CONTENTS

The publisher of this book is Partridge Hill Publishers, Partridge Hill Rd., Hyde Park, NY 12538.

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1 Introduction 1

1.1 Basic concepts 1

1.2 Ultrasonic Nozzles 3

1.2.1 Structure and Function 3

2 Wave Motion as it Relates to Ultrasonic Nozzles 6

2.1 Introduction 6

2.2 Basic Wave Motion 6

2.2.1 Vibrating Strings 8 2.2.2 Sound Waves 16 2.2.3 Other Properties of Sound Waves 19

2.3 Wave Motion in Ultrasonic Nozzles 20

2.4 The Role of Mechanical Stress 26

2.4.1 Stress and Strain 26 2.4.2 Stresses Developed in Nozzles 27 2.4.3 Stress at a Step Transition 31 2.4.4 Tapered Sections 31 2.4.5 Other Considerations 33

2.5 The Basic Physics of Ultrasonic Nozzle Design 35

2.5.1 The Wave Equation 35 2.5.2 The Wave Equation for Standing Waves 38 2.5.3 Boundary Conditions 39

3 The Ultrasonic Atomization Process 43

3.1 Capillary Waves 43

3.2 The Role of Operating Frequency in Nozzle Design 44

Copyright ' 1998 by Sono-Tek Corporation & Harvey L. Berger

All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any informational storage or retrieval system, without permission in writing from the copyright holders.

Requests for permission to make copies of any part of the work should be mailed to Sono-Tek Corporation or Harvey L. Berger, both at 2012 Rte. 9W, Milton, NY 12547.

ISBN: 0-9637801-2-3 First edition

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3.3 The Effects of Liquid Velocity 48

3.4 Spray Shapes 50

3.5 Drop-size Distribution 51

3.5.1 Drop-size Distributions for Ultrasonic Nozzles 53 3.5.2 Experimental Methods for Measuring Drop Diameters 57

3.6 Practical Aspects of Drop-distribution Analysis 58

3.6.1 Coalescence of Drops 58 3.6.2 The Effects of Liquid Properties on Drop Sizes 59

4 The Effects of Liquid Properties 61

4.1 Types of Liquids 61

4.2 Chemical Resistance 63

4.3 Abrasion Resistance 64

5 Electrical Aspects of Ultrasonic Nozzles 65

5.1 The Equivalent Circuit for an Ultrasonic Nozzle 66

5.1.1 Mechanical Quality Factor 72

5.2 Input Power Requirements 73

5.2.1 Optimum Power Levels 73 5.2.2 Power Generator Requirements 75 5.2.3 Power Level Requirements 78

6 Operating Considerations 82

6.1 Liquid delivery methods and requirements 82

6.1.1 Types of Liquid Delivery Systems 84

6.1.1.1 Gear Pumps 84 6.1.1.2 Syringe Pumps 86 6.1.1.3 Piston Pumps 87 6.1.1.4 Peristaltic Pumps 89 6.1.1.5 Pressurized Reservoir Systems 91 6.1.1.6 Gravity Systems 94

6.1.2 Plumbing Requirements 96

6.1.2.1 Tubing 96 6.1.2.2 Fittings 97 6.1.2.3 Valves 98

6.2 Temperature and Pressure Ranges 99

6.2.1 Temperature 99 6.2.2 Pressure 103

6.3 Power Management 106

6.4 Installation Constraints 107

7 Spray Shaping Methods 109

7.1 Wide Sprays 109

7.2 Narrow Sprays 117

7.3 Other Spray Shaping Techniques 119

8 Applications 121

8.1 Electronic Applications 121

8.1.1 Solder Fluxing Printed Circuit Assemblies 8.1.2 Selective Soldering 126 8.1.3 Photolithography 129 8.1.4 Other Electronics Applications 134

8.1.4.1 Electrostatic Sprays 135

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Vii

PREFACE

Ultrasonic liquid spray technology has become a highly useful tool in a wide variety of industrial and research applications. Although the principles upon which it is based can be traced back to 19th century physics, the development of the technology into a commercially viable form began only in the 1970s.

An Historical Perspective

In 1973,1 became aware of the work that the Battelle Memorial Institute in Columbus, OH had done in attempting to make a practical ultrasonic spray nozzle. The device they had developed was not successful because the theoretical and practical foundations needed to produce an ultrasonic nozzle had not yet been established. However, as with many "first tries", this work contained enough substance to stimulate my curiosity. That was in 1973.

My "first try" began then. Over the course of the next year, I dizzied myself with trying to understand the basic requirements that would make ultrasonic nozzles practical. Having been trained as a physicist specializing in low-energy nuclear physics, the transition to this totally unfamiliar setting was difficult for me. Alien topics such as acoustical wave theory, stress analysis, piezoelectricity, and high-frequency amplifiers had to be mastered.

Persistence paid off. In 1974, the Sono-Tek Company (and in 1975, the Sono-Tek Corporation) was founded by my business partner, Carl Levine and me. Our sole intent was to produce an energy-efficient oil burner for residential heating using this new technology. The fact that the year was 1974 is significant in that an oil crisis had taken hold in the United States. To us, this represented a golden opportunity to exploit the virtues of ultrasonic nozzles.

Ultrasonic nozzles are ideal for use in oil burners bauseof their unique properties, such as their ability to operate oyef a wide range of flow rates and the fineness of the spray they produce. The energy savings achievable are extraordinary.

Early in 1975, we received the first of several contract awards from the United States Army for the development of liquid fuel burners using ultrasonic nozzles, for use in portable power generation equipment. This

8.2 Medical Industry Applications 139

8.2.1 Blood-collection Devices 140

8.3 Other Applications 144

8.3.1 Web Coating 146

8.3.1.1 An Example - Coating Float Glass 147

8.3.2 Spray Drying 150

8.3.3 Combustion 153

Appendix A The Effect of Liquid Properties on Drop size in Ultrasonically Atomized Sprays 156

Appendix B Viscosity and Viscosity Conversion Factors 160

Cited References 161

Selected Bibliography 162

Index 163

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event marked the founding of a real business. The revenues derived from these contracts, which lasted for over two years, provided us with the resources to aggressively pursue the development of a commercially viable oil burner.

We indeed succeeded. Off we went with our wares to the US Environmental Protection Agency (EPA) and the US Department of Energy (DOE) in order to seek their approval of the technology we had developed. Both of these agencies praised its merits. Although we received only small amounts of additional funding for our efforts, the fact that these two prestigious organizations had made positive evaluations brought a great deal of credibility to this new technology. In addition, we were able to interest two major oil burner manufacturers in joint-venturing with us.

Things now seemed right for introducing an ultrasonic oil burner into the residential marketplace. During the period from the late 1970s to the early 1980s, we focused all of our attention on making ultrasonic oil burners a commercial reality.

By 1982, we still had not succeeded. The oil crisis had waned, and with it, the high level of motivation for saving energy that had existed before. The principal impediment we faced was high cost. Ultrasonic nozzles are considerably more expensive to produce than conventional pressure nozzles, which are typically used in oil burners. This was the major factor in discouraging our joint-venture oil burner manufacturing partners from moving forward.

Upon taking many deep breaths and pinching ourselves to make sure that the circumstances were real, we grudgingly came to the realization that this revolutionary technology would not make it in the real-world of consumer heating products.

Most entrepreneurial ventures would have thrown in the towel at this point. We didn’t. We knew that since the ultrasonic spray technology we developed had so many distinguishing features that separated it from other spray techniques, there must be other uses for it. After eight years of devoting ourselves to a single purpose, it was difficult to shift gears, but shift them we did.

In the early 1980s, we were able to raise a considerable amount of money for our venture from a large group of private investors, most of whom invested between $5,000 and 20,000. Carl Levine’s brother, Murray,

X

who was also an original investor in the Company, played a pivotal role in securing these funds. The infusion of capital that he was able to arrange allowed us to go forward.

The principal attributes of ultrasonic atomization are its soft, low-velocity spray, the absence of overspray, the ability to deliver extremely small amounts of atomized liquid (down to microliters), a wide range of flow rates from a single nozzle, and freedom from clogging.

These unique attributes, which are discussed in depth in the text, led us to explore possible uses for the technology after the oil burner phase of our venture had run its course.

Early in 1983, our technology was featured in the trade journal Chemical

Engineering. This was our initial attempt to expand beyond the limited horizons of our past. The response was overwhelming. Hundreds of inquiries were received, many of which pertained to applications that we knew might fit our technology. This was the start of what Sono-Tek is today.

Over the next nine years, we expanded the application base into many different areas. Our first triumph was in the semiconductor industry. Ultrasonic nozzles became a preferred method of applying photoresist developer onto silicon wafers, as part of a photolithographic imaging process.

The next major breakthrough was in applying precisely-controlled amounts of biologically sensitive reagents to the interior walls of blood-collection devices. Today, approximately 80% of all blood-collection devices manufactured that separate the serum portion of blood from its other components utilize ultra onic nozzles produced by Sono-Tek.

The success of these two apjlications, together with several others, among which were coating floa glass with anti-stain coatings, applying fragrance to feminine hygiene products, spray drying ceramics and pharmaceuticals products on a laboratory scale, and having our equipment fly aboard two space-shuttle missions, provided tangible evidence that this technology has a wide range of uses.

In 1987, Sono-Tek became a public company. Our successes over the prior few years had made the Company a candidate for this type of structure.

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In 1991, the course of the Company changed again. The applications we had developed previously were all related to equipment that was not ours. We were manufacturers of ultrasonic nozzles, and nothing else. A new opportunity arose that changed our business dramatically.

Our goal at that time was to develop products that incorporated our base technology into larger systems that we could sell as user-ready products.

A golden opportunity arose. An international agreement on phasing-out the use of chiorofluorocarbon cleaning chemicals (better known as freons or CFCs) had been reached in Montreal. This treaty had far-reaching consequences in the electronics industry, particularly in the soldering of printed circuit assemblies where CFCs had traditionally been used to clean chemical residues of solder flux from finished assemblies following the soldering process. These developments afforded us the opportunity to realize our goal of entering the marketplace with a user-ready product.

One alternative that was quickly seized upon by the industry was the use of processing chemicals whose post-soldering residues would not affect circuit performance if left on the board (thereby eliminating cleaning altogether). These chemicals, referred to as "no-clean fluxes", quickly became the rage throughout the industry. However, there were problems associated with using them. For technical reasons, which are discussed in detail in Section 8.1.1, the only practical method of applying these materials to printed circuit assemblies is to spray them on.

AT&T pioneered no-clean fluxes. Early on, we supplied AT&T with ultrasonic nozzles and auxiliary air-handling equipment that were incorporated into systems used in their manufacturing facilities to apply these fluxes. Soon thereafter, they went on to produce and sell their own spray fluxing system. We quickly recognized that this application was ideal for our ultrasonic nozzle technology and set about to develop our own equipment. In May of 1991, Sono-Tek introduced the SonoFlux 591 series of spray fluxers.

Today, spray fluxing is the method of choice for applying all types of fluxes to printed circuit assemblies. The component of AT&T that produced spray fluxers (subsequently Lucent Technologies) no longer participates in this market. This leaves Sono-Tek as the "senior" member of the industry. More importantly, our SonoFlux systems have become to be regarded as an industry standard.

There are now upwards of fifty spray fluxer manufacturers throughout the world. Obviously, there is enormous competition. Our company has remained on top throughout this battle, because of the positive way in which ultrasonic spray technology lends itself to this application.

The Text

The text has been structured in a way so as accommodate various levels of interest. The basic principles underlying the technology are described in Chapters 1 through 3. Some sections within these chapters contain advanced mathematical constructs that may be of limited interest. Those sections can be skipped without losing continuity.

Chapters 4 through 7 contain practical information regarding the "care and feeding" of ultrasonic nozzle systems. This part of the book should be of particular interest to anyone using or contemplating the use of ultrasonic nozzles.

Chapter 8, the final chapter, describes a wide variety of applications in which this technology has found a home. The applications vary from the most basic, such as applying a water mist to dried parsley, in order to "bulk-up" its weight, to the very sophisticated, such as applying photolithographic chemicals to silicon semiconductor wafers.

Some Final Wo ds

Bringing ultrason spray technology from a point where it was virtually nonexistent in 1974, to where it is today, 1997, has been very rewarding to me and to many others. Things have not always gone as well as we would have liked, but the dedication of the people involved has always carried us through. Their enthusiasm has meant the difference between success and failure.

Today, thanks to solid management, the Company is on firm footing. The technology has been accepted in a wide variety of applications, and its organizational framework is sound.

We are pursuing other applications for the technology, many of which are described in Chapter 8. We would encourage readers of this book to add to that list. Many other applications certainly exist. Finding them ultimately rests on end-users, such as you.

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ACKNOWLEDGMENTS

After nearly 25 years of involvement in ultrasonic spray technology and Sono-Tek, the list of people who have made significant contributions to our technology’s development and to the success of the corporate structure under which it has flourished, is obviously long. However, it is important to me that their efforts be recognized.

In the Preface, I mentioned the pivotal roles that Carl and Murray Levine played. It is safe to say that Carl’s entrepreneurial skills were the principal reason why the Company was able to survive its formative years. Carl retired as Chairman and CEO a few years ago.

Charles R. Brandow ("Dick") was our first employee. Dick’s skills were vital in the development of the first electronic circuits used to drive ultrasonic nozzles. His designs were the mainstay of our products for over 18 years. In his long tenure at Sono-Tek, Dick earned the respect and admiration of all his colleagues.

Three other people from the early years deserve special mention, Josephine DeNitto ("Joy"), Edward J. Handler III, and Timothy Snyder.

oy joined us in 1979. Her tenacity, attention to detail, charm, and overall competence, first as a secretary and then as Office Manager and Secretary of the Corporation, was a source of great comfort. She played a key role in keeping us all sane. In terms of loyalty and devotion, she is second to none. Joy left the Company in August 1997 to pursue another career. We miss her.

Edward J. Handler III was our patent counselor for many years. Ed is a partner in a prestigious New York City law firm, Kenyon & Kenyon. In 1976, he took on Sono-Tek as a client with nothing to gain other than to hope that one day, we might be successful. Over the years, he was instrumental in obtaining several patents for us, worldwide, and guided us through many complex contract negotiations. During the early years, it was difficult for us to keep up with the payments for his firm’s services. Yet, Ed and his firm always stuck by us. His graciousness will always be remembered.

Tim Snyder is now our Sales Manager. He started with the Company in 1983, having just graduated with a degree in geology. Unfortunately, 1983 was not a good year for geologists, particularly for Tim, whose

xiv xv

focus was on petroleum. The oil-crisis had ended and the call for geologists in that area became virtually extinct. Fortunately for Sono-Tek, Tim came aboard as a sales engineer who, over the years, demonstrated that he not only is a first-class salesperson, but also is a master of understanding the technical requirements for the vast variety of applications that come our way. His knowledge of ultrasonic spray technology is daunting. It has been a great joy for me to have been associated with Tim through all of these years. He is certainly is a major factor in the Company’s success.

In 1987, Sono-Tek became a public company. David A. Mortman, who was then our corporate attorney, led us through this difficult process. David is a person for whom I hold a,gfeat deal of esteem. His contributions to the development of 3eCompany are significant.

Alan Paul joined Sono-Tek in 1984 s a mechanical engineer. He guided us through many nozzle and power generator design improvements and he was responsible for the design of the first two generations of the SonoFlux system. In the 11 years he was at Sono-Tek, his innovativeness became synonomous with our growth.

There are many individuals deserving recognition that represent the current generation of Sono-Tek’s family. Sam Schwartz is our Chairman, a position he has held since 1993. Prior to that, Sam had been a director of the Company for several years.

Sam’s vast wealth of business and technological experience in high-technology situations, gained over four decades, have been crucial to the Company’s well-being. His financial support has been equally important. Prior to becoming Sono-Tek’s Chairman, he owned and operated Kristanel, a well-known manufacturer of magnetic devices used in electronics applications. He also has been instrumental in starting up several other companies. Sam and I share a common experience. We are both graduates of Rensselaer Polytechnic Institute.

A key figure in the Company’s resurgence is James L. Kehoe, our CEO. Jim is an entrepreneur in his own right. After 22 years with IBM, he founded another company that now is a major player in the flat-panel display industry. Since becoming CEO in 1993 (prior to that, he was a director of the Company), he has guided the Company to new levels of performance, transforming many years of up-and-down results into a situation of sustained profitability. Jim also has been instrumental in

introducing several programs and processes that have enhanced the Company’s image and operating capabilities. His contributions have been enormously important.

J. Duncan Urquhart the the Comptroller of the Company from 1988 to 1997. He remains as a director. Over the years, Duncan was able to adeptly manage our financial circumstances, sometimes under adverse circumstances. He was consistently complimented by our independent auditors for the accuracy and thoroughness of our financial reporting. His steadfast attention to financial control was an important element in the Company’s success. Duncan recently left the Company to pursue a challenging new career.

Vincent F. DeMaio, our Operations Manager, is unique. Vince started at Sono-Tek in 1991 after a long career at IBM. His exuberance, attention to detail, knowledge of manufacturing processes, and "take-charge" attitude have had a major, positive impact on our operations. There is virtually no job, big or small, that Vince will not take on. Whether it is preparing horseshoe pits in our backyard or leading the effort to have Sono-Tek certified as an ISO 9001 manufacturer, Vince is there.

There are many people who work or have worked for Vince or his predecessors that deserve recognition. First, I would like to recognize those people who have given Sono-Tek long years of dedicated service. They include Jane G. DeAngelis, our "no-nonsense" assembler and Keeper of "our conscience"; Rebecca J. Oakley, our combination machinist, Shipping Department leader, and doer of any task that anybody asks of her; George Rodriguez, who worked his magic for many years in putting nozzles together and testing them; William J. Broe, our former machinist, who had a unique ability to provide innovative designs for nozzles; Richard O’Connor, our jack-of-all-trades and master-of-all; and Joseph Conti, who was our principal assembler and tester of spray fluxing systems for many years, and was also a top-notch electronic technician.

Over the last couple of years, the staff reporting to Vince has expanded to include Robert P. Urbanak, who has brought production control within Sono-Tek to new levels; Edward B. Bozydaj, whose exemplary machining and leadership skills are real assets; and Debra A. Casiero, an electronics assembler, who has demonstrated her capabilities in everything she has done at Sono-Tek.

xvi xvii

A competent engineering staff is vital to the success of any technology-oriented enterprise. Sono-Tek has been fortunate in this regard. After Dick Brandow retired, Edward Cohen took over the electrical engineering area. Among a long list of achievements was Ed’s development of a "world-class" ultrasonic power generator that is used today across our entire product line.

Vincent Whipple, our Associate Engineer, is a gifted individual who has the uncanny knack of being able to troubleshoot any problem that comes along. I marvel at Vince’s ability to successfully analyze difficult technical situations, no matter where they may arise, and to provide solutions for the most challenging issues. In many ways, he is one-of-a-kind.

William J. McCormick has guided Sono-Tek’s Engineering Department over the last few years. Bill has brought a new level of professionalism to this position. He is a results-oriented type of person who has been instrumental in bringing our engineering projects forward in a timely fashion, in implementing high standards of quality, and in fully utilizing the resources at his disposal.

Helping Bill in this effort over the past few years has been John C. Vicari, our mechanical engineer. John is one of the most dedicated people I know. His "24 hour a day, 7 days a week" work ethic is immensely appreciated.

The life-line of any company is its ability to sell and then service its products. Here too we have been fortunate in attracting dedicated sales and service people. Over the years there have been many sales managers and sales engineers who have made significant contributions. Paul Rashba was our first head of Marketing & Sales. Paul Hammond was our second. Both played key roles in the development of the Company.

Among the Sales Engineers of the past and present, special thanks go to Dan MacAuliff and Manish Sharma, both of whom pioneered the sales of ultrasonic spray fluxing equipment in the early 1990s, and to Stephen R. Harshbarger, who has developed into a super-salesman, in spite of the fact that his college training is in finance. Today, Steve is setting new sales records for us. David M. Pagano is also making significant contributions in his capacity as a Sales Engineer. Dave not only has a technical background, but also has an MBA.

In order for a sales team to function effectively, someone within the organization must orchestrate communications, data bases, travel arrangements, quote preparation, and a myriad of other responsibilities that come his or her way. The person responsible for all of this at Sono-Tek over the past several years has been Claudine Y. Corda. Recently, Claudine moved up in the organization, taking on corporate level responsibilities. She adds a spark to Sono-Tek that is truly refreshing.

Providing first-class service to our customers is a keystone in our approach to doing business. This philosophy encompasses everything we sell, but is most critical when we sell a SonoFlux system, where it first has to be installed, then operators trained, and finally put into the production. Shawn Royden did a first-class job in this capacity for many years. (Shawn and I can always carry on an interesting dialogue since he shares my passion for things in the culinary arena.) Shawn and Vince Whipple both have been instrumental in providing our customers with the highest level of support a company can give.

The Purchasing Department is a vital part of any operation. Robert J. Burgin, our Purchasing Agent, is an indispensable resource. Bob has a talent for bringing "stuff’ in at the lowest possible cost, and making sure it arrives on time. The enthusiasm he displays is obvious to us all.

Finally, I would like to acknowledge the contributions of my wife, Donna. We have been married since 1979, and have known each other since 1975, just after Sono-Tek began. She, along with me, have witnessed all the years of this adventure. It has not been an easy task to bring this technology from its infancy to the point where it is now successful. Her constant encouragement has been a source of strength for me.

Donna has her own career. She is a co-author of a college textbook on self-management for college students and is Director of the Academic Grants Office at Marist College, in Poughkeepsie, NY. As a college graduate in English and a writer, the critical comments she has made regarding the text have been invaluable. Most importantly, Donna is the love of my life.

xviii xix

I INTRODUCTION

1.1 BASIC CONCEPTS

The phenomenon referred to as ultrasonic atomization has its roots in late 19th century acoustical physics, notably in the works of the English physicist, Lord Rayleigh.’

When a liquid film is introduced onto a smooth, vibrating surface, such that the direction of vibration is perpendicular to the surface, the liquid absorbs some of the vibrational energy, creating a unique wave-pattern on the surface. These waves, known as capillary waves, form a stationary rectangular grid in the liquid on the surface with regularly alternating .rests and troughs extending in both directions as shown on the photomicrograph in Fig. I.I.

When the amplitude of the underlying vibration is increased, the amplitude of the waves increases correspondingly; that is, the crest become taller and troughs deeper. A critical amplitude is ultimately reached at which the height of the capillary waves exceeds that required to maintain their stability. The result is that the waves collapse and tiny drops of liquid are ejected from the tops of the degenerating waves, normal to the atomizing surface. 2 ’ 3

Although these capillary waves can be created at frequencies in the audible range (below 20 kHz), the technique is practical only at ultrasonic frequencies in excess of 20 kHz). There are two reasons for this. Below 20 kHz, the

audible sound produced by the vibrating device would cause physical discomfort to anyone in its vicinity, and second, the drop sizes produced would be too large to be useful in most applications.

A useful analogy that helps visualize the ultrasonic atomization process comes from our everyday experience. Ocean waves coming into shore go through a transition from stability on the open water to instability as they approach shore. The instability is evident as the waves form foamy breakers.

2

Introduction Chapter 1

Chapter 1 Introduction

FIG. 1.1

The reason for instability in this type of wave is that as it approaches shore, the bottom of the wave contacts the ocean floor and is slowed down by frictional forces. The wave top, on the other hand, continues to move ahead unimpeded. The net result is that the wave topples over. In this process of breaking up, a spray of tiny drops is ejected from the wave surface.

In ultrasonic atomization, there is a minimum or threshold wave height, below which the capillary waves remain stable, so that no atomization occurs. Once this threshold is exceeded, spray is ejected. The height of the surface wave is directly proportional to the amplitude of the vibration of the underlying surface which, in turn, is proportional to the amount of high-frequency energy delivered to that surface.

The amplitude range for which ultrasonic atomization will occur is quite narrow. Asjust mentioned, the amplitude must exceed a minimum value in order to create unstable capillary waves. This minimum amplitude will vary depending on liquid characteristics. On the other hand, if the amplitude is too great, the formation of capillary waves is impeded. Instead, the liquid is torn into large chunks and ejected at high velocity. This phenomenon is known as cavitation.

Since the range of amplitudes over which true atomization occurs is :imited, constraints are placed on the design of the electronic generator that provides the motive force to create the vibrations. This issue will

discussed in Chapter 5.

Each "dot" on the grid pattern shown in Fig. 1.1 forms a center for atomization. The size of the "dots" and the spacing between them is dependent on the frequency of vibration. The higher the frequency, the smaller the "dots." In turn, the median drop size of drops in the atomized spray is directly related to the "dot" size. The median drop diameter aims out to be approximately 0.34 times the "dot" size.’ The relationship between drop size and frequency is discussed in depth in Section 3.5.

1.2 ULTRASONIC NOZZLES

1.2.1 STRUCTURE AND FUNCTION

An ultrasonic nozzle is a device designed to generate vibrations of the amplitude required to produce the unstable capillary waves that

aracterize ultrasonic atomization.

Die embodiment of an ultrasonic nozzle is shown in Fig. 1.2. The :ozzle body consists of three principal active sections: the atomizing section (front horn); the rear section (rear horn); and between these sections, a section consisting of a pair of disc-shaped lead zirconate-itanate ceramic piezoelectric transducers. The transducers are capable �f converting high-frequency electrical energy, delivered by an external

wer source, into high-frequency mechanical motion. Working in .riison, these three elements provide the means for creating the

brational amplitude required to atomize liquids delivered to the mizing surface. A pair of tin-plated copper electrodes provide the

:ath through which high frequency electrical energy is introduced into device.

The front and rear horns are fabricated from a high-strength titanium alloy, Ti-6Al-4V, a combination of titanium, aluminum and vanadium. This titanium alloy is the material of choice for three reasons:

extraordinarily high mechanical strength excellent corrosion resistance good acoustical properties

4

Introduction Chapter 1 Chapter 1

Introduction

Front Horn

Front - Housing

Atomizing Surface

0-ring Seal - I 1/ 1 Piezoelectric I Transducers

Active Electrode

Ground Electrode

Rear Horn

Ground Lug

0-ring Seal

Liquid inlet

Electrical Connector

is important to prevent the transducers from becoming wet or otherwise -eing exposed to external contamination. In order to accomplish this,

transducer area is encased in a stainless steel housing. The seal -.tween the housing and nozzle body is made by a pair of 0-rings, located

the front and rear junctures where the nozzle and housing meet. The ngs used are made from a material that is resistant to chemical attack,

.h as a perfluoroelastomer. The electrical connections are brought :i1 through a hermetically-sealed connector located on the rear surface

the housing.

0-Ring Seal Rear Housing

FIG. 1.2

A material with high strength is required because of the large mechanical stresses that are produced as a result of the vibrational nature of the process. The corrosion resistance of titanium and its alloys is well-known. Since ultrasonic nozzles can be used in a variety of applications, it is important that the material in contact with the liquid be capable of withstanding chemical attack. Finally, the light weight of titanium (approximately 4.2 g/cm 3) gives it outstanding acoustical properties, a factor that is important in assuring that the device operates efficiently, minimizing potential heat-related problems.

In the example shown in Fig. 1.2, the two horns are joined together by a threaded tube, machined as part of the front horn and threaded into the rear horn. The threaded tube serves two important functions. First, it provides the means for joining all of the elements of the nozzle so that the energy can be properly transmitted through the device. Second, it provides the conduit through which liquid is transported to the atomizing surface.

Liquid enters through a fitting on the rear, passes through the tube and then through the hollowed-out central axis of the front horn. Finally, it reaches the atomizing surface where atomization takes place.

6 Chapter 2 Wave Motion as it Relates to Ultrasonic Nozzles 7

2 WAVE MOTION AS IT RELATES TO ULTRASONIC NOZZLES

2.1 INTRODUCTION

An understanding of wave motion is essential to an appreciation of how ultrasonic nozzles operate. Most material on the subject is presented using higher mathematics as the foundation for its description. The concepts are presented here using more descriptive concepts, so that they can be readily understood at all levels.

2.2 BASIC WAVE MOTION

The concept of waves plays an important role in many natural processes. Some examples are ocean waves; electromagnetic waves (which include radio, light, microwaves, and x-rays); and sound waves. Ultrasonic nozzles rely on sound waves for their operation.

Excluded from our discussion is the broad subject of electromagnetic waves, which are fundamentally different from the other types of waves mentioned above. We shall focus on waves that occur in solids, liquids, and gases. Electromagnetic waves exist outside of this realm.

When we think of a wave we might invoke an image such as shown in Figure 2.1. For the moment, we won’t concern ourselves about what type of wave this is. Instead we shall focus on its basic characteristics. It consists of a regularly repeating pattern of upward and downward strokes. This is not the only regularly repeating pattern we could draw, but it is representative of many types of waves found in nature.

1 &~ 5 ////~ 9 n 3 ~~/ 7 \"~/ 1 1\’~j

can place a horizontal line (the centerline) through the wave such � -. at the segments below it are identical to the ones on top, only flipped

er. The wave shape from point I to point 3 is identical to that from Tint 5 to 7. The same is true of the shape from point 2 to 4, and that

- Tm 6 to 8.

basic quantity associated with all waves is the distance between any nt on the wave to the next point on the wave where the pattern starts repeat itself. This distance is referred to as the wavelength of the

� ave (X). For example, the distance between 1 and 5, or 2 and 6 is equal one wavelength. The points where the wave is displaced furthest

-- :rn the centerline, such as 2 or 4, are known as anti-nodes. Points -ere the wave crosses the centerline, such as 1 or 3, are referred to as �des. As can be seen, the distance from a node to the nearest anti-node

ne-quarter wavelength (?J4). It will become evident as we proceed at the nodes and anti-nodes are very useful in describing waves.

.vave is not a tangible "thing." It is not an object that has a mass. It not be picked up intact and moved from one place to another. A

aye, in the sense of this discussion, is the outcome of a specific type of - :tion of matter. The word "motion" is key in this definition. Waves

- not exist without motion. A few examples will help explain the nature this motion.

:ean waves arise from wind blowing across the ocean’s surface. This � ases the water near the surface to move in a way that creates waves. These waves generally move at a fairly constant speed in the same

:ection as the wind. However, this does not mean that the water Tecules that make up the wave move along with the wave as the wave

-- % els across the surface. In fact, each water molecule moves at a right - - le to the wave, moving vertically upward on the front side of the

ave and vertically downward on the back side. If no other forces were � work other than wave motion, each water molecule would remain at - same spot in the ocean, simply bobbing up and down as waves moved

- at. Of course, other forces, not related to waves do exist, such as .-rents, thermal effects, and wind, which push the individual water

T lecules over wide reaches of the ocean.

FIG. 2.1

8 Wave Motion as it Relates to Ultrasonic Nozzles Chapter 2 Chapter 2 Wave Motion as it Relates to Ultrasonic Nozzles

2.2.1 VIBRATING STRINGS

Another example that graphically illustrates the distinction between wave motion and the motion of the material through which a wave travels is provided by a string, shown in Figure 2.2. One end is tied down and the other is free to move. A wave can be excited in the string by applying rhythmic motion at the free end. The wave travels back and forth along

ANTI-NODE

(FREE END)

NODE

(FIXED END)

FIG. 2.2

the string, but each point on the string itself only moves vertically upwards and downwards. The end that is tied down is a node since it is always on the centerline. The free end is an anti-node, as it is displaced furthest from the centerline. More will be said later to explain why the free end is always an anti-node. Points in between move above and below the centerline with the same rhythmic pattern as applied at the free end.

Waves of this type, in which the wave motion and the motion of the material are at right angles to each other, are referred to as transverse waves. There is another kind of wave, called a longitudinal wave, in which the wave and material motions are parallel to each other. For this type of wave, the particles in the material move back and forth along a line parallel to the direction of motion of the wave. Sound waves are an example of longitudinal waves. Since sound waves form the basis for ultrasonic nozzles, we will have considerably more to say about them.

The analysis of vibrating strings is a good starting point for understanding the mechanics of ultrasonic nozzles. Figure 2.3 illustrates one type of motion for a string tied down at both ends. Each end is a node, and the distance between ends is exactly one-half of a wavelength (X/2). The anti-node is located exactly halfway between. The series of arcs shown in the illustration represents the position of the string at various points in time.

The wave is transverse because the motion of each point on the string is vertical whereas the wave itself is moving along the horizontal axis. It is not apparent that the wave is moving horizontally. Later, we will show that it is.

FIG 2.3

:ime t o, the string is shown in a position such that the amplitude, :ined as the vertical distance from the centerline to each point on the

is at its maximum. A little later, at time t 3 , the string has moved position where the amplitude is less. At time t 5 , all points on the

.rng lie along the centerline. At times t 6 through t 10, the string moves v from the centerline until it again reaches its maximum amplitude

:ime t. The motion then reverses itself as the string starts to move Io

ard until it again reaches the same position it was at when the time This process then repeats itself. The time it takes for the string

� ye from some given position until it returns to the very same position - -wn as the period, T. For example, the position of the string at time

the same as it is at time t 0+T. The string is said to have executed one :-1 :1e of motion.

�re we move on, we must make an important observation about the -:.3vior of strings (or waves in general) in the real world versus that of

e theoretical description just given. If what were said above were allv true, then a string, once set into motion, would vibrate forever,

-ating the identical motion during every period. This does not happen. T-e reason it does not is that there are frictional forces involved that

energy loss in the string over time and eventually result in the coming to rest. These frictional forces include air resistance and

- ::-nal forces within the string. This same phenomenon occurs in - asonic nozzles. The frictional losses in that case show up as heat.

ar we have looked at only one possible way in which a string that is ed at both ends can vibrate. It is also possible to produce many other

- ave patterns in the same string, some of which are shown in Figures : -a-2.4c. Figure 2.4a shows a wave pattern with an additional node �:d-way between the ends of the string. Notice that the wave consists

10 Wave Motion as it Relates to Ultrasonic Nozzles Chapter 2 pter 2 Wave Motion as it Relates to Ultrasonic Nozzles 11

(a)

(b)

(c)

of

FIG. 2.4

two (2) half-wavelengths (total length, 2 x X12) and that the wavelength (X) is now half as long as it was for the wave pictured in Figure 2.3. The patterns depicted in Figures 2.4b and 2.4c show waves consisting of three (total length, 3 x 2J2) and four (total length, 4 x ?J2) half-wavelengths, respectively. The wavelength, X becomes progressively shorter with each successive increase in the number of wavelengths.

The wave shown in Figure 2.3 is referred to as fundamental. It is the pattern with the fewest number of nodes that can be supported by the string, and is the easiest to produce when the string is set into motion. The other patterns, Figures 2.4a-2.4c, are called harmonics or overtones of the fundamental wave. It is more difficult to generate the harmonics than the fundamental since more twisting of the string is involved and,

� zht be expected, the difficulty increases as the number of cycles in pattern increases. In the real world situation, when a string is

ked," nearly all of the wave motion is of the fundamental type, and - . very small amounts of higher harmonic components are present. If

ck at the fundamental and superimpose upon it the harmonic shown � ure 2.4b, it might look like Figure 2.5. Note that the harmonic - rears as a ripple on the fundamental wave.

FUNDAMENTAL FUNDAMENTAL AND HARMONIC

FIG. 2.5

of the type just described are called standing waves. At the very inning of our discussion of strings, we noted that it was not obvious these waves were moving along the horizontal as they should if they typical transverse waves. The term "standing wave" arises because

-me apparent absence of such motion.

ver. there actually is motion along the horizontal. This can be - stood if we consider the standing wave as consisting of component . - s. two identical waves, which are traveling in opposite directions at

iame speed. The maximum amplitude of each of the two waves is tIy one-half the maximum amplitude of the observed standing wave.

-e situation is depicted in Figure 2.6.

:rier for the patterns shown in Figure 2.6 to make sense, we must - :er-stand that the amplitudes of two waves simultaneously traveling

e same medium (in this case the string) are additive at each point. iustrate this, let us consider two waves traveling in opposite directions

ix our attention at a single point on the string. Assume at some -r:uIar time the wave traveling to the left, at that point, has an ’iitude of +1 (one unit above the horizontal axis) and the wave

� cling to the right, at that point, has an amplitude of -1 (one unit the horizontal axis). Then the net amplitude, defined as the sum

re two wave amplitudes at the same time and place, is 0 since 1 + (-= 0 To the outside world, it appears that the amplitude there is zero _igh the amplitude of each of the component waves is not zero.

t=T/8 -

4� _____�\ 7

- 7Th /Th /

t=2T/8

(4) t--3T/8

4� N

4) t=4TI8

4-

-

t=5T/8

7y ()

t=6TI8

:

-

() t=7T/8 -

12 Wave Motion as it Relates to Ultrasonic Nozzles Chapter 2 iapter 2 Wave Motion as it Relates to Ultrasonic Nozzles 13

i us return to Figure 2.6. Each of the 9 illustrations shows the pattern at different times over a complete period, T of motion. We

� - e arbitrarily selected a 2? length harmonic wave for this exercise. topmost pattern in each illustration is the resultant or actual standing

- that is observed. The two lower patterns are the component waves :r travel in opposite directions. Notice that component waves do not � - ige shape as they move, which is characteristic of traveling waves

- all ocean waves), and they move at a constant speed.

me t = 0 (illustration 1), we assume that the standing wave has rmum amplitude. The component waves are in positions such that

i point along the string, adding the amplitude of the left traveling to that of the right traveling wave, will produce the amplitude of

:-e szanding wave at that point. Note that the amplitude of the standing i.e is twice that of each of the component waves when the standing i’e is at maximum amplitude. Points A and B will be used as markers

ow how much each of the component waves moves over time.

later, at time t = T/8 (illustration 2), both component waves have Again, we add together the amplitudes of the component waves

the amplitude of the standing wave at each point. Notice that the . amplitude of the standing wave is now less than it was at time t = 0.

- ccnponent wave amplitudes remain the same. The next pattern, at �e t = 2T/8 (illustration 3), shows that point in time where the standing

’e has zero amplitude everywhere.

..ations 4 through 8 continue to show how the patterns change over -"e The pattern in illustration 9, at time t = T, is identical to that at - t = 0. as it should be since both component waves have completed -e period of motion. Note that the location of both points A and B

c shifted by exactly one wavelength, in opposite directions, from e-r respective positions at t = 0.

nave been speaking about waves moving at a constant speed, c, but not yet defined what determines that speed. In the example just

.. we saw that the component waves moved a distance ? over the i 77c T. Since speed is defined as distance moved divided by time, wave �ed can be defined by c = X/T. However, this definition does not give

actual value for the speed. It simply tells us how speed, wavelength dw period are related. The speed itself is a property of the material bich the wave is traveling. For example, for vibrating strings the

FIG. 2.6 2.6

It could be argued that the component waves are not real, since outside observers only see the resulting wave motion, that is, the motion of the wave created by the addition. On the other hand, these component waves have all the properties associated with normal wave motion. In that sense they are very real.

ANTI-NODE

FIG. 2.7

u.e this kind of string motion in real life. The key feature of this Lffl is that the ends of the string are always anti-nodes, points with

Eetest amplitude. The reason for this is that the ends are the least Tained parts of the string. All other points have string elements on

side that push and pull from both sides and tend to limit the up wn motion. The ends are only constrained on one side and are

rIore more free to move.

-e rules that apply to the fixed-end case we studied earlier apply here bell. The definitions of harmonics, traveling component waves, and

are the same. Figure 2.8 shows the two wavelength harmonic and component waves associated with that harmonic at time t = 0.

ra-ing Figure 2.8 to illustration I of Figure 2.6, shows the de nce.

4-

14 Wave Motion as it Relates to Ultrasonic Nozzles Chapter 2 - Dter 2 Wave Motion as it Relates to Ultrasonic Nozzles 15

speed is determined by two factors: the tension on the string, and how much the string weighs per unit length. Increasing the tension, increases the speed; decreasing the diameter of the string, and so, the weight per unit length, also increases the speed.

Let us first discuss the effect of tension. We probably all have experimented with vibrating strings at least once. Pulling a string tighter (increasing tension) increases the number of times per second the string vibrates, which is equivalent to decreasing the period, T of the vibration. This would be expected from our relationship c = AlT. Since for a string of fixed length, the wavelength does not change, increasing the wave speed decreases T, the time it takes to complete one cycle. Guitarists and violinists use this property of strings to tune their instruments. Increasing the tension on a string increases the rate at which the string completes one cycle of motion. This results in a rise in the pitch of the tone produced. With respect to string diameter, you may know that the four strings of a guitar all have different diameters. The thickest string has the lowest pitch, and the thinnest string has the highest pitch. This is a consequence of the speed of sound increasing as the diameter decreases.

The speed of other types of waves, such as sound waves also depends on the properties of the material through which the wave travels. For example, the speed of sound waves in solid materials is far greater than it is in air. However, for all types of waves, the relationship c = holds true.

Another definition which will prove useful is wave frequency, f. We have already used it without giving it a name. It is simply the number of complete cycles of wave motion that occur per second. Since each cycle is completed in T seconds, there will be l/T cycles completed per second, so f = lIT. For example, if it takes 0.1 seconds to complete a cycle (T = 0.1 sec), then there will be 10 cycles completed per second; f= 1/0.1 = 10 cycles per second. By virtue of this definition, T can be replaced by fin the relationship c = VT, so that c = 2f.

There is another type of standing wave motion in strings that we will consider because it is similar to that in ultrasonic nozzles. This is the case shown in Figure 2.7. Here instead of fixed ends, the ends of the string are free. The string is constrained at one point, midway between the ends. This type of standing wave pattern in a string is conceptually more difficult to grasp than the fixed end case, since it is not easy to FIG. 2.8

16 Wave Motion as it Relates to Ultrasonic Nozzles Chapter 2 ’at’ter 2 Wave Motion as it Relates to Ultrasonic Nozzles 17

22.2 SOUND WAVES

To complete our discussion of the concepts that relate to the mechanics of ultrasonic nozzles, we will describe some important features of sound waves. As mentioned earlier, sound waves are longitudinal waves; that is, the direction of vibration in the material is parallel to the direction of motion of the wave. This is illustrated in Figure 2.9. Notice that just as with transverse waves, the amplitude of the wave motion is cyclical varying regularly from points of no motion (nodes) to points of maximum vibration (anti-nodes).

DIRECTION OF TRAVEL

1-9 � 4-9 +-+ 44 � 4- +-+ 4-9 � 44 4.-. 44 � ’

ANTI-NODE NODE

FIG. 2.9

How are sound waves generated? Let us look at a guitar string. We already know from our discussion of strings that the standing wave produced by a guitar string is a regularly repeating series of up and down motions of the string. The reason that the string produces sound is that it moves the air molecules surrounding it in such a way as to create a pressure wave in the surrounding air. This situation is depicted in Figure 2.10. When the string is moving upward (Figure 2.10a), it is pushing air ahead of it, causing the air molecules in its path to move upward as well. This creates a region where the density of air molecules (the number of molecules per cubic inch) and therefore, the pressure is greater than normal. This is known as compression. As the string reaches the end of its travel (Figure 2.1 Oh), the string actually stops momentarily since it is about to reverse direction. Just before, at, and just after this reversal.

. NORMAL

NORMAL

COMPRESSION

NORMAL

COMPRESSION

NORMAL

zl*’~_~

:�:�::::�::�:�:-:-::::::::::: COMPRESSION

iF NORMAL

RAREFAC11ON

FIG. 2.10

und the string is being disturbed very little or not at all, so the � sa is normal. As the string starts downward (Figure 2. lOc), it pushes

ar th’wnward, causing the density and pressure of molecules above ,e less than normal. This is known as rarefaction. The combination

;çession and rarefaction is repeated as the string vibrates back kith

NODE

ANTI-NODE

OPEN

NODE

CLOSED

18 Wave Motion as it Relates to Ultrasonic Nozzles Chapter 2 pter 2 Wave Motion as it Relates to Ultrasonic Nozzles 19

The net result is a continuous generation of sound waves, which are regions of high and low pressure that move away from the string. Of course, the air molecules themselves, at each point along the wave, vibrate back and forth in their local area, parallel to the direction of the wave motion; they move closer together in compression and further apart in rarefaction. The greater the maximum amplitude of motion, the louder or more intense is the sound produced.

Just as with transverse waves, it is possible to produce standing longitudinal waves. Organ pipes are a good example; ultrasonic nozzles are another. Let us first examine organ pipes. Two types of organ pipes. both of length L, will be considered. One type consists of a pipe open at both ends; the other has one end open and the other end closed. The nature of the standing wave is different in each of the two types of pipes.

An open end of a pipe is equivalent to the free end of a string; it is an anti-node. A closed end is a node since it acts as a barrier to the motion of the wave produced within the air chamber of the pipe. The waves produced by the two types of pipes are shown in Figure 2.11. The

OPEN OPEN

ANTI-NODE .......... --- A ANTI-NODE

FIG. 2.11

� mmental wave of the double open-ended organ pipe (oo) is one-half eength long ( >/2), whereas the fundamental wave of the open!

:d-ended pipe (oc) is one quarter wavelength (?/4). Since both are the same length L, the wavelength, 7 of the double-ended

0.e: pipe is ?, 0 ,, = 2L, while for the open/closed-ended pipe the �enth. 2 = 4L. Since we know that for any wave, c = Af or f= cl

OC

- frequency of the wave generated in the open-ended pipe is f = c/ =,:)1L. and in the open/closed-ended pipe, f () = c/?= c/4L. In both

.:. the speed, c is the speed of sound waves in air. From this, we can - t the frequency of sound produced in an open-ended pipe of length

:e that of an open/closed-ended pipe, or f = 2f.

should also notice that the length of the pipe affects the frequency; .e k’oger the pipe, the lower the frequency. In order to achieve a wide

of frequencies, organs are made with pipes of differing lengths. This property, the relationship between the frequency of a standing wave

te length of the pipe, will reappear in our discussion of ultrasonic L.

L2..3 OTHER PROPERTIES OF SOUND WAVES

ayes can be generated in virtually any type of solid, liquid or :cs matter. The speed of sound, c in air is about 1000 ft/sec. In

t is approximately 5000 ft/sec, and in most hard metals such as tanium, and aluminum, it is around 17,000 ft/sec. The higher

Lfl most solids, particularly metals, stems from the arrangement of et1es in solids, which are more ordered and closer together than in

or gases, making it easier to transfer energy through these 1is.

e -ange of frequencies of sound waves audible to the human ear is - )).OtiK) Hz. (1 Hz = I cycle per second). At 20 Hz, the wavelength s.xtnl in air X = 50 ft; at f = 20,000 Hz, ? = 0.05 ft or 0.6 in. The

gitrasonic refers to sound frequencies in excess of 20,000 Hz. sound waves can be produced with frequencies up to billions

Benz.

liw– metals, the wavelength of a 20,000 Hz wave is about 0.9 ft or almost vL The wavelength in metals is considerably longer than it is in air because

higher sound speed. Ultrasonic nozzles operate in this "ultrasonic" -’rn range. 20,000 to 120,000 Hz, because it is within this range that

sl size of nozzles is practical for commercial applications.

4 Ai2

t t t -: NODE

ANTI-NODE

FIG. 2.13

20 Wave Motion as it Relates to Ultrasonic Nozzles Chapte:, : 2 flcive Motion as it Relates to Ultrasonic Nozzles 21

2.3 WAVE MOTION IN ULTRASONIC NOZZLES

Cylindrical ultrasonic nozzles are essentially solid organ pipes produce standing longitudinal waves in a metallic structure, rather: in air, as do organ pipes.

The wavelength and frequency of a standing wave in a nozzle determined by the nozzle’s length, L, and the speed of sound, c, as an organ pipe. The two ends of the nozzle are anti-nodes. From discussions of strings with free ends and the double-ended open or pipe, you will recall that the ends of the string and pipe are anti-n( since they are least constrained. The same is true here. The atom molecules at the end surfaces are being pushed and pulled from one only.

EXPANSION COMPRESSION

r+ J1 � &PPLED VOLTAGE

44

FIG. 2.12

i hr same frequency as the changing polarity of the applied The amplitude of the expansion and contraction that occurs is tçonional to the amplitude of the applied voltage.

Vibrations in a free-standing metal bar or rod can easily be producec striking it with some other object. When a chime is struck, for exan: the frequency at which it vibrates and that of the tone produce. determined by the chime’s length. After being struck, the chime Arisonic nozzle, the transducer is placed between two metal vibrate for a number of seconds before frictional losses cause the mc :r. md the whole assembly is clamped together. For reasons of to die out. The only way to maintain the vibration is to strike the ch. :-Iavl baiafion and ease of lead attachment, two identical transducers again and again. L T!v are positioned such that like poles are back-to-back. The

i dw electrical input is at the junction between the transducers. Ultrasonic nozzles use piezoelectric transducers as the "strikers.’ Twv electrodes that are in contact with the metal cylinders are piezoelectric transducer has the unique ability to convert electrical em rected and form the ground connection for the nozzle. applied to it into motion.

The manner in which this accomplished is depicted in Figure 2.12. F a transducer of the type used in ultrasonic nozzles is shown. transducer, composed of lead zirconate-titanate, is in the form circular disk. The two side faces of the disk are coated with an electric: conductive material (usually silver). The transducer is excited applying an electrical voltage between the two electrodes. Since transducer is a polarized device (that is, having both a positive ar negative electrode), the disk will either expand or contract along direction parallel to the central axis of the disk depending on the pola of the applied voltage with respect to the polarity of the transducer.

The two possible modes of motion are illustrated in Figure 2.12. On left, the transducer is shown expanding. When the applied voltag reversed, the transducer contracts as shown on the right. If the transdu is supplied with an alternating voltage, it will alternately expand

22 Wave Motion as it Relates to Ultrasonic Nozzles Chapter ur 2 have Motion as it Relates to Ultrasonic Nozzles 23

This arrangement is shown in Figure 2.13 for a pair of transducer sandwiched between two metal cylinders of the same diameter (not quit: yet a nozzle). As long as there is sufficient coupling between meta cylinders and the transducers, the whole assembly vibrates almost as: it were a solid rod.

When the assembly is set into motion by applying an alternating electric a voltage signal to the transducers, a longitudinal standing wave will lx created only if the frequency of the transducers’ expansion and contractio: (and hence the frequency of the generated wave) is such that the length c the rod, L equals that of the fundamental (which in this case, for anti-node at both ends is one-half wavelength, X/2) or some higher harmonic. A other frequencies, the rod will not support standing waves.

The interface between the two transducers must always be a node. Thi makes sense since both transducers are either pushing or pulling i: opposite directions with equal force. Therefore, the only harmonic that can be excited are those that exhibit a node midway between th, ends. These harmonics are half-integer types (AJ2, 3 X/2, 5 7J2, etc.)

An important difference exists between this arrangement, where an acti\ transducer is involved, and the case where an external "striker" is appliec such as for the solid rod described earlier. For a solid rod of length L when it is struck, a standing wave of wavelength ?J2 will always fort (along with some superimposed higher harmonics). The frequency of fix fundamental is determined by the now familiar relationship f = c/ 1 = c121

Since the only driving force setting the rod into motion is the brief initia strike, the frequency of vibration is determined solely by the length the rod and the speed of sound in the rod. For the transducer assembl:

there is a constant driving force at a specific frequency, equal to th frequency of the expansion and contraction of the transducers. Unles the transducer frequency f 1. is the same as the natural frequency of th: rod assembly, f R = c/2L, the rod cannot support standing waves. Thi condition, where fT = is known as resonance. As long as resonanc exists, the energy delivered by the transducers will reinforce the vibrator motion that is already present and the rod will continue to vibrate wit constant amplitude standing waves. If the transducer frequency, f 1. an the natural frequency of the rod, fRdo not match, these two independer modes of vibration will interfere with each other, resulting in a chaoti. situation. On the one hand, the rod is attempting to vibrate at its natura frequency, fR, and on the other, the transducers are "telling" the rod to vibrat at another frequency, f T. The outcome is that there is no vibration at all.

nozzle operates in the manner just described. The principal between the transducer rod assembly and a nozzle is shape.

’irawnic nozzles have sections of differing diameters, plus a central Liquid delivery to the atomizing surface. The reason that the *omizing surface are smaller in diameter than the rest of the

lazft is that the amplitude of the vibration produced in a uniform r*xl is insufficient to produce atomization. Incorporating a imeter stem, to which the atomizing surface is attached,

amplified level of vibration in this part of the nozzle, making ______ &’ achieve atomization at modest power levels (a few watts),

xc’ding any internal heating problems that would otherwise occur.

oi ittrc’nic nozzle is an example of what is generally referred to as a _Jztructure. It incorporates not only piezoelectric transducers,

abwofteT elements (the titanium horn sections) that act to enhance �yat[c’n capabilities. The use of compound structures is

absommd in the design of ultrasonic devices that deliver power to Ajewd xras. Ultrasonic welders, cell disrupters, and dental cleaning

am cthc- examples.

a)itude is approximately equal to the ratio of the larger asquared to the smaller diameter squared. In typical nozzle -is is gain factor, GI is in the range of 7-10. Incorporating a ’d rrovides an additional gain factor, G 2, approximately equal

ii : f the diameter at the large end of the taper to that at the i it s generally in the range of 1.4-1.8, so that the overall gain

a a in the range 10-18. The transition from large to small ’e occur at or near a node, or the gain factor will be greatly

If the transition were at an anti-node for instance, there would ie josphtude gain at all.

ron point is also a region where the stress on the metal is very necaaw this is a region where the rate of change of amplitude is

aarmL The atoms in the metal on the large diameter side are moving nplitude than those on the small diameter side. Since these

1. we rmal1y arranged in a crystalline lattice, where the binding aoms is quite strong, tremendous interatomic forces can be

the metal in this region. Without very careful design and ’ii the metal can easily fatigue and crack. One reason ultrasonic

we made from a titanium alloy is that its fatigue limit is very - .zied to other metals. An analysis of the stresses associated

cieration of ultrasonic nozzles can be found in Section 2.4.

24 Wave Motion as it Relates to Ultrasonic Nozzles Chapter

Figures 14a to 14d show some of the forms in which ultrasonic nozzle can be made. The nozzle in Figure 14a is one-half wavelength long Notice that the transition from large to small diameter does not occu directly at the central node, thereby resulting in a small gain penalt This is compensated for by virtue of the waveform being the mo fundamental, which as discussed early on, is an easy and efficient mod: to excite. In Figure 14b, a one-wavelength nozzle is depicted. Th: right-most node is at the diameter transition, the optimum location.

- A114

AA

Bave Motion as it Relates to Ultrasonic Nozzles 25

in Figures 14c and 14d are variations of the nozzles lims Is Figures 14a and 14b, respectively. These nozzles incorporate wca section in the stem for use in applications where ttI liquid must be delivered deep within a structure. The nozzle i 4 Fure 14c is one wavelength long; and that in Figure 14d is t c-half wavelengths long.

iikaar regarding the design of nozzles concerns the selection of inarm& la solids. waves other than longitudinal waves can be excited.

or rods. waves can be produced that travel radially, that is, wndkxW to the normal longitudinal wave. According to Mason’,

suppress this type of excitation, it is necessary to keep all kss than XJ4. For example, for a nozzle operating at 48 kHz,

I inch. so that the largest diameter for such a nozzle must be ncb-

(a) (b)

(c) (d)

FIG. 2.14

For each configuration, the maximum amplitude of the longitudinal way: along the nozzle is also shown. Remember that the direction of th: actual vibrations are along the axis of the nozzle. The amplitudes at: shown as vertical displacements for reasons of clearer pictoria representation. At the diameter transition there is a "hitch" in th: amplitude curve. This is typical of all the nozzle designs since that i the point where a dramatic rate of change in amplitude occurs.

Illic ,mmems aozzie types shown in Fig. 2.14 can be fabricated to operate PRO a of frequencies. The practical range is between 20 kHz jw wwwwbffe in the neighborhood of 120 kHz. Below 20 kHz, high

�: Mle noise would be produced, which would have a significant operating environment. Above 120 kHz, the length of a

-_Jr tecemes too short and its diameter too small to be practical MW t frnework of this type of design. One might consider using raft*- waelength design above 120 kHz to "stretch" the nozzle

ir abrviate the length constraint. In fact, prototype nozzles have 3, -mmmucied at frequencies on the order of 300 kHz using a multiple

strategy. A problem that has been encountered is excessive The combination of small total mass coupled with the somewhat

required to support a multi-wavelength structure quickly both temperature to unacceptable levels.

ism 1ed discussion on the subject of thermal management in _____ wziles and other in-practice considerations will be found in

-ii’ ’

26 Wave Motion as it Relates to Ultrasonic Nozzles Chapter

2.4 THE ROLE OF MECHANICAL STRESS

The mechanical stress developed in ultrasonic nozzles is an importa: element in confirming its reliability since the design is highly depende: on its ability to withstand the inherent stresses that are generated by i: vibrations. Stress beyond the limits of the materials of construction ca lead to material fatigue and stress cracking. However, the operation these devices relies on the generation of stresses.

flave Motion as it Relates to Ultrasonic Nozzles 27

- :.Ju1us. F. and is a parameter that can be measured for aefid erial. Mathematically F = Eja. Stiff materials, such as ;am bwm very high values of E; it takes large stresses to produce :. For a ruNier band. E is very low. A small amount of stress can

signi ficant strain. The calculation of strain above for the 5 foot . _neter rod, was in fact based on titanium where Y is known

~Mgd 76_5 i 10’ lbs/in2 .

The molecules that comprise the active elements of the device (the fro: and rear horns, and the piezoelectric transducers) are vibrating -

relatively large amplitudes (several microns). These vibrations caw-mechanical stresses in the material, which must be kept well below if ultimate yield strength of the material if fatigue and stress cracking a: to be avoided.

2.4.1 STRESS AND STRAIN

Stress, is defined as amount of force applied per unit area of materia If we pull or push at both ends of a bar of 1 in. diameter with a tot force of 1000 lbs. (500 tbs. per end), the stress will be about 1270 lbs/i: (1000 lbs. divided by the cross-sectioned area of the bar). If we hal the diameter of the bar, the stress in the bar will increase four-fold: 5090 lbs/in2 .

When an object is put under stress, by pulling or pushing on it, the obje. will deform, generally in the direction of the applied stress. If we p on the I in. diameter rod discussed above, the rod will elongate slighti If we push on it, the rod will compress slightly. The elongation at compression are lumped under the term strain, a defined as the amou of displacement due to elongation or compression per unit length of t1 bar. For example, if the bar above were 5 ft. (60 in.) long and throug the application of 1000 lbs. of pulling force, the bar elongated 0.005 it then the strain, a would be the total elongation divided by the length the bar, or 8.3 x 10 in./in.

Obviously stress and strain are directly related. As the stress, 4 on object is increased, the strain, a developed correspondingly increase This correspondence holds until the stress reaches the point at whi the bar breaks. The relationship between stress and strain, except ne. the breaking point, is linear. That is, the strain produced is direct proportional to the stress applied. The proportionality constant is refem

maN can sxress produce strain, but the reverse situation is equally �ii i.e., strain induced in a material will result in stresses being .. ibis is exactly what happens in an ultrasonic nozzle. The ’LUMMINS Æg the length of a nozzle are equivalent to strain since the - cstantly moving away from their normal positions during � i (motion.

STRESSES DEVELOPED IN NOZZLES

pr,- , he developed along the central axis of a nozzle can best .L1l&4 by examining the wave motion associated with nozzle

discusses in Section 2.3.

woe swa ier consists of standing longitudinal waves along the length as shown in Figure 2.14. The maximum amplitude of

.ioz z each cross-sectional slice varies along the nozzle’s length. --g surface is a region of maximum amplitude (anti-node).

nee iir6e of the rear horn is also an anti-node, but of considerably The interface between the piezoelectric transducers is a

Al . a plane of zero motion. For the half-wavelength nozzle on a Firwe 2.1 4a. these are the only nodes and anti-nodes. For a �,.th1ong nozzle, shown in Figure 2.14b, an additional anti-

s ixd ong the large diameter section and an additional node at the diameter transition.

-Am 1 i4. and 2.14d are variations of the nozzles shown in Figures -Ask Li-Lb. respectively. These nozzles incorporate an extra half-Ammody in the stem section.

�- e . the shape of the waveform is essentially sinusoidal except 5$re there is a tapered section. There, as we shall see later

,ii. is section. the waveform can deviate significantly from a ern. The step, which is the transition plane between large

uIi thaneters, and which gives a nozzle its amplification

28 Wave Motion as it Relates to Ultrasonic Nozzles Chapt" Rave Motion as it Relates to Ultrasonic Nozzles 29

capabilities, is also the point at which the magnitude of the ampli - the molecules on either side of the central node undergoes a significant change. The ratio of maximum amplitude ir .. x’r from each other. Of course, this captures the motion at small diameter section (d 2 ) to that in the large diameter section (d ianL A while before or later, within the same cycle of equal to the ratio (d 1 /d2 )2 Consequently, the waveforms on either 1. be two molecules will be moving toward each other. Figure of the step are different in terms of amplitude, giving rise wnws &series of snapshots of the motion over one period of motion, discontinuity in the smoothness of the curve at this point. As we !T1T that frequency, f and period are related by f = ?JT). see, this transition region is also an area of high stress.

In Figure 2.1 5a, we show a close-up of the amplitude of vibration arc i�* (e) fi�* fi *�fi an arbitrary nodal plane and in Figure 2.15b a close-up in the vicini: +

0 +

an anti-nodal plane. 4- � (U fi+ fi 44)

+ - 0 +

MAXIMUM A

AND AMPLITUDE DIRECTION

(a) -

MOLECULAR MOTION

ANTI- NODAL

AMPLITUDEPLANE AND DIRECTION

(b) -

MOLECULAR MOTION

FIG. 2.15

. S � (g) fi fi fi

+ - 0 +

(h) *fi fi fi-

+ - 0 +

FIG. 2.16

ugilfiJ :hing around the nodal plane is identical to what we strain. The maximum strain occurs when the amplitude

--’- nt is greatest as shown in Figures 2.16a and 2.16e. displacement of a molecule 11, and the maximum

tii---=----- cia rnclecule ’1.n’ the total maximum strain is the total T - 1ma 21l max divided by the "length" of the

Trefore, the strain, Y is

sic be

= AX-

The three (3) circles at the bottom of each sketch represent molecule* ta , at the situation depicted in Figure 2.15b, where the each cross-sectioned plane and the arrows signify the direction 2 in the vicinity of an anti-node. Here, even though the amplitude of the molecular motion at an instant in time. (Remenii iciwar-ic’n is considerably greater than near the node (a factor that vibrations in nozzles are longitudinal in nature, along the no:" s.esnted in the diagrams), there is no strain in this region axis, so that the molecules shown depict the actual spatial orientatios j the molecules are moving in the same direction with the vibrations). - amplitude. Therefore, an anti-node is essentially a

k

LU

-j 0

U) U) Ui

NODAL ANTI-NODAL PLANE PLANE

30 Wave Motion as it Relates to Ultrasonic Nozzles Chaptei ae Motion as it Relates to Ultrasonic Nozzles 31

Comparing the results of these two extreme cases allows us to make RES.S AT A STEP TRANSITION following generalization. Regions where the rate of change displacement is high (such as the nodal region) are regions of high str eitioned that at the step transition between large and where the rate of change of amplitude is low (such as the anti-nc the stress was high in the small diameter section. For region), the stress is low. cshown in Figures 2.14b and 2.14d, this transition occurs at a

ii. as it should in order to maximize the amplitude gain factor. Figure 2.17 depicts the variation in stress along a uniform quar.. in dw small diameter stem at this point is high. In the large wavelength cross-section of a nozzle. Notice that the stress variatic óo the stresses are considerably less since the cross- sinusoidal, just as is the amplitude waveform, but that the two wavefo: is greater and the amplitude of vibration is correspondingly are 900 out-of-phase. The stress is highest where the amplitude iso 1 "T*a6= 11w actualratio of stress in the two sections at this point is and vice versa. �i of the large to small diameter squared.

.. P me uffzdkcs shown in Figures 2.14a and 2.14c, the step transition l;s : icz a nodal plane. However, the transition is relatively

iwrry *r made. The stress generated in the small diameter section at mw ,jBdw case is still high, but about 25% less than nozzles having

� ,M r rs te nodal plane.

&ED SECTIONS

ss in tapered sections is less straightforward. The iiiin’i : r .a -form along the taper is no longer strictly sinusoidal, PiIIiI:i ii u,ctied by a factor that decreases linearly with the U!LIFiZâI &c i.er. The resultant amplitudes and stresses are shown

: hi:h depicts the situation for a tapered section with the rirt.

çlitude of the waveform is more or less linear except the free end, where it levels off, as it must, since the

-node.

QUARTER-WAVELENGTH iiwi= am= is p’’ç.’rtional to the rate of change of amplitude, we can STRAIGHT SECTION Æ .– of the stem, the stress is fairly constant, falling off

the free end where the rate of change of amplitude FIG. 2.17 Notice that the stress peaks at a point somewhere

luIl& cods of the stem.

"1

C

TRANSITION ANTI-NODAL Ah! PLANE

QUARTER-WAVELENGTH TAPERED SECTION WITH CONICAL ATOMIZING SURFACE

32 Wave Motion as it Relates to Ultrasonic Nozzles V.iive Motion as it Relates to Ultrasonic Nozzles 33

U) Cl) uJ I- Cl)

NODAL ANTI-NODAL PLANE PLANE

I-

0.

QUARTER-WAVELENGTH TAPERED SECTION

Fig. 2.19

Figure 2.18 mum value at the base of the tip. This case can

H r!It mm . ep taper angle, which is equivalent to a large rate of iiiiiiuiii I .-ctional surface area per unit length along the taper.

The situation depicted in Figure 2.18 describes nozzles without lIIII -- - pwt4em with this second design is that the stresses can diameter atomizing tips. The description for tapered sections terminaw r at a point that is relatively weak, a potential cause of in a larger diameter tip (such as a conical tip) is somewhat diffe-:,i m_ the metal. This case is shown in Figure 2.19.

- CONSIDERATIONS The general behavior, in terms of the linearity of the amplitude a the taper, is about the same as for the previous example. However rite Tza um displacement,

1max from the equilibrium position presence of the tip can have a significant influence on the amplitude awa=aw sarface of an ultrasonic nozzle is in the range of 2 - 8 hence the stress in the region near the transition point between taper vL !ii pmeraL the maximum stress,

max developed is proportional step. Notice that the stress drops quickly in the tip region. Th i sow=== mmplitude.

max� It is also directly proportional to the primarily due to the large unit mass of the tip compared to that c: f. One might expect this frequency dependence on taper just behind it. 10111140aracirseL As the operating frequency increases, the time required

comprising the nozzle to complete one cycle of Figure 2.19 shows two cases, one in which the stress reaches a maxi: decreases. A nozzle operating at 120 kHz at a point along the taper (case a), just as in Figure 2.18. The other - rs complete cycles in the same time as does a nozzle (case b) is much different. The stress continues to increase along its length is approximately half that ofa60kHz

34 Wave Motion as it Relates to Ultrasonic Nozzles Chapter

nozzle. Both nozzles require about the same maximum amplitude produce atomization. Since the nozzle operating at 120 kHz is so shc compared to the nozzle operating at 60 kHz, its rate of change amplitude along the stem section is about double. The comparison shown in Figure 2.20. Since stress, 4 is proportional to rate of change amplitude, the stress level for a nozzle operating at 120 kHz is abc double that of one operating at 60 kHz.

Ui

I-

Q.

NODAL PLANE

Fig. 2.20

In general, the maximum stress produced is proportional to maximu amplitude, 1ma%’ frequency, f and, of course, Young’s modulus, E:

max 1max f E

Typically, values of 4.. can vary from between 3000 - 30,000 depending on input power level and frequency. These levels are W:

below the yield strength of titanium, which is in excess of 130,000 p So why is it possible to produce stress fractures in the material, giv that the stress levels are so far below the yield strength of the materi. The answer lies in the machining of the part. Factors such as tool mar defects in crystalline structure, off-center holes or other anomalies, su.

z--,- e .lotion as it Relates to Ultrasonic Nozzles 35

- :face finish, can dramatically increase localized lailure. The machining of the nozzle is probably the

’t "- .. rar eTement in assuring that it will be able to withstand the

�� BASIC PHYSICS OF ULTRASONIC NOZZLE ESaGN

deigns for ultrasonic nozzles and other types of power-ii’-r.. - Ic devices can be derived from basic physics and

Fiaciples. In the previous sections of this chapter we imwme. awk wv& tbe ideas of wave motion, standing waves, resonance,

in a descriptive manner, employing mathematical irnuai In this section we shall present these ideas in a

fundamental physical and mathematical principles.

1� 11M.11’emm ieakn interested in this approach, we urge you to read on. Vhr lre t. skipping this part will not disrupt the continuity

1

-E WAVE EQUATION

:: .: for describing the mechanisms that dictate the iiiiiiirnlr nts for ultrasonic nozzles or other ultrasonic power-

Argim is power-

the wave equation that governs this class of devices.

I

-move t. we refer back to Section 2.4, where we described the iii =11in stress and strain play in the design and operation of iiia=wnc .___._ Consider the solid, cylindrical, rod-like structure

L21� The structure has rotational symmetry about the iiii L The shape is purposely amorphous so as to maintain

ammemokLmai dw discussion. It will be assumed that the motion is -.1 d propagates solely along the x-axis. Let us look at a

cylinder with thickness Ax at some arbitrary time, 1!�.-’.pflsing the slice may be pulling, pushing or moving

sct to each other at any given time, creating stresses, ir Siion 2.4. We have depicted the situation where the

1111M IN i,Ies at the two faces of the slice, located at x and x + Ax, against each other. At other times, throughout each motion will be different; hence the magnitude and

LII�’ kres to the left or right) will be different.

36 Wave Motion as it Relates to Ultrasonic Nozzles Chapter Wr;? ’.firion as it Relates to Ultrasonic Nozzles 37

It! hr L:r j - : : he slice, defined in Eq. (1), can therefore be as

: Efl(x +Ax,t) - A(x)t) I (5)

. the net force can also be expressed in terms of the xiaed with the displacements occuring at the faces of

1111111 11,;mkm 177* mass of the slice is Pav’ where p is the density of the rIiIIImwitjit is the average cross-sectional area over the slice. It is

*c cross-sectional area does not vary significantly through ’mum fteftow a( the slice and that the material is homogeneous. The IIItr mten as

Fig. 2.21

The net force, F, acting on the slice is the vectorial sum of the indivkL forces, 2

"t F = PxAvat’ 1 (6)

F = F(x +Ax,t) - F(x,t) (1)

The stress on each face, which is simply the force divided by the croi . 5 i o 6 1 yields sectional area of the face, are

f,(x,t) = F(x,t)/A(x) SLt) -A(x)ax - pA’. a2 11(x,t) (2) (7)

f(x +x,t) = F(x +Ax,t)/ A(x +Ax,t) - Eôt

The strain, is the displacement per unit length, or ai,/3x. Sin :i=L vhr7 ---. 0. we have

stress and strain are linearly related by Young’s modulus, E,

[

- PA(X) a2T1(x,t)

(8) ex - E at’ all(x,t)

(3)

Combining Eq. (3) with Eq. (2) results in the following relationship: the forces at the two faces in terms of strain:

F (x,t) = EA(x) au(x,t)

(4)

F(x +ix,t) = EA(x +x) all (x +Ax,t) ax

equation that governs the design of ultrasonic nozzles. iir ’e wrs familiar with the standard wave equation, the

in Eq. 8) may appear odd. It reduces to the standard -

E ’l(x,t) I - a2n(x,t) (9) at’

4 as for a uniform diameter cylindrical bar, since molimm 2a ir-i from inside the differentiation bracket on the left

!7me it out with the A(x) appearing on the right side.

38 Wave Motion as it Relates to Ultrasonic Nozzles Chapter ��’ fotion as it Relates to Ultrasonic Nozzles 39

The quantity p/E is readily identified as the reciprocal of the speed j OCKPiCARY CONDITIONS sound, c squared for the medium in which the wave travels, 1/c2 = p

2.5.2 THE WAVE EQUATION FOR STANDING WAVES

The wave equation given by Eq. (8) is general in the sense that displacement from equilibrium, r is both spatially and time dependc As described earlier in this chapter, at each cross-sectional plane ak the axis of a structure in which standing waves have been set up,: amplitude of vibration is sinusoidal with repect to time. This beha greatly simplifies the wave equation since it allows us to express 11(i. in terms of independent spatial and time factors. We define a n displacement function, fl(x) that is dependent only on the position alcr the x-axis. Since the time dependence is sinusoidal, we can write 11( as

11 (x,t) = i(x)e (10)

where w =27tf. Substituting Eq. (10) into Eq. (8) yields

a [ an (x) I - p 2A(x)11 (x) (11)ax j A(X) - - E

Once A(x) is specified, the wave equation can be solved for 1(x) a function of x. In some instances, the solution can be obtained in clo form. These include the cases where A(x) is a constant (straight cylino and where A(x) varies linearly with x (linear taper). In the case c straight cylinder, 1(x) takes the form,

1(x) = Acos(kx) + Bsin(kx), (12)

where k2 = c02p/E = w2/c 2 , and A and B are constants.

For a section having a linear taper, the solution is of the form

1(x) = (Acos(kx)+ Bsin(kx))/((xx + j3) (13)

where a and P are constants designating the slope, end diameters, a starting point of the taper.

-A ave equation to a particular standing-wave as found in an ultrasonic nozzle, it is necessary that

i in each region of the configuration conform to the 119110AMUM aspesed by the physical requirements of standing waves;

sm jr a soda] plane. the amplitude, il is zero, and that at an ir.ie dbe rate of change of amplitude (or stress), oi1/ax is

aiii wobam ir vA o requirements, which were covered earlier in we two other requirements that must be met. These

tsr conditions that exist at the boundaries between

If i _1e. The two conditions are that the displacement ibs= F x exerted by the wave must be continuous across a

must be continuous everywhere. Boundaries in AM Acfiwd as points where there is a change in material

iiiiiiwsai as the interface between a piezoelectric transducer --.. ri tion), or a sudden change in lateral dimensions

iisrniw& !ft indwim –ange in diameters at the step transition between 1111rW am ! ers).

Rawam the situation. The front half of a nozzle is depicted, * .i to a half-wavelength. The complete nozzle was

iiiiiisst entirety in Fig. 2.14a. At x = x 11 the boundary s iamgom between the piezoelectric transducer on the left,

11111110111111W MW.–aer portion of the titanium horn section on the right itiiidiii At the second boundary, x = x 2 , there is a change in

ItLtIIIIII

i be divided into three sections (labelled 1, 2, and irmon ____ distinct material and dimensional properties. For

is a specific solution to the wave equation. For the ioii is r ( x). For sections 1 and 2, the solutions

a rr riven in Eq. 12,

� = Acos(k 1 x)+ B 1 sin(k 1 x), (14)

= A,cos(k 7 x)+ B 2sin(k2x).

!..

6 s:on is (15)

= tA.cos(k.x) + B 3sin(k 3x))I(ax +

40 Wave Motion as it Relates to Ultrasonic Nozzles Chapt i rlvrl ’ !.tion as it Relates to Ultrasonic Nozzles 41

- =2 can rewrite the force boundary conditions in

P2, C 2

pcA:(x)r1 1 ’(x 1 ) = p 2c22A2(x 1 ) 2 ’(x1 ) (17)

= p 3c 32A3(x2)1 3 ’(x2 ).

Pi, C1 :cnstitute the required boundary conditions. The

r.r ;::–ijns that must be met are the end conditions. At x t Iftm s & and at x = x 3 , an anti-node. Therefore,

CO

T1 1 ( 0)= 0 (18)

fl(x 3 ) = 0.

I I I a 5 constitute six (6) boundary and end conditions.

0 x1 x2 x3 but i equations defined for sections 1,2, and 3, Eqs. (14) ______ -

______ 6) constants that must be determined in order to HOMBIM111412M the solution. In accordance with the basic principles

FIG. 2.22 awa- mo ft fimfute solutions to differential equations, having six mitiiinmoom ind eW conditions for six unknowns gives us all the

--tw i to obtain a complete solution for this configuration.

At the boundaries between sections, the following conditions mu~ 1111agummumd details of the actual solution are simple yet tedious, md athem here. Readers interested in obtaining actual

met: II[lIiILiLidiI, ijitÆ a1]t a text on ordinary differential equations and

lVxdIUIIIUIIIIUJ)V" ’4em

= rl2(x) (15)

- iiiiiii ultrasonic nozzles, the solution admits only certain

112(x2) - 3(x2), a--- -icn lengths. For example, if x 1 and x2 are specified, --k &- iermined for specific values of the diameters, d.,

and ommmm, . at sound. c. in each section, as well as the frequency ’-.----- f_

F1(x1)=F1(x1) (16)

I* amme-whmd klary conditions given in Eq. (17) can generally F2(x2) = F 3(x2 ). ________

IMKZ I is not typical that both the material properties and

The force condition given by Eq. (16) can be expressed in a more Camomm _____ at the same boundary. For a change of material

form. From Eq. (4), the force F.(x) = EA1(x)11 1 ’. (Since T is now X = X 1 . A 1 (x 1 ) = A2(x 1 ), so that

a function of x, we have substituted the symbol r’ for a,/ax i i p.c1111(x1) = p2c22 7 2 ’(x1 ). (19)

and in what follows.)

42 Wave Motion as it Relates to Ultrasonic Nozzles Chapter 43

For a change in diameters, such as at x = x 2 , p 2c22 = p 3c 32 , so that

A2(x2)11 2 (x2) = A 3(x2)11 3 ’(x2). (20)

An immediate consequence of Eq. (20) is that the stress differentia across a boundary where diameters change is equal to the ratio of large: area to the smaller area. Since stress is directly proportional to strain

= T13’(x2)/112(x2) = A2(x2)/A3(x2) = d 1 2/d2 2 . (21)

It is readily shown from the analysis that the ratio of amplitudes 0:

displacement at a boundary where diameters change, r13(x2)/11,(x2), i also proportional to d 1 2/d22 . This was mentioned earlier when we discussed the gain factor. If the boundary occurs at a node, such a depicted in Fig. 14b, then the gain is exactly equal to d 1 2/d22 . In the case we have been discussing, the diameter transition occurs somewha beyond the nodal plane. Although the gain is still proportional to d i d22 , this design results in a reduction in gain, compared to the case where the transition is right at a node. The gain reduction is typicall on the order of 15 - 25%.

In Section 2.3, we mentioned that an additonal gain factor arises whe-a tapered section is incorporated. This gain factor, 113(x2)1113(x3), can be calculated from the equation for fl in region 3 at points x = x2 and x. The result is that the gain is on the order of d 2/d 3 . The overall gain c: the device, G is on the order of

G = (d 1 2/d2 2 ) � (djd 3 ) = d 1 2 /(d 2/d3)’

3 THE ULTRASONIC ATOMIZATION PROCESS

1 CAPILLARY WAVES

� :he beginning of Chapter 1, we explained that the ultrasonic �ization process results from instabilities created in the liquid capillary

s that form on the atomizing surface as a result of the energy provided - e surface in the form of high-frequency vibrations. An actual capillary

1 . e pattern was shown in the microphotograph of Fig. 1.1. A schematic :rsentation of this pattern is shown below in Fig. 3.1.

The regularly repeating rectangular wave pattern is characterized by 2- ez:sand troughs with a wavelength). (Note: This wavelength is not

confused with the wavelength of the longitudinal pressure waves - rated in the nozzle itself, as discussed in detail throughout Chapter 2.)

- wavelength, k can be related to the frequency of vibration, f; the -iity of the liquid, p; and the surface tension, s of the liquid against atomizing surface, by’

A C = (87ts/pf2 ) 111 (1)

as been shown by Lang’, that there is a good correlation between the - ber median drop diameter produced, dN, 0.5 and A,. His experiments

ed that

dNo0.34Ac. (2)

FIG. 3.1

44 The Ultrasonic Atomization Process Chapter 3 chapter 3 The Ultrasonic Atomization Process 45

The number median diameter, d N 0 . 5 is defined as that diameter, in a

sample of N drops, for which half of the drops are smaller than, and the other half larger than dN

0.5�

Therefore, the number median diameter can be characterized by the relationship

dNas = 0.34(87rs/p12)"3 . (3)

The correlation given by Eq. (2) makes sense on an intuitive level. Since the drops are produced on the crests of the waves, which are squares of size )/2 x A/2, the largest drop diameter that could be created by this mechanism would have a diameter equal to /2. The correlation shows that the number median diameter is approximately two-thirds this amount (2/3 x ), /2

Although surface tension and density have a role in determining the size of drops produced by an ultrasonically generated spray, the frequency, f is the principal factor in determining drop diameter, since it enters the equation as a square, whereas both the density and surface tension enter as the first power. Appendix A contains an extensive listing of the median drop sizes that can be expected for various liquids.

3.2 THE ROLE OF OPERATING FREQUENCY IN NOZZLE DESIGN

The principal consequence of Eq. (3) is that drop diameter is proportional to f �213rn This implies that higher operating frequencies produce smaller drops. As we shall see, this factor is integrally related to other elements of nozzle design, including overall nozzle size and maximum flow rates achievable.

Near the end of Section 2.3, where we discussed some of the design considerations for nozzles, it was mentioned that maximum nozzle diameters must be less than X/4 in order to suppress unwanted radial modes of motion. The length of a nozzle is proportional to ?. Therefore, in terms of order of magnitude, the maximum overall size of a nozzle is proportional to the maximum cross-sectional area times length, or V. Since ? 1/f, the maximum overall size is also proportional to 1/f 3 .

The size constraint means that, in general, nozzles which operate at high aquencies, such as 120 kHz, are limited to relatively low flow rates, - e their size must be relatively small and the amount of room available

-. r atomization on the atomizing surface is limited. Highest flow rates an be achieved by large nozzles, operating at low frequencies, in the agion of 25 - 35 kHz.

Tne corollary to this is that since smaller drop sizes are associated with - gher frequencies, as determined by Eq. (3), the maximum flow rate - apacity decreases as the operating frequency increases. This is so - --cause the size of the atomizing surface and the size of the liquid-feed

-ifice supplying liquid to the atomizing surface are intrinsically linked nd directly proportional to the overall dimensions of the device.

since overall maximum size is proportional to 1/f 3, the theoretical maximum flow rate ratio between a nozzle operating at 25 kHz to one perating at 120 kHz, is (120/25 )3 = 110. This wide range in maximum Tow rate has a major effect on the capabilities of ultrasonic nozzles to roduce drops in a range of sizes consistent with required flow rates for ecific applications.

in terms of the actual magnitude of maximum flow rates and number nedian drop diameters, nozzles operating at 25 kHz have been produced ith flow rate capabilities exceeding 50 gph (3000 ml/min). The number

T.e dian drop diameter, d N. 0.5 at 25 kHz, for water (from Eq. (3)), is about

0 t. The maximum flow rate obtainable from a nozzle operating at 20 kHz is on the order of 0.5 gph (30 ml/min). The value of dNa5 is

approximately 18 t.

To this point, we have considered only maximum flow rates. In many applications, maximum flow rate capacity is not important. Drop size and spray shape are the principal factors. Nozzles can be designed to ptimize both of these parameters at any frequency by reducing the -rincipal nozzle diameter to well below 2J4 and by specifying the proper ;hape and size of the atomizing surface. For example, a nozzle can be esigned that operates at 25 kHz and is optimized to deliver a conically-

Thaped pattern, at a low flow rate. This is accomplished by reducing :he main diameter to about 0.75 in., which is a fraction of the maximum iameter, X/4 (� 2 inches), and by providing an atomizing surface area

and orifice size consistent with the flow rate requirement.

46 The Ultrasonic Atomization Process Chaps - r 3 The Ultrasonic Atomization Process 47

A final discussion of the atomization process and the underl: mechanics that govern it relates to how the spray is actually formc

Each crest on the grid shown in Fig. 3.1 can be viewed as a pote source of drops. Thus, the number of potential atomizing sites per surface area, n (site density) is proportional to 1/,2 or n = W, 2, wh is a proportionality constant.- 5

.2. we show the experimental data, using water, that confirms .iity of Eq. (5). A series of five nozzles operating at frequencies

from 31 to 78 kHz were used. The agreement with the predictions i is excellent. The constant k 28.5 x 10 liters (HZ) 213/(sec

The maximum volume of spray deliverable from a unit of surface per second (the specific flow rate, r) can be viewed as proportion n(dN or

r=f3n(d )3 (4) N. 0.5

where 5 is a proportionality constant containing the time depend associated with flow rate.

Since dNoS = 0 . 34) and n = &’2, we can write r in the form

= (0.34)3aI3) = (0.34)3a(81u/p)113f -2/3, or

r=kf 213 (5)

where k = (0.34) 3c3(8tIp) 1 /3 .

The assumptions made in arriving at Eq. (4) deserve further explana If the atomization process were such that each atomizing site eject drop once per cycle, then the form of Eq. (4) would be

r fn(d )3, N. 0.5

35

E 30

25

4 20

15

10 a

0. 5 U)

0.2 0.4 0.6 0.8 1.0 1.2

f.213 (Hz 2’3 x 1 0)

FIG. 3.2

since the frequency, f would now dictate the number of times per sec each site would produce a drop. The form of Eq. (5) would then bee

r - f 113 -lationship shows that the size of the atomizing surface plays a - e in determining at what rate liquid can be atomized. An atomizing

However, from our earlier discussion, we already know that r doet of a given size obviously has a limitation as to how much liquid behave like this. Therefore, the conjecture that there is a time correI-- - upport and still create the film that is needed for capillary waves. between drop production and frequency is invalid. - quantity "dumped" onto the surface becomes too great, it

helms the capability of the surface to sustain the liquid film. Fig. 3.3, next section, is a table that gives actual flow rate capabilities for a

48 The Ultrasonic Atomization Process Chapter ,, t , The Ultrasonic Atomization Process 49

selection of nozzles of different geometries. It will be noted from table that there is at least one other factor that plays a key role in fl rate determination. That factor is the exit velocity of the liquid stre as it emerges onto the atomizing surface. This will be discussed next

To complete the story, there is a third factor that figures into determini possible flow rates. This relates to the dynamic properties of the liqL being sprayed. Characteristics such as viscosity, polymer chain leng and solids-content are just a few of the large array of liquid propert that can affect ultrasonic atomizability. These will be explored in de in Chapter 4.

3.3 THE EFFECTS OF LIQUID VELOCITY

As was shown in Chapter 1, the most common method of deliveri liquid to the atomizing surface is through a continuous orifice that r from a tube on the rear of the nozzle (the inlet), then through a chan: contained within the body of the nozzle, and finally out of an exit orif at the atomizing surface. The exit velocity at the atomizing surface. is important.

- a wide sample of different type nozzles indicate that v = 0.33 m/s. - :zles atomizing water and oriented such that the emerging stream

zontal. A slight reduction in this value for v is observed for a ally downward stream. One would expect this for a vertical

- ation since the effect of gravity reduces the ability of the stream to the surface through the pressure differential. Fig. 3.3 below

how orifice size impacts flow capabilities. The table also includes :a for flow rate as a function of atomizing surface area, as discussed :ion 3.2.

Orifice Dia. (in.) Atomizing Surface

Dia. (in.) Maximum Flow

Rate (gph)

020 - 0.040 0.09-0.25 0.07-0.3

052 - 0.067 0.24 - 0.35 0.5 - 0.8

386- 0.100 0.30-0.45 0.9-1.7

0.141 0.46-0.50 2.4-3.3

0.250 0.65 6.0

FIG. 3.3

In large measure, it is the ability of the liquid to cling to the surface a emerges from the central hole that determines whether or not it will a apot effect is not the only cause for the observed situation. Another atomized. This in turn depends on such factors as exit velocity of huting factor is the vibration of the atomizing surface itself. It can stream from the orifice, and to a lesser extent, on spatial orientati - ijectured that the vibrations create an attractive force by reducing Experimental observations have shown that if the flow rate exceed - parent surface tension. This can be confirmed through the certain value such that the ye exceeds a value called the critical veloc.. .. mation that more area is covered when the nozzle is powered than v the stream becomes detached from the atomizing surface. This eff - -. is not. appears even when the nozzle is not energized. When it is operati:

exceeding v results in the appearance of some unatomized liquid in - . aiue of the v is of course determined by the feed rate and orifice spray stream. The phenomenon can be partially explained by the - It is possible to reduce the velocity such that

v < v by enlarging

called teapot effect which has been investigated by Reiner’ and Kell :le diameter. Just as in the case of the geometry of the atomizing As is commonly experienced in everyday life, when liquid is poU.

:e. there are form factors to consider which place an upper limit on from a container, such as a teapot, if the pouring is done very slov ze of the orifice and therefore on possible flow rates. there is a tendency for the liquid to cling to and run down the spout. the liquid is poured faster, this effect disappears. The effect can

’ractical matter, optimum performance is achieved when the orifice explained as being caused by pressure differentials in the streamlines’ treamline :d to conform to the intended flow rate. Although the atomizing

the emerging liquid as the stream rounds the spout. The pressure - ility is not affected by varying the flow rate within the range such higher at the outer surface of the stream than it is at the inner surface that there is a net force pushing the liquid against the spout. . is between 0 and v it has been observed that the most uniform

ntroIlable spray is achieved when v, is greater than 20% of v. As :Tcw is reduced, a point is reached where v becomes so low that the

50 The Ultrasonic Atomization Process Chapter ::er 3 The Ultrasonic Atomization Process 51

liquid emerges onto the atomizing surface in a non-unifor circumferential manner, causing the atomization pattern to becon distorted. In some applications, where stable spray patterns a unimportant (e.g. some chemical reaction chambers), this distortion m be tolerable. In other applications, where the integrity of the pattern vital (e.g. surface coatings), the low-velocity stream distortions a unacceptable.

3.4 SPRAY SHAPES

Atomizing surfaces can be shaped to meet specific applicati requirements. Some possibilities are shown in Fig. 3.4. The configuratic on the left shows a cone-shaped spray pattern, used when the spray mi.. be fanned out over an area of a few inches. The center illustration sho

- igh the illustrations above show symmetric and very well-defined � ’atterns, this is often not the case in real life. The reason is the

- ’v velocity of an ultrasonically generated spray. Remember that _rav is produced by the "breaking off’ of drops from the crests of

- av waves. The drops have relatively little momentum when they :cted. To give some idea of the "softness", typical spray velocities Lit a few inches/second, about 1% that of sprays from pressure

� s. This "softness" will be shown to have many advantages in a :v of applications. However, the down-side is that the spray pattern

unstable in terms of remaining stationary in space. The slightest � - vement can cause distortions Even slight turbulence in the liquid

- cing onto the atomizing surface can cause aberrations in the spray

FIG. 3.4

a very narrow spray pattern achieved by minimizing the atomizing surfa area. For this type of nozzle, the orifice size is usually in the rat 0.015-0.040 inches and the atomizing surface diameter is from 0.09 0.120 inches. It is usually recommended for use in applications wh very small amounts of material are to be delivered or where flow ra are very low. The right-most illustration depicts a cylindrical spray sha used in applications where the flow rate can be relatively high, but wh the lateral extent of the spray pattern must be limited.

:rier to handle this characteristic behavior, it has been found useful -ploy auxiliary air streams to manage the spray pattern. The highly

riiant spray is easily entrained and can be shaped into many forms - i’ropriately designed air handling devices. In Chapter 7, we shall

-.cbe the various methods used for spray shaping.

Li DROP-SIZE DISTRIBUTION

e ci the more important topics for those involved in atomization _L: _� s is the distribution of drop sizes in the spray. In many combustion rI:cations, for example, the drop-size distribution is an essential c.ent in the understanding the process.

JFceT. we introduced the concept of number median drop diameter, d N rs arameter is relatively simple to conceptualize. Repeating that definition

ice. i ,, is defined as that diameter, in a sample of N drops, for which the drops are smaller than, and the other half larger than dNos. It own, Eq. (3), that

dNa5 = 0.34(8its/pf2 ) 113 .

� are several other measures that are used to characterize the T ution of diameters in a spray, each having its own particular use. � - f the most commonly employed measures are the number mean

d 10, the surface mean diameter, d 20, the volume (or weight) diameter, d 30, and the Sauter mean diameter, d 32 . Their meaning come clear in the following.

52 The Ultrasonic Atomization Process ChapterE.çtr 3 The Ultrasonic Atomization Process 53

The general expression for these various mean diameters is presented -al mean diameter that we shall consider is the Sauter mean the following form: - d,. This parameter is frequently used in combustion-related

aons. It takes the following form: dab (I n 1d/ njd) 1/(a-b)

(6) 3 2

I d32 n 1d/n 1d 1 (10)

where d represents a drop of diameter d., n. the number of drops w: mmation in the numerator represents the total volume of drops in diameter d., and dab the mean diameter being defined, where a and b a:� /.arnple, while the summation in the denominator is the total surface integers designating the specific type of mean. The summation is ove:- i drops. The quality of combustion of liquid fuels is essentially sample of N drops, so i =1, 2 ......,N. -Ient on the amount of surface area available since combustion

s on the reactions that occur at the interface between the surface of Of the four means we shall consider, for the first three, b = 0, so that t. �:v of fuel and the surrounding gas. Therefore, it is important that summation in the denominator of Eq. (6) reduces to enominator in Eq. (10) be maximized. Similarly, the numerator

..J be minimized. The reason that the numerator should be minimized N st be described by example.

The first mean is d 10, the number mean diameter, given by

d 10 n 1d 1/N (7)

It is simply the average diameter of all the drops in the sample

The surface mean diameter, d 20 , is expressed by

d20 ( nd/N) "2 (8)

It is the diameter of that drop whose surface area, proportional to d 2 the mean surface area of all the drops in the sample.

The volume mean diameter, d 30 , is probably the most widely used oft various mean diameters, since it represents the distribution of the weig of drops. It is given by

3 1/3 d30 ( nd 1/N) (9)

It is the diameter of that drop whose volume, proportional to d 3 , is t mean volume of all drops in the sample.

that one drop in the sample contains 90% of the total volume sample. This one drop would have an inordinately large impact

:e volume of the sample available for combustion, but contain only 20% of the available surface area. The remaining 10% of the not significant in terms of the total volume, would burn nicely,

se they constitute the remaining 80% of surface area. However, tal heat output from a distribution of this type would certainly not

ctimal because the single large drop would constitute most of the e. but little of the heating power of the overall sample.

1 DROP-SIZE DISTRIBUTIONS FOR ULTRASONIC NOZZLES

� ::stribution of drop diameters in an atomized spray, regardless of rce, invariably follows a regular pattern. This means that there is

a relationship between the drop diameter, d, and the frequency urrence of that diameter, n 1 . This relationship is referred to as a

.L7ution function. Several models have been developed for specific :zation processes. The one that works best for the ultrasonic

r -zation process is called the log-normal distribution function, in :he distribution of diameters follows a normal or Gaussian curve,

it horizontal axis, the range of drop diameters, conforming to a �-mic, rather than a linear scale. The shape of a typical distribution

:n in Fig. 3.5. Notice that the distribution follows the familiar I-aped curve, but that the horizontal scale is logarithmic, rather

im :ear.

54 The Ultrasonic Atomization Process Chapter –pter 3 The Ultrasonic Atomization Process 55

MEDIAN DROP DIAMETER

corollary to Eq. (6), which expressed the general diameter parameter, in terms of summations over the drops in the sample, is for a

- :inuous distribution,

dab = J [ �

I

xa n(x) dx / I xhn(x) dx] (12)

o

re the summation has been replaced by an integral.

’stituting Eq. (11) into Eq. (12), the results for the four (4) mean _meters we have been considering are as follows:

AL

U. 0 ’0

w cr0 11.0

1 10 100 1000 d 10 = x0e 32

DROP DIAMETER (microns)

FIG. 3.5

This distribution function can be expressed mathematically in the for

e -o?/2 e -(In x/xo)2/2ad2 (11) n(x) = Gd(21t) 112 x0

where n(x) is the number of drops of diameter x, a d is the measure of ft width or spread of the distribution, and x 0 is a constant that depends e ad and the type of mean diameter considered (i.e., the values of a and t We have replaced n 1 by n(x) and d by x in Eq. (11) since this functic consists of continuous, rather than discrete parameters.

We recognize that Eq. (ii) appears rather formidable. However, it basically the standard normal distribution function modified by ft appearance of In x/x 0 in the argument rather than x itself.

In the following paragraphs we shall not go through the tedioL mathematical details that must be carried out in order to reach our fin. results. It should be pointed out, however, that the results are rath important in obtaining a working understanding of how drops a: distributed, in terms of size, for a spray from an ultrasonic nozzle.

d20 = x0e 2

(13)

d30 = x0e 5(7,’/2

d32 _x0e72

� h x 0 and ad are parameters that must be determined experimentally r at least two of the mean drop diameters are known. Shortly, we Jl examine some of the methods that are in use for determining these

.L-neters.

example,

ad 2 =In (d 30/d 10).

-erefore, one definition for x is,

X0 = d30e -5/2

72 the mean diameters obtained from experimental data to compute T x and a d allows a comparison to be made between actual results Those predicted by the log-normal distribution function model.

A convenient method of representing the various mean drop diamet distributions is to present them in the form of a percentage of the droç in a sample, F(d), having a diameter, surface area, volume, or Saute mean drop diameter, in the range from 0 diameter to some specificall selected drop diameter, d 1 . This is accomplished by integrating n(x given by Eq. (11) over the range 0 to d 1 ,

FJ(d,) � n(x) dx (14)

The actual values of F(d 1 ) for a sample of nozzles operating at differer frequencies is shown in Fig. 3.6.

�

___ ..�:4Ipf.pi4 .1111

I IVA

�ui4wA __ pIIJJZ2 -U..." -U...’ 1’’JAHHI__

_....

IIIIII!IpAI1 �III II 4N’ UUIHl____

A �� UI

4 6 8 10 20 40 60 80 100

200

Drop Diameter (microns)

FIG. 3.6

99.9

99.9

99.5 99 98

95 I- Cl 90

80 :5 70

60 ~ 50

40

.2 30 20

0.1

0.01

56 The Ultrasonic Atomization Process Chapter 1cr 3 The Ultrasonic Atomization Process 57

that each of the curves is a straight line. This is because the axes J out such that the vertical axis is keyed to the values associated

- normal distribution function, whereas the horizontal axis is scaled thmical1y. In addition to the four distributions that we have been

� _ssing in this section, the median drop size distribution has also :ncluded.

interesting feature of log-normal type distributions is that, the ’-z-entage of drops comprising a particular mean or median diameter is

same for each operating frequency. This result comes out of the :ulations related to Eq. (14).

:her interesting aspect of Fig. 3.6 is that for each frequency, the i.ian diameter, dNo5 is the smallest, followed by the mean diameters

w d: i d 30, and d 32 , in order of increasing value. This is obvious from l3).

:Nuving that dNos is the smallest of these diameters requires a more Mailed analysis, which we will not pursue here. We shall only note that

definition, F(d NO

= 0.5, and that for a log-normal distribution, F(d b), -br the various combinations of a and b such that a> b, must be greater

n 0.5.

3.5.2 EXPERIMENTAL METHODS FOR MEASURING DROP DIAMETERS

The determination of drop distributions in actual sprays is a subject that s extensively studied. For those interested in this aspect of spray

hnology, there are a number of sources for information. The best are crnals devoted to sprays and aerosols. Here we give only a brief

s.ription of the various techniques employed.

The most common method in use today employs laser beams directed at spray. The spray causes the light from the beam to be scattered. values of various measurable properties of the scattered light depend

- :’ne distribution of drop sizes in the spray. A particularly useful device :his type is known as a phase/Doppler spray analyzer. Detectors isure the phase shift in the coherent laser beam resulting from the

�

- - ter. Complex algorithms are used to construct a distribution function lrop diameters from the measured data.

58 The Ultrasonic Atomization Process Chapter 2 Llpter 3

The Ultrasonic Atomization Process 59

Another device that relies on light scattering utilizes the diffracted ligh from the incident laser beam to determine drop size distribution. Wher a narrow beam of light impinges on a small particle, such as a spra drop, part of the beam will be bent slightly due to diffraction effects which are a consequence of the wave nature of light. Larger drops benc the light less than smaller drops.

A special type of detector, whose elements are arranged in the shape o concentric rings about the center point of the laser beam is positioned tc receive the light scattered by the spray. The outermost elements of th; detector, those at the greatest distance from the center, detect the mos heavily diffracted rays, corresponding to the smaller drops. Th: innermost rings detect rays from the larger drops. By measuring th amount of light collected by each of the ring elements, it is possible t construct a drop size distribution.

Other techniques used to determine drop size distributions are not neari, as convenient to use as those just described. These include high-spee video camera techniques in which a magnified visual record of the spra is obtained and transmitted to an image processor in order to analyz the distribution; and a permanent record technique in which a sample c spray, composed of a heated liquid, such as wax, is collected on a co( substrate and solidifies. These techniques, while capable of giving goo results, are not very versatile since they can accommodate only extreme small sample sizes.

3.6 PRACTICAL ASPECTS OF DROP-DISTRIBUTION ANALYSIS

3.6.1 COALESCENCE OF DROPS

The theoretical results obtained in Section 3.5.1 form a solid basis fc understanding the nature of the drop-size distributions that can b expected from ultrasonic nozzles. However, there is a circumstance which some modification to the theoretical results is necessary. Th distributions have been shown to be somewhat dependent on flow rat

__-,is is that there is a tendency for drops that are in very close proximity :h other to coalesce into larger drops. This occurs when the spatial

- :t\ of drops is high, such as occurs when the flow rates are on the side of a nozzle’s capacity.

:endency for drops to coalesce is also dependent on the shape of the At the same flow rate, nozzles with conical surfaces, which spread

- e spray, are more immune to coalescence than are sprays from ::es with flat atomizing surfaces, which produce more cylindrically :.d patterns.

a result of this phenomenon, there is a deviation from predicted avior. There are more large drops than theory predicts, and there are er small drops. This has the effect of increasing the median and an diameters, as well as causing the distribution of drops to deviate

log-normal behavior.

ough the magnitude of this effect is fairly small, less than a 20% - :ase in the values of characteristic diameters at worst, it nonetheless - be significant for certain applications that are drop-size dependent.

- :her factor that enters into the coalescence issue is the surface tension -ie liquid being sprayed. Liquids with high surface tension, such as r, tend to coalesce more readily than readily than liquids with lower

� ace tension. This is the result of more free energy being available at - a surface of drops with higher surface tension. The presence of this :sive force at the surface causes two drops to "attract" each other

coalesce. The degree of attraction is proportional to this force (or _ace tension).

6.2 THE EFFECTS OF LIQUID PROPERTIES ON DROP SIZES

(3) of Section 3.1, showed that there drop size is related to two a:erial properties of a liquid, density, p and surface tension, s. That a:ionship, repeated here, is

At the low end of a nozzle’s flow rate range, there is an exceller dNo5 = 0.34(8its/pf 2 )1 /

3 .

correlation between theory and actual results. As flow rate is increase- all the median and mean diameters show an increase in value. The reasc

60 The Ultrasonic Atomization Process Chapter 3 61

The data presented in Fig. 3.6 for F(d 1 ) as a function of drop diameter are based on water. In order to translate these results so that they are applicable to other liquids we define a conversion factor C1 as

1=(s p ’S water )1/3 x water water x

where, for liquid x, p, is its density and s its surface tension. Then we can write a conversion formula as

(d N, 0.5x = ( d N,Owater

Appendix A contains a list of D values for a variety of substances.

4 THE EFFECTS OF LIQUID PROPERTIES

We have already discussed how density and surface tension effect the spray produced by ultrasonic nozzles. In this chapter the focus will be on other material properties that can have a more significant effect on the atomizability of liquids using this technique. These include liquid type (e.g. solutions, mixtures, suspensions), viscosity, corrosivity and abrasive potential.

4.1 TYPES OF LIQUIDS

The physical nature of a liquid plays a central role in the ultimate success of any atomization process. Factors such as viscosity, solids content, miscibility of components, and the specific rheological or dynamic behavior of a liquid affect the outcome.

Pressure nozzles, both hydraulic and pneumatic, are generally unsatisfactory with materials that are abrasive or which tend to quickly solidify and clog the small orifice, because of high solids-content or other type of "stickiness." In addition, it is usually necessary to operate such nozzles at high pressures, which produces overspray and consequent material loss.

Ultrasonic nozzles are just as "fussy" with respect to the nature of the liquid. Although they offer many potential benefits, such as a soft, low-velocity spray, micro-flow capabilities, extensive spray shaping opportunities, and total freedom from clogging, the very nature of the technology presents restrictions on the types of liquids that can be successfully atomized.

Unfortunately, there are no hard-and-fast rules governing the atomizability of a liquid using ultrasonics. There are many documented cases where liquids that are seemingly easy to atomize, are not; and conversely, there have been situations where it appears at the outset that atomization by ultrasonic means will be impossible, but the liquid atomizes perfectly well.

Although there is no specific set of rules governing the ultimate success in atomizing a liquid ultrasonically, there are several guidelines, which have been developed through experience over time, that give a good indication of the probability for success.

62 The Effects of Liquid Properties Chapter 4 Chapter 4 The Effects of Liquid Properties 63

To discuss these guidelines, we first categorize liquids as to type:

� Pure, single component liquids (water, alcohol, bromine, etc.)

True solutions (NaC1/ water, alcohol/water, 10% KOH in water, etc.)

� Mixtures with undissolved solids (coal slurries, polymer beads/water, silica/alcohol, etc.)

The only guideline that applies to most materials is that the higher the viscosity or solids-content of a liquid, the lower will be the maximum flow rate for a given nozzle. The power delivered to a nozzle is adjustable in order to accommodate various liquids, as will be described in Chapter 5. However, the application of higher power to hard-to-atomize liquids does not ensure that the nozzle will be able to atomize at a flow rate near its rated capacity with water.

For pure liquids, the only factor limiting the ability to atomize ultrasonically is viscosity. In general, the upper limit on viscosity is on the order of 50 cps. However, the maximum possible flow rate at 50 cps is severely limited, less than 0.25 ml/sec. As viscosity is reduced, the maximum flow rate increases correspondingly, eventually reaching the maximum flow rate for a given nozzle configuration at viscosities under 10 cps.

For true solutions, the criteria for atomizability are, for the most part, the same as for pure liquids. An additional consideration arises when the solution contains very long-chained polymer molecules. In that case, the possibility exists that the polymer will interfere strongly with the atomization process because of the sheer magnitude of its linear extent. The molecule can inhibit the formation of discrete drops since there is an increased probability that it will span the region of the bulk liquid where two or more drops are about to be formed.

For mixtures with undissolved solids, there are three primary factors that influence atomizability. These are, particle size, concentration of solids, and the dynamic relationship between the solid(s) and carrier(s).

Particle size is a critical parameter. In general we have observed that if the particle size covers an extent that is more than one-tenth the median drop diameter, the mixture will not atomize properly. This is clear on an intuitive level. For drops that contain one or more solid particles, their size must be significantly greater than the size of the solid particle(s) entrapped within. If not, there is a good chance that a majority of the drops will form without entrapping the solid component. The typical result is that the solid component and the carrier separate. The carrier atomizes nicely, but the solid component is left behind, accumulating on the atomizing surface and eventually dropping off as an agglomerated mass.

The concentration of solids in a mixture is an important factor in its atomizability. Obviously, from the discussion above, the particle size must be small enough to allow for any possibility of atomization. Even if the particle size is appropriate, other factors, such as the viscosity of the carrier and the ability of the solid component to remain suspended, play a role in the ultimate atomizability. As a result, there are no clear-cut guidelines to enable us to establish a relationship between atomizability and solids concentration.

From our experience, a practical upper limit on solids concentration is about 40%. This has been established for several materials, including solder fluxes and various inorganic slurries. It must be stressed again that conditions must be just right in order to achieve atomization in this range of concentration.

4.2 CHEMICAL RESISTANCE

Ultrasonic nozzles are fabricated from a highly chemically resistant alloy of titanium, Ti-6A1-4V. Titanium is used not only for its superior chemical resistance, but also because of its excellent acoustical properties and high strength, as pointed out in Chapter 1.

An interesting aspect of the chemical resistance of titanium and its alloys is that titanium is materially aided in its chemical resistance by its natural tendency to form an oxide layer on its surface almost immediately upon exposure to air. Freshly machined titanium is prone to oxidation, combining almost immediately with oxygen in the atmosphere on freshly exposed surfaces.

64 The Effects of Liquid Properties Chapter 4 65

The naturally created oxide layer offers an additional measure of protection to the underlying metal because of its own high resistance to chemical attack.

Of course, titanium and its oxide layer are not impervious to attack by all chemicals. It is particularly susceptible to attack by substances that can breach the oxide layer and initiate other types of oxidizing reactions. Strong acids such as hydrofluoric and sulfuric acid will attack the metal. Aside from strong oxidizing agents, titanium is chemically compatible with most other liquids.

The only other material that is generally in the liquid path within a nozzle is a liquid inlet fitting. Generally, this fitting is made from 316 stainless steel. If necessary, it can be fabricated in titanium. In environments where the sprayed substance is liable to permeate the atmosphere, the housing that protects the active elements within the nozzle, also generally made from 316 stainless steel, can also be fabricated in titanium.

4.3 ABRASION RESISTANCE

The orifices in ultrasonic nozzles are generally large and the velocity of liquids flowing through are relatively low. This gives ultrasonic nozzles a decided advantage over other types of spray nozzles when dealing with liquids containing abrasive components. Most nozzles that operate under pressure, whether hydraulic or air-assisted, wear rapidly in the presence of abrasive liquids.

However, the advantages that ultrasonic nozzles offer do not make them completely immune to the effects of abrasion. Over long periods of time, the effects of an abrasive material, coupled with the large amplitude of vibration at the exit orifice on the atomizing surface can lead to wear. This phenomenon has been observed over the years in nozzles that operate for 8 to 16 hours a day, spraying a substance containing a concentration of 5 - 10% silica particles through a 0.030 inch diameter orifice. The wear manifests itself in erosion around the periphery of the orifice. The atomizing surface itself is unaffected. Although the period of time for this erosion to become noticeable may be a couple of years, it nonetheless is persistent.

5 ELECTRICAL ASPECTS OF ULTRASONIC NOZZLES

In order for the transducers, which are contained within the core of a nozzle, to convert incoming electrical energy into useful mechanical energy (i.e., standing waves), power must be provided in a manner that assures sustained oscillations. Since nozzles are resonant devices, as described in Chapter 2, it is necessary that the circuitry providing electrical input power is capable of meeting the very specific needs associated with this mode of operation.

There are two basic requirements that must be met by a power generator designed for this purpose:

� It must be capable of tracking the resonant frequency of a nozzle under various load conditions and maintain the appropriate level of power.

� It must be adjustable in terms of the amount of power it delivers to a nozzle.

The first of these two requirements is the most demanding. The resonant frequency will drift as a function of liquid load, nozzle temperature, and age. Although the drift will generally be less than I kHz, the power source must be capable of compensating for these dynamically changing conditions.

The second requirement relates to being able to achieve optimum atomization. You may recall that in Chapter 1 it was mentioned that the true atomization process was possible only within a narrow range of atomizing surface amplitudes. The control over amplitude is achieved by precise control over the power level provided to a nozzle.

This chapter will examine the various electrically related aspects of ultrasonic nozzles and show how the generator and nozzle are completely interactive. We shall also describe the power level control requirements that lead to acceptable atomization.