Dispersion
Technology, Inc.
Phone (914) 241-4791
3 Hillside Avenue
Fax (914) 241-4842
Mount Kisco, NY 10549 USA
Email info@dispersion.com
“ULTRASOUND for CHARACTERIZING COLLOIDS - Particle
sizing, Zeta Potential, Rheology”
- 425 pages, 475 references, by A. Dukhin and P. Goetz. This book is being published as the next volume in the Elsevier series “Studies in Interface Science”, edited by D. Moebius and R. Miller. It has been submitted to Elsevier and should be published by July 2002.
You will find the Table of Contents and Introduction below.
CHAPTER
1. Introduction
1
1.1
Historical overview.
5
1.2
Advantages of ultrasound over traditional characterization techniques.
10
Bibliography 15
CHAPTER 2. Fundamentals of interface and colloid science 21
2.1
Real and model dispersions.
22
2.2
Parameters of the model dispersion medium.
24
2.2.1
Gravimetric parameters.
25
2.2.2
Rheological parameters.
25
2.2.3
Acoustic parameters.
26
2.2.4
Thermodynamic parameters.
27
2.2.5
Electrodynamic parameters.
28
2.2.6
Electroacoustic parameters.
29
2.2.7
Chemical composition.
30
2.3
Parameters of the model dispersed phase.
31
2.3.1
Rigid vs. soft particles.
33
2.3.2
Particle size distribution.
34
2.4.
Parameters of the model interfacial layer.
39
2.4.1.
Flat surfaces.
41
2.4.2
Spherical DL, isolated and overlapped.
42
2.4.3
Electric Double Layer at high ionic
strength.
45
2.4.4
Polarized state of the Electric Double Layer
47
2.5.
Interactions in Colloid and Interface science
50
2.5.1.
Interactions of colloid particles in equilibrium. Colloid stability
51
2.5.2
Interaction in a hydrodynamic field. Cell and core-shell models.
Rheology.
55
2.5.3
Linear interaction in an electric field. Electrokinetics and dielectric
spectroscopy.
62
2.5.4
Non-linear interaction in the electric field. Electrocoagulation and
electro-rheology.
68
2.6.
Traditional particle sizing.
73
2.6.1
Light Scattering. Extinction=scattering+absorption.
74
Bibliography
80
CHAPTER 3. Fundamentals of acoustics in liquids 89
3.1.
Longitudinal waves and the wave equation.
89
3.2.
Acoustics and its relation to Rheology.
92
3.3.
Acoustic Impedance.
98
3.4
Propagation through phase boundaries - Reflection.
100
3.5
Propagation in porous media.
102
3.6
Chemical composition influence.
105
Bibliography
112
CHAPTER
4. Acoustic theory for particulates
119
4.1
Extinction=absorption + scattering. Superposition approach.
122
4.2
Acoustic theory for a dilute system.
133
4.3
Ultrasound absorption in concentrates.
137
4.3.1
Coupled phase model.
138
4.3.2
Viscous losses theory.
143
4.3.3
Thermal losses theory.
147
4.3.4
Structural loss theory.
152
4.3.5
Intrinsic loss theory.
156
4.4.
Ultrasound scattering
157
4.4.1
Rigid sphere.
163
4.4.2
Rigid Cylinder.
164
4.4.3
Non-rigid sphere.
165
4.4.4
Porous sphere.
166
4.4.5
Scattering by a group of particles.
167
4.4.6
Ultrasound resonance by bubbles.
168
4.5
Input parameters.
169
Bibliography
174
CHAPTER
5. Electroacoustic theory
179
5.1
The Theory of Ion Vibration Potential (IVP).
183
5.2
The Low frequency electroacoustic limit -
Smoluchowski limit, (SDEL).
185
5.3
The O’Brien theory.
187
5.4
The Colloid Vibration Current in concentrated systems.
191
5.4.1
CVI and Sedimentation Current.
193
5.4.2
CVI for polydisperse systems .
198
5.4.3
Surface conductivity.
200
5.4.4
Maxwell-Wagner relaxation. Extended frequency range.
201
5.5
Qualitative analysis.
202
Bibliography
205
CHAPTER
6. Experimental verification of the acoustic and electroacoustic theories
211
6.1
Viscous losses.
211
6.2
Thermal losses.
217
6.3
Structural losses.
219
6.4
Scattering losses.
223
6.5
Electroacoustic phenomena.
227
Bibliography
232
CHAPTER
7. Acoustic and electroacoustic
measurement techniques
237
7.1
Historical Perspective.
237
7.2
Difference between measurement and analysis.
238
7.3
Measurement of attenuation and sound speed using Interferometry.
239
7.4
Measurement of attenuation and sound speed using the transmission
technique.
240
7.4.1
Historical development of the transmission technique.
240
7.4.2
Detailed Description of the Dispersion Technology DT-100 Acoustic
Spectrometer.
243
7.5 Precision, accuracy,
and dynamic range for transmission measurements.
253
7.6
Analysis of Attenuation and Sound Speed to yield desired outputs.
257
7.6.1 The ill-defined
problem.
257
7.6.2 Precision, accuracy,
and resolution of the analysis.
263
7.7
Measurement of Electroacoustic properties.
268
7.7.1 Electroacoustic
measurement of CVI.
268
7.7.2 CVI measurement using
energy loss approach.
271
7.8
Zeta potential calculation from the analysis of CVI.
274
7.9
Measurement of acoustic Impedance.
275
Bibliography
278
CHAPTER
8. Applications of acoustics for
characterizing particulate systems
283
8.1
Characterization of aggregation and flocculation.
283
8.2
Stability of emulsions and microemulsions.
293
8.3
Particle sizing in mixed colloids with several dispersed phases.
301
8.3.1
High density contrast - Ceramics, oxides, minerals, pigments.
304
8.3.2
Cosmetics - Sunscreen.
317
8.3.3
Composition of mixtures.
321
8.4.
Chemical-mechanical polishing. Large particle resolution.
326
8.5.
Titration using Electroacoustics.
336
8.5.1
pH titration.
336
8.5.2
Time titration, kinetic of the surface-bulk equilibration.
338
8.5.3
Surfactant titration.
339
8.6.
Colloids with high ionic strength - Electroacoustic background.
344
8.7
Effect of air bubbles.
.
351
8.8
Table of Applications.
352
Bibliography
360
List
of symbols
373
Bibliography alphabetical 381
Index 419
Two key words define the scope of this book: “ultrasound” and “colloids”. In turn, each word is a key to a major scientific discipline, Acoustics on one hand and Colloid Science on the other. It is a rather curious situation that, historically, there has been little real communication between disciples of these two fields. Although there is a large body of literature devoted to ultrasound phenomena in colloids, mostly from the perspective of scientists from the field of Acoustics, there is little recognition that such phenomena may be of real importance for both the development, and application, of Colloid Science. From the other side, colloid scientists have not embraced acoustics as an important tool for characterizing colloids. The lack of any serious dialog between these scientific fields is perhaps best illustrated by the fact that there are no references to ultrasound or Acoustics in the major handbooks on Colloid and Interface Science [1,2] nor any reference to colloids in handbooks on acoustics [3,4,5].
One might ask “Perhaps this link does not exist because it is not important to either discipline?’’ In order to answer this question, let us consider the potential place of Acoustics within an overall framework of Colloid Science. For this purpose, it is helpful to classify non-equilibrium colloidal phenomena in two dimensions; the first determined by whether the relevant disturbances are electrical, mechanical, or electro- mechanical in nature and the second based on whether the time domain of that disturbance can be described as stationary, low frequency, or high frequency. Table 1.1 illustrates this classification of major colloidal phenomena. The low and high frequency ranges are separated based on the relationship between either the electric or mechanical wavelength l, and some system dimension L.
Clearly, light scattering represents electrical phenomena in colloids at high frequency (the wavelength of light is certainly smaller than the system dimension). There was, however, no mention in colloid textbooks, until very recently, of any mechanical or electro-mechanical phenomena in the region where the mechanical or electrical wavelength is shorter than the system dimension. This would appear to leave two empty spaces in Table 1.1. Such mechanical wavelengths are produced by “Sound” or, when the frequency exceeds our hearing limit of 20 KHz, by “Ultrasound”. For reference, ultrasound wavelengths lie in the range from 10 microns to 1 mm, whereas the system dimension is usually in the range of centimeters. For this reason, we consider ultrasound related effects to lie within the high frequency range. One of the empty spaces can be filled by acoustic measurements at ultrasound frequencies, which characterize colloidal phenomena of a mechanical nature at high frequency. The second empty space can be filled by electroacoustic measurements, which allow us to characterize electro-mechanical phenomena at high frequency. This book will help fill these gaps and demonstrate that acoustics (and electroacoustics) and can bring much useful knowledge to Colloid Science. As an aside, we do not consider here the use of high power ultrasound for modifying colloidal systems, just the use of low power sound as a non-invasive investigation tool that has very unique capabilities.
Table 1.1 Colloidal phenomena
|
|
Electrical
nature |
Electro-mechanical
|
Mechanical
nature |
|
Stationary |
Conductivity, Surface conductivity. |
Electrophoresis, Electroosmosis, Sedimentation potential, Streaming current/potential, Electro-viscosity |
Viscosity, Stationary colloidal hydrodynamics, Osmosis, Capillary flow. |
|
Low frequency (l>L) |
Dielectric spectroscopy. |
Electro-rotation, Dielectrophoresis. |
Oscillatory rheology. |
|
High frequency (l<L) |
Optical scattering, X-ray spectroscopy. |
Empty?Electroacoustics! |
Empty? Acoustics! |
There are several questions that one might ask when starting to read this book. We think it is important to deal with these questions right away, at least giving some preliminary answers, which will then be clarified and expanded later in the main text. Here are these questions and the short answers.
Why should one care
about Acoustics if generations of colloid scientists worked successfully without
it?
While it may be true at present that the usefulness of Acoustics is not widely understood, it seems that earlier generations had a somewhat better appreciation. Many well-known scientists applied Acoustics to colloidal systems, as will be described in a detailed historical overview in the next section. Briefly, we can mention the names of Stokes, Rayleigh, Maxwell, Henry, Tyndall, Reynolds, and Debye, all of whom considered acoustic phenomena in colloids as deserving of their attention. The first colloid-related acoustic effect to be studied was the propagation of sound through fog; contributions by Henry, Tyndall and Reynolds made more than century ago between 1870-80. Another interesting, but not so well known fact, is that Lord Rayleigh, the first author of a scattering theory, entitled his major books “Theory of Sound”. He developed the mathematics of scattering theory mostly for sound, not for light as is often assumed by those not so familiar with the history of Colloid Science. In fact, the main reference to light in his work was a paragraph or two on “why the sky is blue”.
If Acoustics is so important why has it remained almost unknown in Colloid Science for such a long time?
We think that the failure to exploit acoustic methods might be explained by a combination of factors: the advent of the laser as a convenient source of monochromatic light, technical problems with generating monochromatic sound beams within a wide frequency range, the mathematical complexity of the theory, and complex statistical analysis of the raw data. In addition, acoustics is more dependent on mathematical calculations than other traditional instrumental techniques. Many of these problems have now been solved mostly due to the advent of fast computers and the development of new theoretical approaches. As a result there are a number commercially available instruments utilizing ultrasound for characterizing colloids, produced by Matec, Malvern, Sympatec, Colloidal Dynamics, and Dispersion Technology.
What information does
ultrasound based instruments yield?
For colloidal systems, ultrasound provides information on the three important areas of particle characterization: Particle sizing, Rheology, and Electrokinetics.
In addition ultrasound can be used as a tool for characterizing properties of pure liquids and dissolved species like ions or molecules, but we will cover this aspect only briefly.
An Acoustic spectrometer may measure the attenuation of ultrasound, the propagation velocity of this sound, and/or the acoustic impedance, in any combination depending on the instrument design. The measured acoustic properties contain information about the particle size distribution, volume fraction, as well as structural and thermodynamic properties of the colloid. One can extract this information by applying the appropriate theory in combination with a certain set of a’priori known parameters. Hence, an Acoustic spectrometer is not simply a particle-sizing instrument. By applying sound we apply stress to the colloid and consequently the response can be interpreted in rheological terms, as will be shown below.
In addition to acoustics there is one more ultrasound-based technique, which is called Electroacoustics. The Electroacoustic phenomenon, first predicted by Debye in 1933, results from coupling between acoustic and electric fields. There are two ways to produce such an Electroacoustic phenomenon depending on which field is the driving force. When the driving force is the electric field and we observe an acoustic response we speak of ElectroSonic Amplitude (ESA). Alternatively, when the driving force is the acoustic wave we speak, instead, of the Colloid Vibration Potential (CVP) if we observe an open circuit potential, or a Colloid Vibration Current (CVI) if we observe a short circuit current. Such electroacoustic techniques yield information about the electrical properties of colloids. In principle, it can also be used for particle sizing.
Where can one apply
ultrasound?
The following list gives some idea of the existing applications for which the ultrasound based characterization technique is appropriate:
Aggregative
stability, Cement slurries, Ceramics, Chemical-Mechanical Polishing, Coal
slurries, Coatings, Cosmetic emulsions, Environmental protection, Flotation, Ore
enrichment, Food products, Latex, Emulsions and micro emulsions, Mixed
dispersions, Nanosized dispersions, Non-aqueous dispersions, Paints, Photo
Materials.
This list is not complete. A table in Chapter 8 summarizes all experimental works currently known to us.
What are the advantages of ultrasound over traditional characterization techniques?
There are so many advantages of ultrasound. The last section of this chapter is devoted to describing the relationship between ultrasound based and traditional colloidal characterization techniques.
Finally, we would like to stress that this book targets primarily scientists who consider colloids as their major object of interest. As such we emphasize those aspects of acoustics that are important for colloids and, thereby, neglect many others.
On the other hand, scientist working with ultrasound will already be familiar with many of the theoretical and experimental developments presented in this book. At the same time they will find several important new developments. In particular we would like to mention:
· a general approach to acoustics in colloids by combination of ultrasound absorption and ultrasound scattering;
· a general solution for eliminating multiple scattering;
· a theory of ultrasound absorption in concentrated systems;
· an electroacoustic theory for concentrates;
· experimental verification of theses theories for concentrated systems;
· multiple existing applications.
The roots of our current understanding of sound go back more than 300 years to the first theory for calculating sound speed suggested by Newton [6]. Newton’s work is still interesting for us today because it illustrates the importance of thermodynamic considerations in trying to adequately describe ultrasound phenomena. Newton assumed that sound propagates while maintaining