# School of Food Science and Nutrition FACULTY OF MATHEMATICS AND PHYSICAL SCIENCES Ultrasonic Techniques for Fluids Characterization Malcolm J. W. Povey.

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School of Food Science and Nutrition FACULTY OF MATHEMATICS AND PHYSICAL SCIENCES Ultrasonic Techniques for Fluids Characterization Malcolm J. W. Povey May 18 th to May 22 nd 2009

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Welcome Welcome to the School of Food Science and Nutrition This course addresses the fundamental physical questions needed to understand a range of practical applications of ultrasound. Many of these applications have been developed here. There are no course pre-requisites, apart from an interest in ultrasound as a practical tool for the study of materials. Some of you may feel that I am teaching my grandmother to suck eggs. Please be patient, sucking eggs is not as easy as it looks. Not everyone knows how to do it.

The Beginnings 1826, the first determination of the speed of sound in water http://en.wikipedia.org/wiki/Jacques_Charles_Fran%C3%A7ois_Sturm

You need the proper tools to understand SoundSound Digital oscilloscope Microphone Ultrasound transduction system

Recommended books Keywords: Ultrasound, ultrasonics, ultras*, acoustic*, sound, propagation, scattering, diffraction, interference, Ultrasonic techniques for fluids characterization, Malcolm Povey, Academic Press, San Diego, 1997

Metaphors Use light as a metaphor Here the suns rays are scattered from the back of the cloud, creating mini- images of the sun. The cloud absorbs the light, with darkness at the front and light at the back. These are called anti- crepuscular rays.

Sound pulse in air

A shear pulse http://www.acoustics.salford.ac.uk/feschools/waves/wavetypes.htm

Surface waves Lamb wave in a plate Diving grebe (wikipedia)

Piston source Region of confusion

The density of phonon modes A phonon is a quantum of sound. Heat is composed of phonons, so all heat is made up of sound waves. But most of them are very high frequency.

Light and ultrasound UltrasoundVisible Light Transducers are phase sensitiveTransducers are phase insensitive Wavelength between m and mWavelength between 0.5 and 1 m Frequency between 0.1 and 10 13 Hz Frequency between 3 10 16 and 6 10 16 Hz Coherence between pulsesNo coherence between pulses Responds to elastic, thermophysical, and density properties Responds to dielectric and permeability properties Particle motion parallel to the direction of propagation; no polarization Field displacement perpendicular to direction of propagation; polarization is therefore possible Propagates through optically opaque materials Sample dilution is normally required

The adiabatic approximation Heat flow restricted to a small region of a half wave

Mathematical description

Decaying wave

Sound velocity measurement

Group and Phase velocity Group velocity Phase velocity is the speed of a given frequency component within the wave This is the velocity of the wave envelope k is called the wave number, λ is the wavelength e.g ocean waveswaves

Attenuation

Velocity and attenuation Attenuation coefficient This is called the wave VECTOR because it comprises two numbers, the first one is sometimes called the real number and the second the imaginary, because it is multiplied by the square root of minus one.

Velocity, phase and attenuation Particle displacement Instantaneous sound pressure Maximum sound pressure

Definitions of attenuation Neper, x = 1 meter. dB, x = 1 meter

UVM

Waveforms and group velocity

Transducer construction

Impedance Z In words: The impedance is the ratio of the pressure change resulting during the passage of the wave to the particle velocity. This approximates to the product of the density times the speed of sound.

Reflection and transmission Transmission coefficient Reflection coefficient

Reverberation

Coupling and buffering Piezo-ceramic disk transducers

Power levels and propagation parameters Table 2-1 Typical power levels and other propagation parameters for ultrasound propagation in water at 1 MHz and 30 C. at 1 MHz and 30 o C.

Point spread function courtesy of Nick Parker Axial intensity Near field Far field Focus

Wavefronts and phase

Fraunhofer diffraction

Incoherence The wave front can break up like this due to diffraction and scattering. The transducer will not detect the wave front because the phase variation across the transducer face sums to zero.

Trigger errors

The wood equation Bulk modulus Density Adiabatic compressibility

Sound velocity in air/water mixtures

Urick equation Phase volume of jth phase

Velocity of sound in water N. Bilaniuk and G. S. K. Wong (1993), Speed of sound in pure water as a function of temperature, J. Acoust. Soc. Am. 93(3) pp 1609-1612, as amended by N. Bilaniuk and G. S. K. Wong (1996), Erratum: Speed of sound in pure water as a function of temperature [J. Acoust. Soc. Am. 93, 1609-1612 (1993)], J. Acoust. Soc. Am. 99(5), p 3257. C-T Chen and F.J. Millero (1977), The use and misuse of pure water PVT properties for lake waters, Nature Vol 266, 21 April 1977, pp 707-708. V.A. Del Grosso and C.W. Mader (1972), Speed of sound in pure water, J. Acoust. Soc. Am. 52, pp 1442-1446. Marczak c = 1.402385 x 103 + 5.038813 T - 5.799136 x 10-2 T2 +3.287156 x 10-4 T3 - 1.398845 x 10-6 T4+2.787860 x 10-9 T5 Marczak (1997) combined three sets of experimental measurements, Del Grosso and Mader (1972), Kroebel and Mahrt (1976) and Fujii and Masui (1993) and produced a fifth order polynomial based on the 1990 International Temperature Scale. Range of validity: 0-95OC at atmospheric pressure W. Marczak (1997), Water as a standard in the measurements of speed of sound in liquids J. Acoust. Soc. Am. 102(5) pp 2776- 2779. The Marczak polynomial is recommended for calibration purposes

Compressibility of water

Sound velocity in margarine

Dependence of sound velocity on solids a) % solids b) v for 80% w/w oil c) v for 60% w/w oil d) v for 10% w/w oil

Modified Urick Equation

Partial molar volume

Acoustic scattering Basic science Molecules as particles LFPST Soft solids Viscosity measurement Bat sounds

The classical model for attenuation Attenuation - radial frequency - density – velocity - shear viscosity Bulk viscosity - ratio of specific heats - thermal conductivity

Underlying physics Conservation of momentum -Newtons second law, force is mass (m) times acceleration ( where v is velocity). Conservation of mass Together conservation of momentum and conservation of mass give rise to the Navier-Stokes equation for fluids. In soft solids an even more complicated relationship exists due to time dependent shear and compressibility. Conservation of energy Second law of thermodynamics

Attenuation in water

Data for water Shear viscosity Attenuation data Density of water Frequency Speed of sound Ratio of specific heats Thermal conductivity

Bubbles On Musical Air Bubbles and the Sounds of Running Water, Minnaert, M., Phil. Mag., 1933.

Surface active and microbubbles Key authors Andrea Prosperetti Gaunaurd and Uberall

1. Introduction 1.1 The Beginnings 1.2 Understanding Sound 1.3 Representations of Sound 1.4 Sounds Classical and Sounds Quantum 1.5 Comparisons between Light and Ultrasound 1.6 The Adiabatic Idealization 1.7 Common Sense is Unsound 1.8 Scope of This Work How to Use This Book

2. Water 2.1 Measurement of Sound Velocity 2.1.1 Introduction 2.1.2 Accuracy and Errors 2.1.2.1 Temperature 2.1.2.2 Acoustical Delays 2.1.2.3 Impedance 2.1.2.4 The Control of Reverberation with Buffer Rods 2.1.2.5 Acoustical Bonds 2.1.2.6 Power Levels 2.1.2.7 Diffraction and Phase Cancellation 2.1.2.8 Timing Errors Due to Trigger Point Variation 2.1.2.9 Measuring Group Velocity 2.1.3 Calibration 2.2 The Dependence of Velocity of Sound on Density and Compressibility 2.2.1 The Velocity of Sound in Mixtures and Suspensions 2.2.2 The Velocity of Sound in Air/Water Mixtures 2.2.3 The Importance of Removing Air from Samples 2.2.4 The Effects of Temperature on Propagation in Water 2.2.5 The Effects of Pressure on Propagation in Water 2.2.6 Sound Velocity in Equidensity Dispersions 2.3 The Relationship between Velocity and Attenuation Conditions of High Attenuation 2.4 The Compressibility of Solute Molecules 2.4.1 Introduction 2.4.1.1 Empirical and Semiempirical Methods 2.4.1.2 Concentrations 2.4.2 Determining Partial Volumes 2.4.2.1 The Method of Intercepts 2.4.3 Apparent Molar Quantities 2.4.3.1 Apparent Specific Volume 2.4.3.2 Apparent Compressibility 2.4.3.3 Concentration Increments 2.4.4 The Dilute Limit 2.4.4.1 Partial Specific Volume and Partial Specific Adiabatic Compressibility 2.4.5 Sound Velocity and Concentration The Urick equation 2.4.6 Determining the Compressibility of Solute Molecules a Summary 2.4.7 Experimental Data on Compressibility and Its Interpretation Protein

3. MULTIPHASE MEDIA 3.1 Apparatus 3.2 Determining Composition in the Absence of Phase Changes 3.2.1 Alcohol 3.2.2 Sugar 3.2.3 Concentration of a Dispersed Phase in a Colloidal Phase 3.2.4 Analysis of Edible Oils and Fats 3.2.5 Cell Suspensions 3.2.6 Temperature Scanning 3.3 Following Phase Transitions 3.3.1 General Comments 3.3.2 Attenuation Changes 3.3.3 Crystallizing Solids 3.3.4 Crystallization in Colloidal Systems. 3.4 Determination of Solid Fat Content 3.4.1 Introduction 3.4.2 General Method 3.4.2.1 Region I 3.4.2.2 Region III 3.4.2.3 Region II 3.4.3 Margarine 3.4.4 Chocolate 3.4.5 Accuracy 3.4.6 Anomalies Close to the Melting Point 3.4.7 Comparison with Dilatometry and pulsed Nuclear Magnetic Resonance 3.4.8 Solid Content and Particle Size 3.5 Crystal Nucleation 3.5.1 Crystal Nucleation Rates 3.5.2 Ice 3.6 The Solution-Emulsion Transition and Emulsion Inversion 3.6.1 Emulsion Inversion 3.7 Determination of Emulsion Stability by Ultrasound Profiling 3.7.1 Introduction 3.7.2 History 3.7.3 The Leeds profiler 3.7.4 Interpretation of Ultrasound Velocity Profiles 3.7.4.1 Renormalization 3.7.4.2 Limits of Applicability of Renormalization Method 3.7.5 Examples of Profiling Summary

4. SCATTERING OF SOUND 4.1 Theories of Sound 4.2 A Comparison of Electromagnetic and Acoustic Propagation 4.3 Scattering theory 4.3.1 Why scattering theory? 4.3.2 What Is Scattering? Assumptions of Scattering Theory 4.3.2.1 Long Wavelength Limit 4.3.2.2 Low Attenuation 4.3.2.3 Plane Wave 4.3.2.4 Scattering Is Weak 4.3.2.5 Random Distribution of Particles 4.3.2.6 Adiabatic Approximation 4.3.2.7 Navier–Stokes Form for the Momentum Equation 4.3.2.8 Thermal Stresses Neglected 4.3.2.9 No Changes in Phase 4.3.2.10 Linearization of Equations 4.3.2.11 Temperature Variations 4.3.2.12 System Is Static 4.3.2.13 Particles Are Spherical 4.3.2.14 Infinite Time Irradiation 4.3.2.15 Pointlike Particles 4.3.2.16 No Overlap of Thermal and Shear Waves 4.3.2.17 No Interactions between Particles 4.3.2.18 Lack of Self-consistency 4.3.3 A Description of Weak Scattering 4.3.3.1 Wave Potentials 4.3.3.2 Modes in a Pure Liquid 4.3.3.3 Thermoelastic Scattering 4.3.3.4 Viscoinertial Scattering 4.3.3.5 Scattered Waves Combine within the Transducer 4.3.4 Plane Wave Incident on a Single-particle 4.3.4.1 Introduction 4.3.4.2 Spherical Harmonics 4.3.4.3 Boundary Conditions 4.3.5 Scattering by Many Particles 4.3.5.1 Introduction 4.3.5.2 Multiple Scattering Theories 4.3.6 Numerical Calculations Using Scattering Theory. 4.3.6.1 Particle Size Distribution and Change in Phase 4.3.7 The Results of Scattering Theory 4.3.8 Simplified Scattering Coefficients 4.3.9 Working Equations 4.3.9.1 The Urick equation 4.3.9.2 The Multiple Scattering Result 4.3.9.3 The Modified Urick equation 4.3.9.4 Experimental Determination of the Scattering Coefficients 4.3.10 Multiple Dispersed Phases 4.3.11 MathCad Calculation Results 4.3.12 Experimental Validation of Acoustic Scattering Theory Scattering from Bubbles

5. ADVANCED TECHNIQUES 5.1 Particle Sizing. 5.1.1 Introduction 5.1.2 Review 5.1.3 Theoretical Limitations of Acoustic Particle Sizing 5.1.4 Relaxation Effects 5.1.5 Ultrasonic Methods of Particle Sizing 5.1.5.1 Simultaneous Measurement of Velocity and Attenuation 5.1.5.2 Determinination of Particle Size from Velocity and Attenuation 5.1.5.3 Bandwidth and Signal-to-Noise Ratio 5.1.5.4 A Particle Sizing Apparatus Pulsed Method 5.1.5.5 Continuous-Wave Interferometer 5.1.5.6 Commercial Particle Sizing Apparatus 5.1.5.7 Electroacoustics 5.1.5.8 The Future Measurement Systems 5.2 Propagation in Viscoelastic Materials 5.2.1 Introduction 5.2.2 Measuring Aggregation in Viscoelastic Materials 5.2.2.1 Introduction 5.2.2.2 Detecting Aggregation with Ultrasound Profiling 5.2.2.3 Computer Modeling 5.2.2.4 Aggregation of Casein 5.2.3 Frequency-Dependent Ultrasound Profiling 5.2.4 Particle Size Effects in Ultrasound Profiling 5.3 Bubbles and Foams 5.4 Automation and Computer Tools 5.4.1 The Computer as Controller 5.4.2 Windows 5.4.3 Prototyping 5.4.4 RS232C 5.4.5 IEEE Bus 5.4.6 Instrument Programming 5.4.7 Oscilloscope 5.4.7.1 Fourier Analysis 5.4.8 Timer–Counter 5.4.9 The UVM 5.4.10 Transducer Excitation 5.4.11 Cabling 5.4.12 Calibration 5.4.13 Sample Changer 5.4.14 Temperature Control 5.4.15 Data Storage and Analysis Conclusion APPENDIX, GLOSSARY, AND BIBLIOGRAPHY Appendix A Basic Theory Appendix B MathCad Solutions of the Explicit Scattering Expressions Glossary Bibliography

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