasonic Waves in Liquids : The Situation in 1948. Pinkerton's Classification of Liquids
Developments Since 1948. Critical Review of Pinkerton's Classification
Velocity of Sound Waves of Ultrahigh Frequency (UHF)
IX. Experimental Methods to Determine Dispersion and Absorption of Ultrasonic Waves in Liquids
Methods for Low Frequencies
The Ultrasonic Interferometer
Pulse Methods
Mechanical Method: Radiation Pressure Measurements
Optical Methods
X. Review of Theories of Liquids
Introduction
Connection with Internal Pressure. Theory of Jäger
Heat Produced by Friction. Number of Collisions
Cubic Cell Model. Available Volume
Spherical Cell Model. "Free Volume" According to Thermodynamics
Spherical Cell Model. The Motion Treated as Simple Harmonic Motion
The Distribution Function; Calculation of and '
The Relaxation Time of the Distribution. Green's Theory
Brillouin's Theory of Viscosity
Eyring's Theory of Viscosity
The Theory of Bulk Viscosity by Gierer and Wirtz
Theory of Relaxation Time. Theory of Absolute Reaction Rates
XI. Kneser Liquids
Discussion of Specific Heats in Nonassociated Organic Liquids with Molecules of Moderate Size
A Cooperative Theory of Relaxation Time for Kneser Liquids
Comparison of Relaxation Time in the Gaseous and Liquid States. Thermal Relaxation as due to Interaction between a Pair of Molecules
Temperature Dependence of the Absorption in Kneser Liquids
Carbon Disulfide CS2
Relax…