Presentation on theme: "School of Food Science and Nutrition FACULTY OF MATHEMATICS AND PHYSICAL SCIENCES Ultrasonic Techniques for Fluids Characterization Malcolm J. W. Povey."— Presentation transcript:
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
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.
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
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
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
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
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.
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
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
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 184.108.40.206 Temperature 220.127.116.11 Acoustical Delays 18.104.22.168 Impedance 22.214.171.124 The Control of Reverberation with Buffer Rods 126.96.36.199 Acoustical Bonds 188.8.131.52 Power Levels 184.108.40.206 Diffraction and Phase Cancellation 220.127.116.11 Timing Errors Due to Trigger Point Variation 18.104.22.168 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 22.214.171.124 Empirical and Semiempirical Methods 126.96.36.199 Concentrations 2.4.2 Determining Partial Volumes 188.8.131.52 The Method of Intercepts 2.4.3 Apparent Molar Quantities 184.108.40.206 Apparent Specific Volume 220.127.116.11 Apparent Compressibility 18.104.22.168 Concentration Increments 2.4.4 The Dilute Limit 22.214.171.124 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 126.96.36.199 Region I 188.8.131.52 Region III 184.108.40.206 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 220.127.116.11 Renormalization 18.104.22.168 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 22.214.171.124 Long Wavelength Limit 126.96.36.199 Low Attenuation 188.8.131.52 Plane Wave 184.108.40.206 Scattering Is Weak 220.127.116.11 Random Distribution of Particles 18.104.22.168 Adiabatic Approximation 22.214.171.124 Navier–Stokes Form for the Momentum Equation 126.96.36.199 Thermal Stresses Neglected 188.8.131.52 No Changes in Phase 184.108.40.206 Linearization of Equations 220.127.116.11 Temperature Variations 18.104.22.168 System Is Static 22.214.171.124 Particles Are Spherical 126.96.36.199 Infinite Time Irradiation 188.8.131.52 Pointlike Particles 184.108.40.206 No Overlap of Thermal and Shear Waves 220.127.116.11 No Interactions between Particles 18.104.22.168 Lack of Self-consistency 4.3.3 A Description of Weak Scattering 22.214.171.124 Wave Potentials 126.96.36.199 Modes in a Pure Liquid 188.8.131.52 Thermoelastic Scattering 184.108.40.206 Viscoinertial Scattering 220.127.116.11 Scattered Waves Combine within the Transducer 4.3.4 Plane Wave Incident on a Single-particle 18.104.22.168 Introduction 22.214.171.124 Spherical Harmonics 126.96.36.199 Boundary Conditions 4.3.5 Scattering by Many Particles 188.8.131.52 Introduction 184.108.40.206 Multiple Scattering Theories 4.3.6 Numerical Calculations Using Scattering Theory. 220.127.116.11 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 18.104.22.168 The Urick equation 22.214.171.124 The Multiple Scattering Result 126.96.36.199 The Modified Urick equation 188.8.131.52 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 184.108.40.206 Simultaneous Measurement of Velocity and Attenuation 220.127.116.11 Determinination of Particle Size from Velocity and Attenuation 18.104.22.168 Bandwidth and Signal-to-Noise Ratio 22.214.171.124 A Particle Sizing Apparatus Pulsed Method 126.96.36.199 Continuous-Wave Interferometer 188.8.131.52 Commercial Particle Sizing Apparatus 184.108.40.206 Electroacoustics 220.127.116.11 The Future Measurement Systems 5.2 Propagation in Viscoelastic Materials 5.2.1 Introduction 5.2.2 Measuring Aggregation in Viscoelastic Materials 18.104.22.168 Introduction 22.214.171.124 Detecting Aggregation with Ultrasound Profiling 126.96.36.199 Computer Modeling 188.8.131.52 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 184.108.40.206 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