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Keywords:

  • Attenuation;
  • particle size;
  • tomato paste;
  • ultrasound
Symbols
A0, A1

zero- and first-order scattering coefficients

a1, a2

modified scattering coefficients (radius of particles relative to the wavenumber)

b1, b2

functions see. eqn (3)

Cp

specific heat at constant pressure (J kg−1 K−1)

H

function see eqn (3)

I

complex vector

k1

wavenumber of the continuous phase (dispersion medium) (m−1)

k2

wavenumber of the dispersed phase (m−1)

RAn

real part of the scattering coefficient

r

radius of spherical particles of the dispersed phase (μm)

T

absolute temperature (K)

α

total attenuation coefficient (Np m−1)

αs

coefficient of attenuation resulting from wave scattering at suspension particles (Np m−1)

α1

coefficient of attenuation in continuous phase (dispersion medium) (Np m−1)

α2

coefficient of attenuation in pure dispersed phase (Np m−1)

β

adiabatic compressibility (Pa−1)

δ

viscous skin depth (m)

η

dynamic viscosity (Pa s)

ϕ

volume fraction of the dispersed phase (−)

κad

adiabatic exponent (−)

ρ

density (kg m−3)

τ

thermal conductivity (W m−1 K−1)

ω

angular frequency (rad s−1)

Introduction

  1. Top of page
  2. Introduction
  3. Materials and methods
  4. Results
  5. Discussion
  6. Conclusions
  7. Acknowledgements
  8. References

Acoustic spectroscopy is a promising tool to determine the particle size distribution (PSD) and concentration of a dispersed media, such as semi-liquid systems. This technique is based on the measurements of ultrasound propagation parameters such as the attenuation coefficient and wave velocity in the medium as a function of frequency (usually 1–100 MHz) and subsequently fitting those measures with the suitable mathematical model to obtain PSD (Povey, 1997). Ultrasonic spectroscopy can be used to measure particle size between 10 nm and 1000 mm, and it is suitable for the analysis of concentrated matrices (up to 50 wt%) and optically opaque systems without any sample preparation (McClements et al., 1987). Moreover, it enables real-time analysis and is not destructive to examined medium. For these reasons, it can be applied in many industrial areas including food, cosmetics and petroleum industry, as well as in medicine (Mougin et al., 2003).

Many food manufacturing processes involve fragmentation of raw ingredients or homogenisation of liquid emulsions. In products such as dairy beverages, plant oils, fruit and vegetable juices or purees, PSD is recognised as a significant parameter of food quality and its technological properties (Meyer et al., 2006). Ultrasonic attenuation measurements were recently applied to PSD determination in plant oils, such as canola (Shukla et al., 2010), corn (McClements et al., 1987), sunflower and olive oils (Wang & Povey, 1999; Mougin et al., 2003; Richter et al., 2007), in tomato ketchup (Bayod et al., 2008) and in dairy beverages (Meyer et al., 2006). It was also used to evaluate the solid fat content in opaque fat blends (Wassell et al., 2010) and carbohydrate content and density of fruit juices and drinks (Contreras et al., 1992). Particle size reduction is a particularly important consideration in the production of baby foods (Ahmed & Ramaswamy, 2006), while the most recent studies suggest that ultrasound measurements can also provide an information on rheological changes in studied medium (Bayod et al., 2008; Pierre et al., 2013).

When ultrasound wave passes through material, the signal strength is reduced. This may be caused by absorption, reflection, scattering or diffraction. The attenuation coefficient (α) is determined by the reduction in amplitude of an ultrasonic wave, which has travelled through known distance of material. Povey (1997) evaluated PSD based on the phenomenon of diffraction. When propagated in multiphase liquids, ultrasonic waves are refracted by inclusions in the dispersed phase. To describe this phenomenon, the following eqn (1) was proposed (Povey, 1997). It combines the coefficient of wave attenuation (αs) resulting from scattering at particles with the particle radius (r):

  • display math(1)

The correlation between the total attenuation coefficient (α) and attenuation resulting from wave scattering (αs) may be described by eqn (2):

  • display math(2)

The above equations can be applied only at low volume fraction values. In highly concentrated suspensions, medium particles cause multiple refractions of the wave, and the relevant equations become more complex (Povey, 1997). Richter et al. (2007) verified this model by performing measurements in the frequency range of 1–100 MHz in a water–oil emulsion. Their analyses proved that the sum produced by eqn (1) is a satisfactory representation of measurement data when = 1.

Tebbutt & Challis (1996) analysed four models combining the following values: wave propagation velocity, attenuation coefficient, material density, radius of dispersed phase particles, liquid viscosity, thermal conductivity and specific heat capacity of mixture ingredients. The above-mentioned authors demonstrated that the proposed model (1) was most versatile because it accounted for the greatest spectrum of material properties. The discussed model can be applied when the thermophysical properties of the continuous phase (dispersion medium) and the dispersed phase vary significantly. The complexity of the presented model is also its main weakness – the model requires detailed knowledge of a wide range of thermophysical properties of the studied material.

The aim of this study was to verify the usefulness of mathematical model (1) describing the relationship between the coefficient of ultrasonic wave attenuation (αs) resulting from scattering at particles and the size of dispersed phase particles for the determination of PSD in diluted tomato paste in reference to microscopic measurements.

Materials and methods

  1. Top of page
  2. Introduction
  3. Materials and methods
  4. Results
  5. Discussion
  6. Conclusions
  7. Acknowledgements
  8. References

Experimental material consisted of tomato paste with the concentration of 30% (w/v), supplied from the same production batch and purchased in a wholesale outlet. Tomato paste was stored in original 150 mL packaging at the temperature of 4 °C. For the needs of ultrasonic measurements, the material was diluted with distilled water to achieve the concentration of 3% (v/v). All measurements were taken at the temperature of 20 °C.

Microscopic analysis

Microscopic measurement was the reference method for determining particle size distribution (PSD). For microscopic analysis, tomato paste was suspended in sterile saline solution and stirred for 30 s. The resulting suspension was placed on a microscope slide and covered with a cover glass. The analysis was performed in five repetitions.

Particle size was measured under an OLYMPUS BX51 light microscope equipped with a CCD ColorView II camera (Olympus Optical Ltd., Tokyo, Japan), at 100 ×  and 400 ×  magnification to measure representative particles in diluted tomato paste. The resulting images were analysed using Cell^F Soft Imaging System software (Olympus Optical Ltd). The images were captured under constant exposure time. At least twenty fields of view per microscopic slide were counted. The length of the maximum chord of tomato sections was adopted as the size of particles in dispersed phase.

Ultrasonic attenuation spectroscopy

Ultrasonic measurements were taken with the use of an UMT-12 ultrasonic defectoscope (Ultramet, Radom, Poland). The ultrasonic echo technique was used. Based on the preliminary studies, the head generated a longitudinal wave with the frequency of 1 MHz was selected as the most promising for this application. The test stand is presented in Fig. 1. The analysed material was placed in a vertical measuring chamber containing an ultrasonic head. The head's vertical displacement was controlled by an arm of the tripod. A digital slide caliper was mounted on the tripod, and the displacement of the ultrasonic head was measured with ± 0.01 mm accuracy. The measuring chamber was positioned in a water bath whose temperature was stabilised at 20 ± 0.05 °C by the GR150 thermostatic head (Grant Instruments Ltd., Cambridge, UK). The temperature of the studied material was measured with ± 0.05 °C accuracy using a type 2700 DMM multimeter system with a 7710 multiplexer module (Keithley Instruments, Inc., Cleveland, OH, USA). A K-type thermocouple was positioned near the ultrasonic head in a manner that prevented distortion of the emitted and received signal. The following parameters were measured during ultrasonic tests: time of flight, amplitude of the received signal and displacement of the ultrasonic head.

image

Figure 1. Diagram of an acoustic test stand. 1 – measuring chamber, 2 – ultrasonic head, 3 – water bath, 4 – tripod, 5 – thermostat head of the water bath, 6 – grip for mounting the acoustic head, 7 – slide caliper for measuring displacement of the ultrasonic head, 8 – micrometre screw for moving the head grip.

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Data analysis and attenuation predictions

The time of acoustic wave propagation and the displacement of the ultrasonic head were used to determine the velocity of ultrasonic wave propagation. The theoretical model of ultrasonic wave propagation in a dispersion medium was used to determine the attenuation coefficient. The PSD in tomato paste was determined using eqn (1) for the first two terms in the series, which are defined as scattering coefficients (A0, A1) and are described by eqn (3) (Wang & Povey, 1999):

  • display math(3)

where

  • display math
  • display math
  • display math
  • display math
  • display math
  • display math
  • display math
  • display math

Thermal properties of tomato paste (specific heat at constant pressure, thermal conductivity) were obtained from Aparicio et al. (2011), who studied the product of similar composition, while the thermodynamic properties of water were derived from National Institute of Standards and Technology (NIST, 2011). Values used in the calculation are presented in Table 1. All of simulations were performed using MATLAB R2010b software (MathWork, Natick, MA, USA).

Table 1. Physical parameter values of diluted tomato paste (18%, v/v) and pure water at 20 °C used in simulations
Parameter (20 °C)Material
WaterTomato paste
  1. The data taken from aown measurements, bNIST (2011), cAparicio et al. (2011).

Ultrasound velocity (m s−1)1480a1568a
Attenuation (Np m−1)6.07 10−3a16.97a
Density (kg m−3)998.2a1094.4a
Thermal conductivity (W m−1 K−1)0.59846b0.6c
Specific heat capacity (at constant pressure) (J kg−1 K−1)4184b4200c
Adiabatic compressibility (Pa−1)2.2 109b1.8 109c

Results

  1. Top of page
  2. Introduction
  3. Materials and methods
  4. Results
  5. Discussion
  6. Conclusions
  7. Acknowledgements
  8. References

The percentage of tomato particles in the size range of 1 − 100 μm, at 1-μm intervals, obtained using microscopic technique is presented in Fig. 2. An analysis of PSD (n = 445) determined by reference method revealed that 96.5% of particles (n = 429) in homogenised tomato paste were in the size range of 1–50 μm. Particles larger than 50 μm had a negligent percentage (3.6%, n = 16), and the size of the largest particles was determined at 381.5 μm. In an aforementioned predominant range (1–50 μm), the highest percentage of particles (66.8%, n = 297) was noticed for the size of 4.0 ± 0.5 μm, while the tomato particle sizes smaller than 3.5 μm and >4.5 μm were 9.2% (n = 41) and 20.5% (n = 91), respectively.

image

Figure 2. Particle size distribution (PSD) in diluted (3%, v/v) tomato paste within the size range of 1–100 μm, based on the reference microscopic analysis shown in resolution of 1 μm (solid line). The above circular graph represents the total PSD of tomato paste, and numbers in brackets denote the measured particle count.

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Preliminary ultrasonic investigation showed that undiluted tomato paste 30% (v/v) could not be subjected to measurements; therefore, tomato puree with the maximum concentration of 18% (v/v) was adopted as the pure dispersion phase. The values of attenuation coefficient, wave propagation velocity and density in a pure dispersed phase needed to determine PSD in tomato paste based on ultrasonic measurements are summarised in Table 1. Values of attenuation coefficient for water and the tomato puree with a maximum concentration (18%, v/v) of the dispersed phase were 6.07 10−3 and 16.97 Np m−1, respectively. The coefficient of attenuation resulting from wave scattering at the solid particles of diluted 18% (v/v) tomato paste (αs) was determined using eqn (2) and it equalled 0.238 Np m−1.

Due to the high complexity of eqn (1), a computer simulation was carried out to determine the value of the attenuation coefficient (αs) according to the value of particle size in the range of 1 do 50 μm, at steps of 0.02 μm. The results are shown in Fig. 3. Simulation results showed that the estimated PSD measured by ultrasonic methods was equal to 4.14 ± 0.02 μm (Fig. 3).

image

Figure 3. Values of the coefficient of attenuation (αs) resulting from scattering at tomato paste particles subject to PSD estimated based on the ultrasound measurements at low working frequency (1 MHz) at 20 °C. The dashed line represents the calculated coefficient of attenuation value (αs) in relation to the predicted tomato particles size.

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Discussion

  1. Top of page
  2. Introduction
  3. Materials and methods
  4. Results
  5. Discussion
  6. Conclusions
  7. Acknowledgements
  8. References

The characteristic PSD of dispersed phase determined by ultrasonic measurements reflects the size of predominant fraction of particles, which are responsible for wave scattering. As our findings indicated, the estimated size of the tomato paste particles (4.14 ± 0.02 μm) based on the determined value of the attenuation coefficient (αs) equalled to 0.238 Np m−1, closely corresponded to the size (4.0 ± 0.5 μm) of dominant fraction of particles measured by microscopy, within the limits of the accuracy of size analysis by both methods. The character of the wave scattering phenomenon suggests that smaller particles are more likely to cause scattering than larger particles and that the resulting correlation is nonlinear (Mougin et al., 2003). Results of the simulation, which was carried out for eqn (1), and the results are shown in Fig. 3 confirm the nature of this relationship. For this reason, the size of particles measured by the above-mentioned method is determined by the distribution of particle size fractions (not necessarily a normal distribution or an average size). Solid particles in tomato paste do not have a spherical shape, and their size varies significantly in the range of 1.5–380.5 μm. Our results suggest that greater particles (>50 μm) did not affect the final PSD prediction. The simplified model worked well at the frequency of 1 MHz with PSD between 1 and 50 μm in our diluted tomato paste. Similar observations and PSD measurements in tomato paste and ketchup were observed previously (Bayod et al., 2008). Despite the above, the discussed ultrasonic method with low working frequency (1 MHz) determines the characteristic PSD of tomato paste with satisfactory accuracy. Lower working frequencies <10 MHz are recommended for PSD measurements by many authors (Wang & Povey, 1999; Aparicio et al., 2011). Both investigated methods produced comparable results, indicating that ultrasonic techniques can be used to determine the characteristic PSD in tomato paste suspensions.

Conclusions

  1. Top of page
  2. Introduction
  3. Materials and methods
  4. Results
  5. Discussion
  6. Conclusions
  7. Acknowledgements
  8. References

The application of Povey model resulted in good agreement with the reference measurements. In our study, PSD determined using the ultrasound technique at proposed configuration was consistent with microscopic data. Further improvements in the ultrasonic-based measurements can be obtained using more than one wave frequency simultaneously, while more studies on other food matrices of different concentrations and PSDs are necessary to make this method universal. In addition, it should be underlined that proposed technique might be very promising for the suspensions characterised by homogeneous PSD. Our results may contribute to the development of a new, rapid and noninvasive technique to improve the quality control and standardise homogenized tomato products, performed during food processing.

Acknowledgements

  1. Top of page
  2. Introduction
  3. Materials and methods
  4. Results
  5. Discussion
  6. Conclusions
  7. Acknowledgements
  8. References

This study was financially supported by the Ministry of Science and Higher Education (Poland), grant No. N N313 036036.

References

  1. Top of page
  2. Introduction
  3. Materials and methods
  4. Results
  5. Discussion
  6. Conclusions
  7. Acknowledgements
  8. References
  • Ahmed, J. & Ramaswamy, H.S. (2006). Viscoelastic properties of sweet potato puree infant food. Journal of Food Engineering, 74, 376382.
  • Aparicio, C., Guignon, B., Otero, L. & Sanz, P.D. (2011). Thermal expansion coefficient and specific heat capacity from sound velocity measurements in tomato paste from 0.1 up to 350 MPa and as a function of temperature. Journal of Food Engineering, 104, 341347.
  • Bayod, E., Willers, E.P. & Tornberg, E. (2008). Rheological and structural characterization of tomato paste and its influence on the quality of ketchup. LWT – Food Science and Technology, 41, 12891300.
  • Contreras, N.I., Fairley, P., McClements, D.J. & Povey, M.J.W. (1992). Analysis of the sugar content of fruit juices and drinks using ultrasonic velocity measurements. International Journal of Food Science and Technology, 27, 515529.
  • McClements, N.I., Fairley, P., McClements, D.J. & Povey, M.J.W. (1987). Ultrasonic measurements in particle size analysis. International Journal of Food Science and Technology, 22, 491499.
  • Meyer, S., Berrut, S., Goodenough, T.I.J., Rajendram, V.S., Pinfield, V.J. & Povey, M.J.W. (2006). A comparative study of ultrasound and laser light diffraction techniques for particle size determination in dairy beverages. Measurement Science and Technology, 17, 289297.
  • Mougin, P., Wilkinson, D. & Roberts, K.J. (2003). In situ ultrasonic attenuation spectroscopic study of the dynamic evolution of particle size during solution-phase crystallization of urea. Crystal Growth & Design, 3, 6772.
  • NIST (2011). National Institute of Standards and Technology.
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  • Povey, M.J.W. (1997). Ultrasonic Techniques for Fluids Characterization. San Diego, CA: Academic Press.
  • Richter, A., Voigt, T. & Ripperger, S. (2007). Ultrasonic attenuation spectroscopy of emulsions with droplet sizes greater than 10 μm. Journal of Colloid and Interface Science, 315, 482492.
  • Shukla, A., Prakash, A. & Rohani, S. (2010). Particle size monitoring in dense suspension using ultrasound with an improved model accounting for low-angle scattering. AIChE Journal, 56, 28252837.
  • Tebbutt, J.S. & Challis, R.E. (1996). Ultrasonic wave propagation in colloidal suspensions and emulsions: a comparison of four models. Ultrasonics, 34, 363368.
  • Wang, Y. & Povey, M.J.W. (1999). A simple and rapid method for the determination of particle size in emulsions from ultrasound data. Colloids and Surfaces B: Biointerfaces, 12, 417427.
  • Wassell, P., Wiklund, J., Standing, M. et al. (2010). Ultrasound Doppler based in-line viscosity and solid fat profile measurement of fat blends. International Journal of Food Science and Technology, 45, 877883.