Properties of Gases, Liquids, and Solutions: Physical Acoustics

482 Pages·1965·7.61 MB·English

by  WARREN P. MASON (Eds.)

PHYSICAL ACOUSTICS
PRINCIPLES AND METHODS
Volume I-Part A and B Methods and Devices
Volume Il-Part A Properties of Gases, Liquids, and Solutions
Volume Il-Part B Properties of Polymers and Nonlinear Acoustics
Volume III Applications to the Study of Imperfections
and Lattice Dynamics. (In two parts)
Volume IV Applications to Quantum and Solid State
Physics
CONTRIBUTORS TO VOLUME II A
H.-J. BAUER
C. M. DAVIS
MARTIN GREENSPAN
H. 0. KNESER
JOHN LAMB
T. A. LITOVITZ
JOHN STUEHR
ERNEST YEAGER
PHYSICAL ACOUSTICS
Principles and Methods
Edited by WARREN P. MASON
BELL TELEPHONE LABORATORIES, INCORPORATED
MURRAY HILL, NEW JERSEY
VOLUME ll-PART A
Properties of Gases,
Liquids, and Solutions
1965
ACADEMIC PRESS
NEW YORK AND LONDON
COPYRIGHT © 1965, BY ACADEMIC PRESS INC.
ALL RIGHTS RESERVED.
NO PART OF THIS BOOK MAY BE REPRODUCED IN ANY FORM,
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United Kingdom Edition published by
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LIBRARY OF CONGRESS CATALOG CARD NUMBER : 63-22327
PRINTED IN THE UNITED STATES OF AMERICA
CONTRIBUTORS
H.-J. BAUER
I. Physikalisches Institut der Technischen
Hochschule, Stuttgart, Germany
C. M. DAVIS
U.S. Naval Ordinance Laboratory, White Oak,
Silver Spring, Maryland
MARTIN GREENSPAN
National Bureau of Standards, Washington, D.C.
H. 0. KNESER
I. Physikalisches Institut der Technischen
Hochschule, Stuttgart, Germany
JOHN LAMB
Department of Electrical Engineering, The
University, Glasgow, Scotland
T. A. LITOVITZ
Physics Department, Catholic University of
America, Washington, D.C.
JOHN STUEHR
Morley Chemical Laboratories, Western Reserve
University, Cleveland, Ohio
ERNEST YEAGER
Morley Chemical Laboratories, Western Reserve
University, Cleveland, Ohio
v
PREFACE
In Volume II the methods for detecting and generating sound waves
which were discussed in Volume I of this treatise have been applied to
determining the properties and interactions between atoms and
molecules of gases, liquids, solutions, and polymer materials. The
first three chapters deal with the properties of gases. Starting with a
gas so rarefied that the molecules can be regarded as similar to ping
pong balls that seldom collide, the properties of gases are considered
up to condensed phases. The longitudinal motion of the acoustic wave
is often converted into rotational and vibrational motions of the
molecules. This occurs because of the collisions of molecules and
requires a certain time known as a relaxation time. When the angular
frequency of the sound waves multiplied by the relaxation time is near
unity, a marked increase in the attenuation and a dispersion in the
velocity occur. Hence, acoustic measurements are one of the principal
methods for determining these interactions, which are known as
relaxations. These relaxations satisfy certain thermodynamic princi-
ples, and when one uses irreversible thermodynamics, the measured
results can be related to the molecular properties.
Relaxations also occur in liquids and can be of either the thermal
relaxation type found in gases or the type due to a structural rearrange-
ment of the molecule. These later relaxations are usually associated
with longer chain molecules. At very high frequencies, the liquids have
many of the properties of a solid, i.e., they have shear elastic moduli
and shear and longitudinal stiffnesses in the order of the values found
for polymer materials. In fact, the structurally relaxing liquids form a
bridge between the gaslike behavior of liquids and the solidlike behavior
of glasses and polymer materials which are treated in Volume IIB.
Another interesting case for which acoustic measurements can
provide significant information on the arrangement of matter is
electrolytic solutions. The introduction of electrolytic ions tends to
disrupt the prevailing short range order in the solvent and to establish
a new structure in which the solvent dipoles are oriented around the
electrolytic ions. Here again the measurements of attenuations and
sound velocities in these solutions provide considerable information on
the arrangement and motions of atoms possible in the solution. This
type of attenuation is important for underwater sound transmission in
sea water.
Volume IIB deals with more closely packed materials than found in
liquids which, however, retain the ability to perform some atomic
movements. These are the polymer materials and the glasses. They
vii
viii Preface
form a bond between the liquids discussed in Volume IIA and the
solids discussed in Volumes III and IV. Relaxations occur in these
materials and one of the most useful methods for investigating them
is the measurement of acoustic attenuation and velocities. Three
chapters in this volume are devoted to various methods for investigat-
ing these relaxations and to the information concerning molecular
motions that can be derived from these measurements.
As the energy of the sound wave introduced into the transmission
medium increases, nonlinearities in the transmission occur. One of these
nonlinearities is the production of cavitation in liquids as discussed
in Volume IB. Other phenomena which occur are the generation of
harmonics and the increase of the propagation velocities. These
effects at very high amplitudes converge on a new phenomenon, the
acoustic shock wave. High amplitude waves also produce some mass
motion in a liquid which is known as acoustic streaming. Interesting
biological and chemical phenomena can be produced by this streaming.
An important method for measuring nonlinearities in liquids and
solids is the light diffraction method. In liquids, the sound waves
produce dense and rarefied regions which act as phase diffraction grat-
ings for light transmitted parallel to the wave fronts. For low sound
amplitudes light spectra of equal intensities are produced at equal
angles from the main beam, the angles being determined by the ratio
of the sound wavelength to the light wavelength. When nonlinearities
in the sound wave motion occur, one of the side spectra predominates
over the other, and an analysis of the relative intensities gives a measure
of the nonlinearity. For a solid it is the piezo-optic effect rather than
the density change that produces the spectra. The last chapter of
Volume IIB discusses these relations.
The editor wishes again to thank the many contributors who have
made these volumes possible and the publishers for their unfailing help
and advice.
December, 1964 WARREN P. MASON
CONTENTS OF VOLUME I—PART A
Wave Propagation in Fluids and Normal Solids
R. N. THURSTON
Guided Wave Propagation in Elongated Cylinders and Plates
T. R. MEEKER and A. H. MEITZLER
Piezoelectric and Piezomagnetic Materials and Their Function in
Transducers
DON A. BERLINCOURT, DANIEL R. CURRAN, and HANS JAFFE
Ultrasonic Methods for Measuring the Mechanical Properties of Liquids
and Solids
H. J. MCSKIMIN
Use of Piezoelectric Crystals and Mechanical Resonators in Filters and
Oscillators
WARREN P. MASON
Guided Wave Ultrasonic Delay Lines
JOHN E. MAY, JR.
Multiple Reflection Ultrasonic Delay Lines
WARREN P. MASON
XUl
CONTENTS OF VOLUME I—PART B
The Use of High- and Low-Amplitude Ultrasonic Waves for Inspection
and Processing
BENSON CARLIN
Physics of Acoustic Cavitation in Liquids
H. G. FLYNN
Semiconductor Transducers—General Considerations
WARREN P. MASON
Useof Semiconductor Transducers in Measuring Strains, Accelerations,
and Displacements
R. N. THURSTON
Use of p-n Junction Semiconductor Transducers in Pressure and Strain
Measurements
M. E. SIKORSKI
The Depletion Layer and Other High-Frequency Transducers Using
Fundamental Modes
D. L. WHITE
The Design of Resonant Vibrators
EDWARD EISNER
xiv
CONTENTS OF VOLUME II—PART B
Relaxations in Polymer Solutions, Liquids, and Gels
W. PHILIPPOFF
Relaxation Spectra and Relaxation Processes in Solid Polymers and
Glasses
I. L. HOPKINS and C. R. KURKJIAN
Volume Relaxations in Amorphous Polymers
ROBERT S. MARVIN and JOHN E. MCKINNEY
Nonlinear Acoustics
ROBERT T. BEYER
Acoustic Streaming
WESLEY LE MARS NYBORG
Use of Light Diffraction in Measuring the Parameter of Nonlinearity of
Liquids and the Photoelastic Constants of Solids
L. E. HARGROVE and K. ACHYUTHAN
xv
—1—
Transmission of Sound Waves in Gases at
Very Low Pressures
MARTIN GREENSPAN
National Bureau of Standards, Washington, D.C.
I. Introduction 1
II. Nomenclature 3
A. General 3
B. List of Symbols 4
III. Theory 7
A. The Boltzmann Equation and Its Integrals 7
B. The Constitutive Relations 10
C. Plane Waves 16
D. The Propagation Constant 17
E. The Direct Attack 27
IV. Experimental Methods 28
A. General 28
B. Single-Crystal Interferometer 30
C. Double-Crystal Interferometer 32
V. Results and Discussion 34
VI. Mixtures 35
VII. Free-Molecule Propagation 37
VIII. Appendix: Tables 40
References 43
I. Introduction
The study of sound propagation in a fluid is essentially a problem in
the hydrodynamics of small motions, and, if attention be confined to
situations in which viscous, thermal, and relaxational effects are
negligible, then no especial interest attaches to the problem. 1 It is only
when circumstances are such that these ordinarily small effects become
easily measurable that useful information about the structure of the
1 Nevertheless, such measurements find many applications, as for instance
in the determination of specific-heat ratios and in instruments which measure
temperature, composition, etc.
1