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Ultrasonic Techniques for Fluids Characterization. Malcolm J. W. Povey May 18 th to May 22 nd 2009. Reproduction. You may freely use this presentation. You may reproduce the material within on condition that you reference the original source(s).
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Ultrasonic Techniques for Fluids Characterization Malcolm J. W. Povey May 18th to May 22nd 2009
Reproduction • You may freely use this presentation. • You may reproduce the material within on condition that you reference the original source(s). • The author asserts his moral and paternity rights regarding the work.
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 Sound Digital oscilloscope Ultrasound transduction system Microphone
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.
A shear pulse http://www.acoustics.salford.ac.uk/feschools/waves/wavetypes.htm
Surface waves Lamb wave in a plate Diving grebe (wikipedia)
Region of confusion Piston source
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.
Ultrasound Visible Light Transducers are phase sensitive Transducers are phase insensitive Wavelength between m and m Wavelength between 0.5 and 1 m Frequency between 0.1 and 1013 Hz Frequency between 3 1016 and 6 1016 Hz Coherence between pulses No 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 Light and ultrasound
Heat flow restricted to a small region of a half wave The adiabatic approximation
Sound velocity measurement Pulse envelope
Group and Phase velocity Group velocity Pulse envelope k is called the wave number, λ is the wavelength Phase velocity is the speed of a given frequency component within the wave This is the velocity of the wave envelope e.g ocean waves
Velocity and attenuation 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. Attenuation coefficient
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
Coupling and buffering Piezo-ceramic disk transducers
Table 2-1 Typical power levels and other propagation parameters for ultrasound propagation in water at 1 MHz and 30 C . Power levels and propagation parameters at 1 MHz and 30 oC .
Axial intensity Near field Far field Focus Point spread function courtesy of Nick Parker
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.
The wood equation Bulk modulus Adiabatic compressibility Density
Urick equation Phase volume of jth phase
Velocity of sound in water 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. 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. The Marczak polynomial is recommended for calibration purposes
Dependence of sound velocity on solids d) v for 10% w/w oil c) v for 60% w/w oil b) v for 80% w/w oil a) % solids
Acoustic scattering • Basic science • Molecules as particles • LFPST • Soft solids • Viscosity measurement • Bat sounds
The ‘classical’ model for attenuation Bulk viscosity - ratio of specific heats - thermal conductivity Attenuation - radial frequency - density – velocity - shear viscosity
Underlying physics • Conservation of momentum -Newton’s 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.