HIGH-INTENSITY ULTRASONIC FIELDS

HIGH-INTENSITY ULTRASONIC FIELDS

ULTRASONIC TECHNOLOGY A Series of Monographs General Editor Lewis Balamuth Ultrasonic Systems, Inc., Farmingdale, N. Y. 1967: RAYLEIGH AJ'jl> LAMB WAVES Physical Theory and Applications I. A. Viktorov 1969: SOURCES OF IDGH-INTENSITY ULTRASOUND Volume 1 Edited by L. D. Rozenberg SOURCES OF IDGH I~"TENSITY ULTRASOUND Volume 2 Edited by L. D. Rozenberg 1971: ULTRASONIC TRANSDUCER MATERIALS Edited by 0. E. Mattiat IDGH-INTENSITY ULTRASONIC FIELDS Edited by L. D. Rozenberg

HIGH-INTENSITY ULTRASONIC FIELDS Edited by L.D. Rozenberg Acoustics Institute Academy of Sciences of the USSR Moscow, USSR Translated from Russian by James S. Wood 9? SPRINGER SCIENCE+BUSINESS MEDIA, LLC 1971

The original Russian text, published by Nauka Press for the Acoustics Institute, Academy of Sciences of the USSR, in 1968, has been corrected for the present edition. The English translation is published under an agreement with Mezhdunarodnaya Kniga, the Soviet book export agency. JI.,ll. P03EHBEPr MOillHhiE Y JlbTPA3BYKOBbiE nomj MOSHCHNYEUL~RAZVUKOVYEPOLYA Library of Congress Catalog Card Number 78-128509 ISBN 978-1-4757-5410-0 ISBN 978-1-4757-5408-7 (ebook) DOI 10.1007/978-1-4757-5408-7 1971 Springer Science+Business Media New York Originally published by Plenum Press. New York in 1971 All rights reserved No part of this publication may be reproduced in any form without written permission from the publisher

Dedicated to Nikolai Nikolaevich.Andreev Preface This is the second volume in the series, "Physics and Engineering of High-Intensity Ultrasound,"* and is devoted to the specific characteristics of high-intensity sound fields. The characteristics of such fields constitute the subject of nonlinear acoustics, and the boo.k submitted herewith does not aspire to be an exhaustive treatise in that area. As the reader is aware, nonlinear processes are typified by interrelatedness and the inadmissibility of superposition, so that one should properly investigate the whole complex of phenomena in the large. However, the state of the art of research in this direction is such that we cannot yet pursue that approach and must be content to treat isolated aspects of nonlinear sound fields. This approach, of course, while only approximate, nevertheless has distinct advantages. Our orientation in this area is still, so to speak, "linear," and by the investigation of individual effects we are better able to grasp their physical significance, i.e., they are more comprensible to us. Consequently, the investigation of individual aspects of nonlinear sound fields, which can lead us to qualitative and sometimes quantitative insight, is not only of practical importance, but also fits better into our accustomed "linear way of thinking. As far as the individual aspects are concerned, they have been set apart not only for the extent to which they can be utilized to construct the physical foundations of ultrasonic technology, but also from considerations of their timeliness and the contributions of Soviet scientists, particularly members of the Acoustics Insti- "Reference here is to the series of Russian works, of which sources of High Intensity Ultrasound was the first translated as part of the present series- Publisher. v

vi PREFACE tute of the Academy of Sciences of the USSR. Thus, the book does not contain material on the nonlinear interaction of nonlinear absorption of high-intensity acoustic oscillations in solids, etc. Although the main body of the text generally encompasses the results of the author of the given part of the book, the materials of other Soviet and foreign researchers working in the particular field are also incorporated in the interest of clarity and completeness. Part I presents a survey of the results of investigations conducted by the author in the nonlinear absorption of,sound in liquids and gases. Of special interest are the effects on nonlinear absorption in convergent and divergent cylindrical and spherical fronts. Part n is based on results obtained by the author largely during his tenure at the Acoustics Institute. It is given over to the rather complex and beguiling problem of the radiation pressure, an area that is often imprecisely and at times incorrectly handled. Part lli comprises a survey of our knowledge concerning acoustic streaming. Even though the advances made in this area at the Acoustics Institute are relatively limited, the subject is still important enough to warrant its inclusion as an independent part of the book. The last three parts (IV, V, and VI) are concerned with a problem that is exceedingly complex, multifaceted, and often vague, despite the great many papers that have been published on it, namely ultrasonic cavitation. As the reader is aware, cavitation is the most active factor in a large majority of practical applications; moreover, it is extremely important as a unique physical process in itself. There is a certain arbitrariness in the breakdown of the subject into three parts. All three parts are based on investigations conducted at the Acoustics Institute and marked by many conceptually new quantitative and qualitative materials. For example, Part IV represents a probing analysis of the equations describing the motion of an individual bubble and an assessment of the instability effect. The results are compared with the data of highspeed motion pictures of cavitation bubbles. Part V describes the recently discovered effect of the multiplication of cavitation bubbles, a procedure developed for determining the acoustic energy losses in the formation of cavitation bubbles, and an investigation of the very interesting effects of the static pressure on the be-

PREFACE vii havior of cavitation bubbles, primarily on the enhancement of cavitation eros ion. Part VI is devoted to the vital, though so far, comparatively neglected problem of the behavior of the cavitation zone in general. The work in this area is currently in the state of development, but the results to date already permit a clear conceptualization of the phenomena evolving in a cavitation zone and occassionally certain inferences useful for practical applications. The pioneer in the formulation and development of problems in nonlinear acoustics in the large is Academician N. N. Andreev, on whose initiative some of the earliest investigations in this area were undertaken. The editor is grateful to V. S. Grigor 'ev and G. A. Ostroumov, who assumed the task of reviewing the manuscript of the book and offered many valuable comments. Also deserving acknowledgment is the considerable service rendered by V. A. Akulichev in preparing the manuscript for publication. L. D. Rozenberg

Contents PART I- ABSORPTION OF FINITE-AMPLITUDE WAVES K. A. Naugol 'nykh Introduction.............................. 3 Chapter 1 - Plane Waves of Finite Amplitude.. 5 1. Absorption of a!..ow-intensity Sound Wave. 5 2. Qualitative Description of the Propagation of Finite-Amplitude Waves...... 7 3. Fundamental Equations.... 10 4. Formation of First-Order Discontinuities in a Sound '"'ave........................ 15 5. Variation of the Spectral Composition of a Finite-Amplitude Wave during Propagation. 23 6. Absorption of a Finite-Amplitude Wave.. 30 Chapter 2 - Spherical and Cylindrical Waves of Finite Amplitude....... 35 1. Formation of First-Order Discontinuities in Spherical Waves.... 35 2. Variation of the Spectral Composition of Spherical and Cylindrical Waves... 42 3. Absorption of Spherical and Cylindrical Waves of Finite-Amplitude................ 45 Chapter 3 - Dependence of the Gain of a Focusing System on Sound Intensity........ 51 1. In.troduction......................... 51 ix

X CONTE::-ITS 2. Spherical Concentrator... 52 3. Cylindrical Concentrator.... 56 Chapter 4 - Absorption of Finite-Amplitude Waves in Relaxing Media and in Solids....... 59 1. Sound Absorption in Relaxing Media... 59 2. The Absorption of Finite-Amplitude Sound in Sol ids.......... 65 References.............. 67 PART II- ACOUSTIC RADIATION PRESSURE Z A. Gol' dbe rg Introduction............................. 75 Chapter 1 - The Initial Equations.... 77 1. Initial Equations in Euler Variables. 77 2. Initial Equation in Lagrange Variables.... 81 Chapter 2 - The Radiation Pressure...... 85 1. General............. 85 2. The Rayleigh Radiation Pressure..... 88 3. The Langevin Radiation Pressure... 94 Chapter 3 - Problems Associated with the Radiation Pressure............................... 99 1. The Energy of Sound Waves..... 99 2. Momentum Flux in Sound Waves... 103 Chapter 4 - Radiation Forces Acting on a Particle in a Sound Field................... 109 1. Derivation of the Initial Equation... 109 2. Forces Acting on a Spherical Obstacle 113 3. Forces Acting on a Disk......... 117 Chapter 5 -Radiation Pressure Effects and Their Applications........ 121 1. The Fountain Effect...... 121 2. Absolute Measurement of the Field Intensity 121 3. Nonlinear Properties of a Medium.... 125 4. Acoustic Streaming Velocity and the Coefficient of Sound Absorption. 126 References.............................. 127

CONTENTS xi PART ill - ACOUSTIC STREAMING L. K. Zarembo Introduction............ 137 Chapter 1 -Theory of Stationary Streaming in a Sound Field.............................. 141 1. General Theory of Stationary Acoustic Streaming in the Second Approximation (Slow Streaming) 142 2. Eckart Streaming...... 147 3. Streaming Outside the Boundary Layer.. 156 4. Acoustic Streaming in the Boundary Layer 159 Chapter 2 - The Experimental Investigation of Acoustic Streaming........... 171 1. Methods for the <llservation of Streaming and Measurement of Its Velocity.. 171 2. Streaming Near <llstacles, Microstreaming, and Streaming in Standing Waves... 176 3. Eckart Streaming... 190 References............................... 197 PART IV- PULSATIONS OF CAVITATION VOIDS V. A. Akulichev Introduction.............................. 2 03 Chapter 1 - Fundamental Equations for the Pulsations of a Cavitation Void........ 2 05 1. Pulsations of a Void in an Incompressible Liquid............ 205 2. Pulsations of a Void with Regard for Compressibility of the Liquid.... 208 Chapter 2 - Investigation of the Pulsations of Cavitation Voids........... 215 1. Similarity of the Solutions of the Equations for Different frequencies of the Ultrasonic Field........................... 215 2. Structure of the Solutions; Structural Stability............. 221 3. Collapse of Cavitation Voids...... 227

xii CONTEJ.'ITS 4. Analysis of the Solutions of the Equations in the Phase Plane....... 230 5. Experimental Investigation of the Pulsations of Cavitation Voids...... 233 Chapter 3 - Relationship of the Pulsations of Cavitation Voids to the Emission of Shock Waves and Cavitation Noise................... 239 1. Shock Waves in Cavitation............ 239 2. Discrete Spectral Components of Cavitation Noise................. 245 3. The Continuous Cavitation Noise Spectrum.. 250 Conclusion.................... 257 References.............................. 257 PART V -EXPERIMENTAL INVESTIGATIONS U..l.<' ULTRASONIC CAVITATION M. G. Sirotyuk Introduction.............. 263 Chapter 1 -The Strength of Liquids... 265 1. Theoretical and Actual Strength..... 265 2. Cavitation Nuclei..... 267 3. The Cavitation Strength.......... 273 4. Size Distribution of the Nuclei........ 280 Chapter 2- Characteristics of Cavitation Bubbles and Properties of the Cavitation Zone... 285 1. Oscillations of Cavitation Bubbles in a Sound Field............... 285 2. Acoustic Pressure in the Cavitation Zone. 290 3. Maximum Cavitation Bubble Radius....... 294 4. Gas Pressure in a Bubble at the Time of Collapse; the Gas Content Parameter.. 299 5. The Collapse Time..... 3 02 6. The Cavitation Zone and Number of Cavitation Bubbles.... 306 Chapter 3 - Energy Balance of the Sound Field in Cavitation.............. 315 1. Cavitation Formation Energy; Streaming. 315

CONTENTS xiii 2. Cavitation Energy.... 32 0 3. Cavitation Efficiency... 321 Chapter 4 -Influence of the Acoustic Pressure and Characteristics of the Liquid on the Shock Wave In.tensity.............................. 325 1. The Acoustic Pressure...... 326 2. Temperature and Gas Content of the Liquid.. 328 3. The Hydrostatic Pressure 333 Conclusion.......... 339 References.................. 340 PART VI- THE CAVITATION ZONE L. D. Rozenberg Introduction........... 347 Chapter 1 - Phenomenological Treatment. 349 1. The Cavitation Index..... 349 2. Uniformity of the Cavitation Zone.. 350 3. Energy Losses in the Formation of the Cavitation Zone...... 353 4. The Loss Function and Its Application. 356 5 The Developed Cavitation Zone (in a High- Intensity Focusing Concentrator). 359 6. Experimental Determination of the Cavitation Index.. 363 Chapter 2 - Oscillations of a Bubble in a Cavitation Zone........................ 369 1. Statement of the Problem.. 369 2. On the Interaction of Adjacent Bubbles.. 371 3. Experimental Estimation of the Interaction Criterion......................... 373 Chapter 3 - Variationofthe Average Acoustical Characteristics of the Medium.. 377 1. The One-Dimensional Cavitation Zone.. 377 2. Experimental Investigations of the Equivalent Wave Resistance in Cavitation.. 380 3. Compressibility of Cavitation Bubbles.. 384 Chapter 4 -The Cavitation Efficiency. 389

xiv CONTENTS 1. Fundamental Definitions....... 389 2. Experimental Determination of "K. 392 3. On the Measurement of the Acoustic Energy Cavitation Efficiency 395 4. Estimation of T/T 0 398 Chapter 5 -Analysis of Bubble Oscillations. 403 1. Introductory Considerations 403 2. The Cavitation Zone in a Plane Wave 408 3. Cavitation in a Convergent Spherical Wave 411 4. Acoustic Streaming Induced by the Formation of Cavitation... 415 References............................... 417 Index................................. 421