Transcript Ultrasonic Techniques for Fluids Characterization

School of Food Science and Nutrition
FACULTY OF MATHEMATICS AND PHYSICAL SCIENCES
Ultrasonic Techniques for Fluids
Characterization
Malcolm J. W. Povey
December 9th to December 11th 2014
Reproduction
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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.
What’s special about soft solids?
Very many foods are ‘soft’ solids
Soft solids have the properties of BOTH fluids and solids
Soft solids show time dependent elastic properties on human time
scales.
The elastic properties of soft solids are time dependent.
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 miniimages of the sun. The
cloud absorbs the light, with
darkness at the front and
light at the back.
These are called anticrepuscular rays.
Sound pulse in air
Expanded
Compressed
Undisturbed
Pressure
Restored
X
Amplitude and
direction of
particle
displacement
Pressure variation
Shear strain
A shear pulse
Undisturbed
Restored
X
http://www.acoustics.salford.ac.uk/feschools/waves/wavetypes.htm
Surface waves
Diving grebe (wikipedia)
Lamb wave in a plate
Piston source
Region of confusion
The density of phonon modes
5
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.
Density of phonon modes
4
3
2
1
0
0
0.2
0.4
Frequency / 10
0.6
13
Hz
0.8
1
Light and ultrasound
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
The adiabatic approximation
Expanded
Compressed
Undisturbed
Pressure
Restored
X
Heat flow restricted to a
small region of a half wave
Amplitude and
direction of
particle
displacement
Mathematical description
Pressure
Period T=1/f
Time
v  f
Pressure
Wavelength 
Distance
Decaying wave


x
Sound velocity measurement
Source
Transducer
32.5 mm
t=0s
Receiver
transducer or
reflector
t=50 s
Velocity in sample equals distance / time,
32.5 mm / 50 s = 1500 m s-1 for single transit and
75 mm / 100 s = 1500 m s-1 for a single reflection.
Group and Phase velocity
Group velocity
d
v
dk
ce
sducer
This is the
velocity of
the wave
envelopet=0s
k is called the wave number,
λ is the wavelength
k
32.5 mm


Receiver
transducer or Phase velocity is
reflector
the speed of a
vp 
s
e.g oceant=50
waves
2
k
given frequency
component
within the wave
Attenuation


exp   x 
x
Velocity and attenuation
k  k   ik 
k   

k 
vp
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.
1
Attenuation coefficient
Velocity, phase and attenuation
Particle displacement
 

   0 expikx   0 expik x  x    0 exp i  x 
 vp

p  p0 expi(t  kx
Instantaneous sound pressure
Maximum sound pressure
p  p0 expi(t  k ' x)exp x
Definitions of attenuation
p ~
2
1 
ln  
x 0
 
1
10 log  
x

 0
Neper, x = 1 meter.
dB, x = 1 meter
UVM
Pulser
Timer start
Timer stop
Thermostated
water bath
Magnetic stirrer
Temperature
Probe
Four-wire Resistive
Temperature Device (RTD) mV output to computer
Time-offlight
reading to
computer
Computer
Accepts time of flight and RTD mV and
produces velocity of sound and temperature
readings.
Waveforms and group velocity
140 s repetition period
Trigger Pulse
Trigger Pulse
Transducer(1)
first echo
Transducer(2)
second echo
30 s ultrasound propagation
delay
80 s second echo propagation
delay
Transducer construction
Silver loaded
epoxy
electrode
Electrical
connection
welded to
transducer
electrode
Tungsten
loaded epoxy
backing plate
Piezo-ceramic
transducer
disk
Wear plate
Silver loaded
epoxy ground
plane
Impedance Z
p

Z
   v

k
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
Incident (I)
Transmitted (t)
Reflected (r)
t
2Z 1
 
i Z1  Z 2
Reflection coefficient
r Z1  Z 2
 
i Z1  Z 2
Material Impedance Z1
Material Impedance Z2
Reverberation
Reverberations
2t
Incident
acoustic field
+2t
+
+4t
+
+6t +
+
Glass slide suspended
in water
Coupling and buffering
Sample
Buffer rod
Buffer rod
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 .
f
(MHz)
1
1
1
T
0
(oK)
p
0
(MPa)
303 0.1
303 0.1
303 0.1
I
p0
s


’
Z
T
’/v
(kW m-2)
(MPa)
x 10-6
(nm)
(mm s-1)
(km s-2)
(MPa s m-1)
(mK)
x 10-6
0.1 0.017 7.6 1.8
10
0.17 76 18
1000 1.7 760 180
11.5
115
1150
72
720
7200
1.47
1.47
1.47
.38
3.8
38
7.6
76
760
Here f is frequency (in MHz), T0, absolute temperature (K); P0, absolute pressure (MPa); I, intensity
(kW m-2); p, pressure change from P owing to the passage of ultrasound (MPa); s, the condensation (
0
=[0-]/0); 0, the static density (kg m-3); , the instantaneous density (kg m-3); , the particle
displacement (nm); ‘, the particle velocity (mm s-1); ‘’, the particle acceleration (km s-2); T, the
temperature change owing to the passage of the ultrasound (K); Z ( = P /‘ = vl), the specific acoustical
impedance (Pa s m-1); and v the velocity of a compression ultrasound wave. From Povey and McClements
(1988
Axial intensity
1
Acoustic intensity
Near field
Far field
Focus
a2/3
a2/
a2/2
0
0
1
X/a
Point spread function courtesy of Nick Parker
2
Wavefronts and phase
Pressure
Advancing
wavefront
Lines of constant
phase
Distance
Fraunhofer diffraction
Pressure
Advancing
wavefront
Lines of constant
phase
Distance
Incoherence
The wave front can
break up like this due to
diffraction and
scattering.
Pressure
The transducer will not
detect the wave front
because the phase
variation across the
transducer face sums to
zero.
Distance
Trigger errors
The wood equation
Bulk modulus
v
Density
B


1

Adiabatic compressibility
Sound velocity in air/water
mixtures
Urick equation
Phase volume of jth phase
v
1

,
   j j ,    j  j
j
   2  (1   ) 1 ,
j
   2  (1   )  1
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 27762779.
The Marczak polynomial is
recommended for calibration purposes
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.
Compressibility of water
v  1402.39  5.03711T  0.0580852T 2  3.33420  10 4 T 3
 1.47800  10 6 T 4  314643
.
 10 9 T 5  1.6  10 6 ( p 0  10 5 )
Sound velocity in margarine
Dependence of sound velocity on
solids
i
1
 2
2
v
i 1 vi
n
d) v for 10% w/w oil
c) v for 60% w/w oil
b) v for 80% w/w oil
a) % solids
Modified Urick Equation
1
1
2
2  2 1     
v
v1
 a 2   a 1
2  1 

 

1 
  a 1
1 
 2

 C
1C p1 
2
p2

R
1





C
1
p
1


2C p 2 2
  (  1)
R
1C p1
  a 2   a1
  2  1  2 2  1 

 
  
31 2
  a1
  1 
2
Partial molar volume
Acoustic scattering
Basic science
Viscosity measurement
Molecules as particles
Bat sounds
LFPST
Soft solids
The ‘classical’ model for
attenuation
Bulk viscosity - ratio of specific heats - thermal conductivity
 2v
 cl 
3
2 0v
 4  B   1 

 

C Pv 
 3 v
Attenuation - radial frequency - density – velocity - shear viscosity
Underlying physics
Conservation of momentum -Newton’s second law, force is mass (m)
times acceleration (dv dt where v is velocity).
d
Conservation of mass
F
dt
m.v 
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
Total attenuation
Total attenuation /dB m-1
10000
Experiment
y = 0.200x2 + 1.361x - 17.93
R² = 1
1000
Classical
continuum
theory
y = 0.218x2 + 1E-12x - 4E-11
R² = 1
100
10
100
f /MHz
Data for water
Shear viscosity
Attenuation data
[°C]
10
20
25
30
40
50
60
70
80
90
100
[Pa·s]
0.00130
0.00100
0.00089
0.00080
0.00065
0.00054
0.00046
0.00040
0.00035
0.00031
0.00028
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
2.4 The Compressibility of Solute Molecules
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2.1.1 Introduction
2.1.2 Accuracy and Errors
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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
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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
2.4.1 Introduction
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2.4.1.1 Empirical and Semiempirical Methods
2.4.1.2 Concentrations
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2.4.2 Determining Partial Volumes
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2.4.3 Apparent Molar Quantities
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2.4.2.1 The Method of Intercepts
2.4.3.1 Apparent Specific Volume
2.4.3.2 Apparent Compressibility
2.4.3.3 Concentration Increments
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2.4.4 The Dilute Limit
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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
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Protein
2.4.4.1 Partial Specific Volume and Partial Specific Adiabatic Compressibility
3. MULTIPHASE MEDIA
3.1 Apparatus
3.2 Determining Composition in the Absence of Phase Changes
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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
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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
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3.4.1 Introduction
3.4.2 General Method
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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
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3.5.1 Crystal Nucleation Rates
3.5.2 Ice
3.6 The Solution-Emulsion Transition and Emulsion Inversion
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3.6.1 Emulsion Inversion
3.7 Determination of Emulsion Stability by Ultrasound Profiling
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3.7.1 Introduction
3.7.2 History
3.7.3 The Leeds profiler
3.7.4 Interpretation of Ultrasound Velocity Profiles
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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
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4.3.1 Why scattering theory?
4.3.2 What Is Scattering? Assumptions of Scattering Theory
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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–Stoke’s 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
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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
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4.3.4.1 Introduction
4.3.4.2 Spherical Harmonics
4.3.4.3 Boundary Conditions
4.3.5 Scattering by Many Particles
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4.3.5.1 Introduction
4.3.5.2 Multiple Scattering Theories
4.3.6 Numerical Calculations Using Scattering Theory.
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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
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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.
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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
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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
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5.2.1 Introduction
5.2.2 Measuring Aggregation in Viscoelastic Materials
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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
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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
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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
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5.4.7.1 Fourier Analysis
Conclusion
APPENDIX, GLOSSARY, AND BIBLIOGRAPHY
Appendix A Basic Theory
Appendix B MathCad Solutions of the Explicit Scattering
Expressions
Glossary
Bibliography