Ultrasonic Techniques for Fluids Characterization

1. Ultrasonic Techniques for Fluids Characterization Malcolm J. W. Povey May 18th to May 22nd 2009

2. 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.

3. 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.

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

5. You need the proper tools to understand Sound Digital oscilloscope Ultrasound transduction system Microphone

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

7. 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.

8. Sound pulse in air

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

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

11. Region of confusion Piston source

12. 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.

13. 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

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

15. Mathematical description

16. Decaying wave

17. Sound velocity measurement Pulse envelope

18. 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

19. Attenuation

20. 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

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

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

23. UVM

24. Waveforms and group velocity

25. Transducer construction

26. 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.

27. Reflection and transmission Transmission coefficient Reflection coefficient

28. Reverberation

29. Coupling and buffering Piezo-ceramic disk transducers

30. 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 .

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

32. Wavefronts and phase

33. Fraunhofer diffraction

34. 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.

35. Trigger errors

36. The wood equation Bulk modulus Adiabatic compressibility Density

37. Sound velocity in air/water mixtures

38. Urick equation Phase volume of jth phase

39. 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

40. Compressibility of water

41. Sound velocity in margarine

42. 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

43. Modified Urick Equation

44. Partial molar volume

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

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

47. 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

48. Attenuation in water

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

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