7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Experimental study of using ultrasonic methods to determine the solid fat content and
particle size during phase transitions
Liu jianhual, Wang jinl, Xue minghual, Gu jinhong2
1. University of shanghai for science and technology, shanghai, china, 200093; 2. Fishery machinery and instrument research
institute of Chinese academy of fishery science, shanghai, china, 200092
Email: lwnlwnliu@163.com
Keywords: ultrasonic methods, the SFC, fat, particle size
Abstract
The SFC (solid fat content) is not a neglectable factor and it affects fat plasticity, making fat play an important role in the food
function. General measurement of the SFC uses expansion method. However, the method is time consuming and is not capable
of measuring the SFC when it tends to be over 50%. Another method is magnetic resonance, which is too expensive. This
paper introduces a method which uses ultrasonic to determine the SFC of the fat. The particle size and SFC in two kinds of fats
can be measured by ultrasonic attenuation spectra method and ultrasonic multiple echo reflection method. Based on theoretical
analysis and numerical results, measurements of ultrasonic spectrum over a frequency range 36 MHz were carried out in fats
during the time of phase transitions. Combined with the inverse algorithm, particle sizes were determined from experimental
data. The SFC were obtained by combining acoustic impendence with ultrasonic multiple echo reflection method. The result of
experiment shows that by measuring the ultrasonic echo velocity through a vessel or a pipe with fat in it, the value of the SFC
of double phase coexisting fat can be calculated, as there is a time difference between the first and second echo, where the
first echo is reflected from the wall directly and the second echo has to transmits through the fat sample first. This
experimental model is called the ultrasonic multiple echo reflection model. Furthermore, the ultrasonic method has also many
advantages, such as that it is noninvasive, that it can be used in realtime test and be used in other industrial areas.
Introduction
In recent years, with the dramatic development in food
engineering concerned fields, phase transitions of adipose is
very common in different industrial areas and production
processes. It is often necessary to know the solid fat content
and particle size of the dispersed phase. For example, solid
fat content and particle size are important indicators of food
manufacture field. The bulk physiochemical properties and
sensory attributes of many fatty foods are determined by the
fraction of the fat phase that is solidified at a particular
temperature. It is therefore important to develop analytical
techniques that can measure the variation in solid fat content
and particle size (Singh 2003).
For solid fat content and particle size measurements, several
techniques have been developed. General measurement of
the SFC uses expansion method. However, the method is
time consuming and is not capable of measuring the SFC
when it tends to be over 50%. Another method is magnetic
resonance, which is known to give a good estimate of water
content. However, magnetic resonance is an expansive and
slow technology (Shannon 2004). Optical scattering is
currently the most widely used technique for particle sizing
of the fat. However, since the principle usually requires
transmission of light and assumes single particle scattering,
the optical method is limited to making measurement on
dilute fat. The ultrasound wave interacts with particles in a
similar way to light but has the advantage that it can travel
through concentrated particulate twophase flow. Therefore
ultrasonic method is more suitable to characterize the dense
slurries and hence it is hopeful for the online/inline
applications (Su 2009).
The characterization of twophase flow by ultrasound
requires a formal theoretical basis, a reasonable
experimental data, a stable and rapid inversion algorithms.
The formal theoretical basis relates the properties of the
mixture, particularly the dispersed phase particle size
distribution, to the complex wavenumber governing
propagation. These propagation problems can be identified
two approaches: scattering and coupled phase models
(Challis 2005). A significant scattering theoretical model on
acoustical wave propagation in particulate mixtures can be
traced back to the Epstein and Carhart (Epstein 1953).
Combined with the work of Allegra and Hawlay (Allegra
1972), the classical ECAH model was established. This
model combined viscous and thermal absorption into
scattering, a fully thinking about sound propagation and
interaction with particles was made. Riebel (Riebel 1989)
focused on the ultrasonic scattering by particles in short
wave limit. He has developed a scattering model by
analogism with LambertBeer model of light extinction.
McClements (McClements 1991) provided indepth
discussions about droplets size measurement theories in
emulsions. He contributed an explicit solution of ECAH in
long wave limit. Coupled phase models, as a substitute of
scattering models for small hard core particles were studied
by Harker (Harker 1988) and Dukhin (Dukhin 2002).
In this paper, the SFC and particle size in fat can be
measured by ultrasonic attenuation spectrum method and
ultrasonic multiple echo reflection method. Based on
theoretical analysis and numerical results, measurements of
ultrasonic spectrum over a frequency range 36 MHz during
phase transitions were carried out during phase transitions.
Combined with the inverse algorithm, particle size
distribution were determined from experimental data. The
SFC were obtained by combining acoustic impendence with
ultrasonic multiple echo reflection method. The
experimental results show that the ultrasonic measurements
is suitable for characterizing the fat, for the advantage of the
compact, noncalibrating, noninvasive and realtime
measurements.
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
Theoretical models and numerical computations
Ultrasound attenuation spectrum and inverse
technique
The coupledphase theory is commonly used to model the
acoustic propagation in dense particulate twophase flow.
This theory has generally been addressed from the view of
hydrodynamic point, which consists of the basic formulation
of the wave problem involving the elasticity of each phase,
conservation of mass, and momentum. The aim of this
model is to establish dispersion relationship which relates
the complex wavenumber k for compression waves in the
particulate mixture to the physical properties of the
components of the twophase flow.
Harker and Temple investigated the acoustic propagation in
suspension and they extended the model to include the
irreversible heat transfer between the phases. They used
Vand's view for viscosity and obtained an expression for the
complex wave number:
k2 = o2 x[fP+ifi(1 )]
P, [Pp(1 + OS)+ pS(1 0)] (1)
px (l )2 + [S + (1 )]
1 1+ 20 9 6 9 6 52
2S=4 ++ (2)
2 10 4 r 4 r r2
The subscript p refers to the particle, 1 refers to the liquid
and ) is the volume fraction of the particles in the twophase
flow. The imaginary part of k gives the attenuation and the
ratio of o to the real part of k gives the velocity. S is the
function of the density, viscosity of continuous phase and
the particle size, volume fraction of particulate phase. For
using the conception of "effective volumeaveraging",
Eq.(1) is selfconsistent.
The acoustic attenuation is determined by factors such as
scattering, absorption, thermal loss, viscous loss and so on.
Based on the assumption of the particulate phase being a
continuum, there is no scattering description in the
coupledphase model. So it is necessary to combine the
coupledphase model with the scattering model for the
purpose of available attenuation prediction. The attenuation
coefficient is given by (Riebel 1995):
30 2(2+)K
a, 2iP (2n+l1) An 2 (3)
2c2r n=o
Here C is the dimensionless particle diameter, given by
 = or / c, o is the frequency, r is the particle radius, c is
the acoustic velocity in the fat. AN is the scattering
coefficient of a single particle.
Numerical simulations have been carried out for fat whose
properties are given in Table I. The ultrasonic attenuation
spectra versus the frequencies up to 12MHz are calculated
for solid fat content increasing from 10% to 40%.
Tab.I Physical properties of solid and liquid fat
p c Cp r G
Kg/m m/s J/kg K Pa S Pa
3
Solid fat 950 1550 729 / 3e+010
Liquid fat 900 1400 1923 6.3e2
to
60 10%v/v
40
E 20
Q o
0 2 4 6 8 10
8 600
500 um
400
30%v/v
300
zuu
100 1200
0 01
0 2 4 6 8 10 12
flMHz
400
300 30um
20%v/v
200
0 2 4 6 8 10 12
40%v/v
,"''''" _____
2 4 6 8 10 12
Figure 1: Ultrasonic attenuation spectra of fat
Usually, a root mean square expression describing error of
spectrum simulated and spectrum measured could be written
as:
.N 2
ERME = s ( (f, mR, P) a ,,)2 (4)
Where N is number of selected frequencies. An inverse
process, whose critical problem is minimizing errors
function to get particle size distribution, is one of the main
interests of many researchers. Two types of such algorithms
have been developed: dependent and independent. The
dependent model algorithm assumes that the particle system
to be measured conforms to a given size distribution, e.g.
lognormal or RosinRammler function, which is usually
characterized by two parameters to be determined by the
dependent model algorithm. And the independent model
algorithm does not assume any particle size distribution in
advance, but solves directly the Fredholm integral equations
of the first kind (Su 2002).
Ultrasonic multiple echo reflection method
The solid fat content is determined by the ultrasonic
multiple echo reflection method. A schematic diagram of the
experimental apparatus is shown in Figure 2. A longitudinal
transducer is mounted upon a thin plate of stainless steel
plate and the opposite face is contact with the fat. An
ultrasonic pulser sends a signal to the transducer. The
resulting ultrasound makes multiple reflections within the
steel plate by reflecting each time the signal strikes the
steelfat interface or the steeltransducer interface. The
multiple echoes are recorded by the same transducer and
then are also acquired by highspeed data acquisition card.
Figure 3 shows the multiple echoes observed in steel plate.
Ultrasonic S
pulseecho Trasd t
transmitter/ ucer Sample
receiver e
L
Figure 2: Schematic diagram of experimental apparatus
When the ultrasound strikes the steelfat interface, some of
0
the ultrasound is reflected and some is transmitted into the
fat. The reflection coefficient is given by:
R = + (5)
Z +Z
Inverting Eq.5 gives the acoustic impedance of the liquid:
Zf = Z R (6)
Where Zf is the acoustic impedance of the fat and Zs, that of
steel.
0 2 4 6 8 10
tx 106/s
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
The left of Eq.(7) is just the slope. Water is used for
calibration of the slopes. Then the Eq.(7) is transferred into
the following equation:
R/R, = exp(K, K) (10)
Where Rf and R, are the reflection coefficients, Kf and K,
are the slope that refers to the slope on a logarithmic plot
shown in Fig.4. Since the reflection coefficient for water
can be calculated, the reflection coefficient for the fat can be
determined. Then the acoustic impedance of the fat is
obtained. The acoustic impedance (Z) is defined as the
product of the density (p) of the liquid and the velocity of
the sound (C) in the liquid. The density can be determined
by coupling the acoustic impedance measurement with an
acoustic velocity measurement. If the system is the
particulate twophase flow such as the solid fat, the content
is determined as follows:
.m =[P (Pm
12 14
Figure 3: Multiple echoes observed in steel plate
Each echo, such as those shown in Fig.3, is analyzed by
taking the fast Fourier transform of the signal to determine
the amplitude at a specified frequency. Fig.4 shows that a
straight line results when the logarithm of the FFT
amplitude is plotted versus the echo number. A leastsquares
fit is used to obtained the slope of the line. For different
liquids, the slopes are different because the reflection
coefficients at the steelfat interface are different (Margaret
2002).
40
38 1 Linear FitCurve
36
3 34.
t 32
LL
Z 30
J
28
26
1 2 3 4 5 6
Echo Number
Figure 4: LN FFT amplitude versus echo number
In order to obtain the relationship between the slope and the
reflection coefficient, the voltage of the Nth and N1h
are given by:
A,, =exp(2aDn,) Ao R"' (7)
A = exp(2aDn ) Ao R (8)
Where Ao is the original amplitude, a is the ultrasonic
attenuation coefficient of steel, D is the thickness of the
steel, R is the reflection coefficient at the steelfat interface.
Taking the logarithm of Eq.(7) and Eq.(8) and subtracting,
the result is given by:
Pi)]/[Pm (Pp Pl)] (11)
1~111"
)=InR 2aD (9)
Where < is the content, p mis the fat density and the p and
P 1, that of solid and liquid.
Experimental Facility
Two kinds of animal adipose: pig and chicken fats were
prepared in this paper. These fats were placed in ultrasonic
measurement cell and cooled from 60 C to 5C with two
different cooling methods: natural cooling and compulsory
cooling. That means air and icewater mixtures are adopted.
The high temperature of fats was controlled by constant
temperature water bath.
An ultrasonic measurement setup showed in Fig.5 was
developed to obtain testing data of frequency dependent
ultrasonic attenuation. Ultrasonic waves, generated by
broadband ultrasonic transducer(V317SU) worked with an
ultrasonic pulser/receiver (PR5800,Parametric, Inc),
transmit through samples in cell, and reflected, in which
echoes signals could acquired by highspeed data
acquisition card, and recording in a personal computer. The
ultrasonic transducer could be designed as a style of probe,
being convenient for online measurement in fat.
transducer C11 control
Ultrasonic Data ]
pulser/receivr acquisition Computer
pulser/receiver cn
Figure 5: Schematic diagram of ultrasonic measurement
An original signal and corresponding spectrum by FFT are
showed in Fig.6. Signal was generated and received by a
PR5800 ultrasonic pulseecho transmitter/receiver
(Parametric, Inc), worked with a broadband transducer of
center frequency 5MHz. As showed in Fig.6, spectrum at
37MHz could be acceptable considering a high
signalnoise ration (SNR).
(In A,, I AJ O f
I 1/ 2
A. Original signal
A O r l 15 n
A. Original signal
02 
Frequency(MHz)
B. Magnitude spectrum
Figure 6: Original signal and spectrum by FFT
The ultrasonic velocity is measured based on the distance
between the transducer and the reflector plate and the
timeofflight of the ultrasonic pulse.
The attenuation coefficient is calculated by comparing the
reduction in amplitude of different positions. To obtain
accurate attenuation measurements, it is necessary to
measure the amplitude by using Fast Fourier Transform
(FFT) analysis of broadband echoes.
Results and Discussion
The principle of particle size measurement is based on the
properties of attenuation spectrum generated by different
particle sizes. With the optimization analysis algorithm, the
particle size measurement distribution of fats can be
obtained from the experimental attenuation spectrum. In this
work, the optimum regularization technique is employed. As
an example, the attenuation spectra measured from 3 MHz
to 6 MHz in two kinds of fat with different times adopting
natural cooling were shown in Fig.7 and Fig8. The results of
particle size at a certain time were shown in Fig.9 and
Fig. 10.
350
300
E 250
Z
200
0
S150
S100
S60s
0 120s
 180s
2403
S300
360s
S420 '
A 540
o 
0~~~~~~
35 40 45 50 55 60 65 70
Frequency [MHz]
Figure 7: Measured attenuation spectra from 3 MHz to 6
MHz in pig fat
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
350
60s
  180s
300   300s
..A 420s
 a 540s
E 250  60cs
S  780
Z 0 900s
200 1020s
.o'
0
3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0
Frequency [MHz]
Figure 8: Measured attenuation spectra from 3 MHz to 6
MHz in chicken fat
0 5 10 15 20 25
Diameter [im]
Figure 9: Measured PSD with natural cooling in pig fat
40
D
S30
N
O3
20
a
t:
Natural cooling
0 5 10 15 20 25 30 35
Diameter [inm]
Figure 10: Measured PSD with natural cooling in chicken
fat
The range of the measured particle size with ultrasonic
method was from 1 l m to 15 u m in the pig fat and the
measured mean diameter was 6.8 v m. In the chicken fat, the
range of the measured particle size was from 9 u m to 42 v
m and the mean diameter was 16.6 v m. The mean
diameters of two fats at different times with two cooling
methods were shown in Fig. 11 and Fig. 12. Considering that
the longer time of phase transitions of natural cooling
method, it was reasonable that the mean diameter obtained
with natural cooling was a little smaller.
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
30
* Compulsory cooling
25 .0 Natural cooling
20
1 5
0, .*0,. ..... ""0 ........ O
S0 10
0 0 O 0. 0,O O0 0
O O0
40
30
E 20
5
600 800 1000 1200 0 500 1000 1500
Time [s] Time [s]
d mean diameters in pig fat with Figure 12: Measured mean diameters in chicken fat with
different time different time
Data measured for the eight compounds, ranging in time
from 0 second to 1080 second, and data measured with
independent measurements made by pig fat with natural
cooling during phase transitions were shown in Table II.
The measured SFC of two kings of fats was shown in figure
12 and figure 13. With the phase transition time increasing,
the solid fat content increased accordingly. It is reasonable
that the natural cooling spent more time than the
compulsory cooling.
Tab.II The measured pig fat SFC with natural cooling during phase transitions
Sample slope Reflection coefficient Impedance Velocity Density SFC
(pig fat) (106.kg.m2s1) (m/s) (kg/m3) ()
water 0.2261 0.935 1.499 1497 998
OS 0.2166 0.9438 1.242 1380 0.90 0
60S 0.2172 0.9432 1.2552 1391 0.9023 5
180S 0.2188 0.9418 1.2886 1413 0.9120 25
360S 0.2209 0.9398 1.3332 1437 0.9278 57
540S 0.2230 0.9378 1.3782 1475 0.9344 70
720S 0.2240 0.9369 1.4001 1491 0.9390 79
900S 0.2251 0.9359 1.4232 1504 0.9463 93
1080 0.2260 0.9350 1.444 1520 0.9510 100
Natural cooling
1 0 Compulsory cooling 000000000
0
1 0
C
0 0 0
So *
6 4 0
0) 0
2
0
0 200 400 600 800 1000 1200 1400 1600
Time [s]
Figure 12: Measured SFC versus cooling time during phase
transitions in pig fat
1 Cormpulsory coaling * *
S Natural cooling
0 o
C O
4 *
0
0
0 0 0
0 500 1000 1500 2000 2500
Time [s]
Figure 13: Measured SFC versus cooling time during phase
transitions in chicken fat
Conclusions
Solid fat content and particle size are important indicators of
food manufacture field. In this paper, two kinds of animal
fats were measured during the phase transitions with the
natural cooling and compulsory cooling methods. Two
independent ultrasonic methods, ultrasonic multiple echo
reflection method and ultrasonic attenuation spectra method,
t Compulsory cooling
0 Natural cooling
..0 .0''
O.
0
0 200 400
Figure 11: Measure
d
7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30June 4, 2010
are described. Multiple reflections within the steel wall are
used to determine the acoustic impedance of the fat. The
solid fat content is obtained by coupling the acoustic
impedance measurement with an acoustic velocity
measurement. To measure the particle size, a combined
model of the couplephase model and the scattering model is
presented, the attenuation spectra is measured within the
frequency range of 3MHz6MHz and the optimum
regulation technique is employed in the inversion procedure.
Acknowledgements
The Authors gratefully thank the National Science
Foundation of China awards (No.50706029.No.50836003).
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