3.1. Determination of dielectric properties by open-ended coaxial probe (OECP) and cavity perturbation technique
Table 1 shows the moisture content (% wet basis, w.b.) and water activity (aw) of the original products, as well as the dielectric properties measured by OECP and cavity perturbation technique.
Table 1
Physical and dielectrical properties of low moisture foods at 2450 and 915 MH measured by open-ended coaxial probe and cavity perturbation.
PRODUCT | Tapped density (g/cm3) | Moisture content (%) | aw | Open-ended coaxial probe 2450 MHz | Cavity perturbation 2450 MHz | Open-ended coaxial probe 915 MHz | Cavity perturbation 915 MHz |
\({\text{ε}}_{\text{r}}^{{\prime }}\) | \({\text{ε}}_{\text{r}}^{\text{''}}\) | \({\text{ε}}_{\text{r}}^{{\prime }}\) | \({\text{ε}}_{\text{r}}^{\text{''}}\) | \({\text{ε}}_{\text{r}}^{{\prime }}\) | \({\text{ε}}_{\text{r}}^{\text{''}}\) | \({\text{ε}}_{\text{r}}^{{\prime }}\) | \({\text{ε}}_{\text{r}}^{\text{''}}\) |
Corn starch | 0.464 ± 0.006 | 5.33 ± 0.000 | 0.124 ± 0.000 | 1.00 ± 0.02 | 0.06 ± 0.01 | 1.72 ± 0.00 | 0.36 ± 0.00 | 1.14 ± 0.02 | 0.12 ± 0.00 | 1.56 ± 0.13 | 0.12 ± 0.12 |
Curry | 0.659 ± 0.006 | 6.85 ± 0.001 | 0.435 ± 0.002 | 1.23 ± 0.04 | 0.02 ± 0.01 | 1.72 ± 0.16 | 0.28 ± 0.05 | 1.37 ± 0.04 | 0.07 ± 0.00 | 1.96 ± 0.00 | 0.02 ± 0.00 |
Paprika | 0.619 ± 0.001 | 7.19 ± 0.001 | 0.479 ± 0.001 | 1.06 ± 0.09 | 0.10 ± 0.04 | 1.72 ± 0.00 | 0.24 ± 0.00 | 1.53 ± 0.09 | 0.20 ± 0.04 | 1.96 ± 0.00 | 0.24 ± 0.00 |
Dried chives | / | 9.50 ± 0.002 | 0.45 ± 0.002 | 0.70 ± 0.01 | 0.12 ± 0.01 | 1.24 ± 0.00 | 0.04 ± 0.05 | 1.34 ± 0.02 | 0.41 ± 0.01 | 1.24 ± 0.24 | 0.20 ± 0.07 |
Rice grain | / | 11.09 ± 0.001 | 0.491 ± 0.001 | 2.69 ± 0.02 | 0.22 ± 0.00 | 3.17 ± 0.16 | 0.84 ± 0.08 | 2.75 ± 0.02 | 0.11 ± 0.00 | 4.36 ± 0.00 | 0.64 ± 0.21 |
Wheat grain | / | 10.74 ± 0.001 | 0.538 ± 0.002 | 2.91 ± 0.09 | 0.50 ± 0.02 | 2.52 ± 0.11 | 0.56 ± 0.05 | 2.38 ± 0.05 | 0.53 ± 0.01 | 2.92 ± 0.00 | 0.48 ± 0.00 |
The dielectric properties found were close to those reported on the literature, although there are few published data for low moisture foods, particularly regarding the products that were measured in this study. In can be seen in Table 1 that products with higher moisture contents and water activity did not necessarily present higher \({\text{ε}}_{\text{r}}^{{\prime }}\), which implies that the nature of the food (composition and physical state) is an important factor that influences the given values.
Additionally, temperature and moisture content are the most investigated factors whilst measuring the dielectric properties of food products. These properties usually drop quickly with the decrease in water content up to a critical moisture level (for example, about 12% w.b. for diced apples at 22°C). Below this level, there is little reduction in the loss factor, due to the bound water. The reduced loss factor with decreasing moisture content makes dehydrated foods less able to convert electromagnetic energy into thermal energy (Routray and Orsat 2018; Tang 2005).
Depending on the evaluated frequency (2450 or 915 MHz), the dielectric properties changed slightly (for the \({\text{ε}}_{\text{r}}^{{\prime }}\) of all products at 2450 and 915 MHz, there was a standard deviation of 0.65 for OECP and 0.92 for the cavity perturbation technique). At higher frequency, 2450 MHz, \({\text{ε}}_{\text{r}}^{{\prime }}\) and \({\text{ε}}_{\text{r}}^{\text{''}}\) tended to decrease in comparison to 915 MHz, for most tested samples and regardless of the measurement technique. Indeed, the lower the frequency, the more charges can be set in motion and therefore polarize the medium, which is directly related to the dielectric constant.
Table 2 displays the permittivity of semi-skimmed milk powder stored at several relative humidity (resulting in different water activity). Evaluating the results of dielectric properties measured by OECP, it can be seen that the \({\text{ε}}_{\text{r}}^{{\prime }}\) of the product with 13.08% of moisture content, for example, decreased from 2.10 to 1.95 when frequency was increased from 915 to 2450 MHz. However, the values overlap considering the standard deviations, so only a behavior trend can be implied. The loss factor, likewise, decreased from 0.26 at 915 MHz to 0.16 at 2450 MHz. Nevertheless, it seems that the dependence of the loss factor on frequency may be less predictable than that of dielectric constant (Berbert et al. 2002). Guo et al. (2008) reported that the dielectric constant and loss factor of chickpea flour, measured by OECP, were influenced by the frequency, especially at high moisture contents (15.8 and 20.9% w.b.).
Table 2
Dielectric properties of semi-skimmed milk powder at different moisture contents and water activity measured by open-ended coaxial probe at room temperature.
PRODUCT | Tapped density (g/cm3) | Moisture content (%, w.b.) | aw | Open-ended coaxial probe 2450 MHz | Open-ended coaxial probe 915 MHz |
\({\text{ε}}_{\text{r}}^{{\prime }}\) | \({\text{ε}}_{\text{r}}^{\text{''}}\) | \({\text{ε}}_{\text{r}}^{{\prime }}\) | \({\text{ε}}_{\text{r}}^{\text{''}}\) |
Semi-skimmed milk powder | 0.612 ± 0.005 | 8.54 ± 0.001 | 0.458 ± 0.001 | 1.01 ± 0.04 | 0.07 ± 0.00 | 1.10 ± 0.05 | 0.15 ± 0.00 |
0.585 ± 0.005 | 9.97 ± 0.003 | 0.654 ± 0.002 | 1.22 ± 0.07 | 0.06 ± 0.01 | 1.73 ± 0.08 | 0.11 ± 0.00 |
0.570 ± 0.006 | 13.08 ± 0.003 | 0.786 ± 0.003 | 1.95 ± 0.08 | 0.16 ± 0.00 | 2.10 ± 0.09 | 0.26 ± 0.01 |
Ozturk et al. (2016), using a precision LCR meter and liquid test fixture to measure the dielectric properties of vegetable powders, noted smaller values of dielectric constant and loss factor with the increase in the radio frequency range (from 1 to 30 MHz), generally agreeing with the moisture content of each product. However, two of the vegetable powders, chili powder and potato starch, had higher moisture content but lower \({\text{ε}}_{\text{r}}^{{\prime }}\) and \({\text{ε}}_{\text{r}}^{\text{''}}\). The authors pointed out that the dielectric properties are not only affected by moisture content, that is, the bulk density and particle size of the product may also impact on the permittivity. Working with red pepper powder at 10.4% w.b. moisture content and at room temperature, Guo & Zhu (2014) verified that when the frequency increased from 27.12 to 4500 MHz the dielectric constant decreased on a smaller scale, from 3.75 to 2.76. At 30.8% w.b. moisture content, the decrease in \({\text{ε}}_{\text{r}}^{{\prime }}\) was much more pronounced, from 35.07 to 12.53. Although this study is based on much larger frequency variations, the fact that the samples used in the present work had no more than 13% w.b. moisture content may explain the small differences in dielectric properties with the increase in frequency.
Table 3 shows the measurements of semi-skimmed milk powder at room temperature and heated up 50 and 60°C. The powder at room temperature presented a \({\text{ε}}_{\text{r}}^{{\prime }}\) between 1.28 to 1.72 and \({\text{ε}}_{\text{r}}^{\text{''}}\) of 0.02 up to 0.16, depending on the frequency and measurement technique. At higher temperatures, both \({\text{ε}}_{\text{r}}^{{\prime }}\) and \({\text{ε}}_{\text{r}}^{\text{''}}\) increased, but the loss factor remained low, especially when OECP was used. For skimmed milk powder at frequencies above 200 MHz up to 3 GHz and using the probe, Lau et al. (2020) reported values of \({\text{ε}}_{\text{r}}^{{\prime }}\) from 2.5 and 3.5 and \({\text{ε}}_{\text{r}}^{\text{''}}\) between 0 and 0.5, for temperatures from 20 to 60°C, respectively. An increase in the dielectric constant with the increase in temperature may be attributed to the operating frequency, the ratio between bound-water and free water contents, and the raise of ionic conduction and mobility of ions (Calay et al. 1995; Stuart O. Nelson and Bartley 2002). The changes in permittivity of semi-skimmed milk powder were relatively small, as well as noticed by Guo et al. (2008) for chickpea flour at temperatures below 40°C. Nevertheless, the effect of increasing frequency on the decrease of permittivity was much more pronounced for the powder at higher temperatures than at room temperature. Dependence of dielectric properties on frequency, temperature and moisture content is very common in the literature and has also been reported by other authors (Boreddy and Subbiah 2016; Li et al. 2018; Y. Lin et al. 2016; Ozturk et al. 2016, 2018; Qi et al. 2021; Zhu et al. 2012).
Table 3
Dielectric properties of semi-skimmed milk powder at different temperatures and measured by open-ended coaxial probe and cavity perturbation.
PRODUCT | Tapped density (g/cm3) | Moisture content (%, w.b.) | aw | T (°C) | Open-ended coaxial probe 2450 MHz | Cavity perturbation 2450 MHz | Open-ended coaxial probe 915 MHz | Cavity perturbation 915 MHz |
\({\text{ε}}_{\text{r}}^{{\prime }}\) | \({\text{ε}}_{\text{r}}^{\text{''}}\) | \({\text{ε}}_{\text{r}}^{{\prime }}\) | \({\text{ε}}_{\text{r}}^{\text{''}}\) | \({\text{ε}}_{\text{r}}^{{\prime }}\) | \({\text{ε}}_{\text{r}}^{\text{''}}\) | \({\text{ε}}_{\text{r}}^{{\prime }}\) | \({\text{ε}}_{\text{r}}^{\text{''}}\) |
Semi-skimmed milk powder | 0.582 ± 0.001 | 7.19 ± 0.001 | 0.339 ± 0.002 | Room temperature | 1.28 ± 0.06 | 0.02 ± 0.01 | 1.72 ± 0.00 | 0.16 ± 0.05 | 1.45 ± 0.10 | 0.02 ± 0.01 | 1.49 ± 0.00 | 0.16 ± 0.00 |
50.2 ± 0.13 | 2.05 ± 0.01 | 0.08 ± 0.00 | 1.73 ± 0.00 | 0.32 ± 0.05 | 2.04 ± 0.01 | 0.03 ± 0.00 | 2.12 ± 0.21 | 0.32 ± 0.11 |
60.03 ± 0.04 | 2.27 ± 0.01 | 0.08 ± 0.00 | 1.89 ± 0.11 | 0.37 ± 0.00 | 2.30 ± 0.01 | 0.08 ± 0.00 | 2.20 ± 0.24 | 0.24 ± 0.00 |
Comparing the same frequency and both tested measurement techniques, it is noticeable that the use of the cavity perturbation technique resulted in higher dielectric constant and loss factor for almost all products. The loss factor values obtained with OECP, in particular, were closer to zero for most products. During the tests, some of the repetitions gave negative results for the \({\text{ε}}_{\text{r}}^{\text{''}}\) and therefore were disregarded. This may be due to inaccuracies related to a bad contact between the probe and the surface of the samples and the disturbances when the device filled with sample was connected to the measurement system. Also, all the products showed oscillations in the measured values with the shift in frequency (as represented by Fig. 4 for the semi-skimmed powder at different moisture contents). This behavior was noticed by published studies that worked with low moisture foods, such as egg white powder (Boreddy and Subbiah 2016), whey protein gel and mashed potato (Chen et al. 2013), chestnut flour (Zhu et al. 2012), soy flour (Terigar et al. 2010), red pepper powder (Wenchuan Guo and Zhu 2014), legume flour (Wenchuan Guo et al. 2010). Because of the extreme low values, the signal-to-noise ratio was low. Similar noise in the dielectric properties data were reported in the literature for various other products. There are possible sources of error that could happen even after calibration and that could cause these oscillations and affect the accuracy of the measurement, such as cable stability, air gaps, and sample thickness (Chen et al. 2013). Additionally, the value of \({\text{ε}}_{\text{r}}^{{\prime }}\) for dried chives at 2450 MHz, for example, was aberrant, as it was smaller than the value for air (equal to 1). This may be proof of the limitation of OECP measurement method, that is, it highlights the range of values that this technique is capable of measuring accurately.
During measurements by cavity perturbation, the standard deviations in the dielectric properties of some products were zero. This means that when the same sample from each replicate was inserted into the cavity, the change in resonance frequency with respect to the resonance frequency of the empty cavity frequency was the same, leading to the same \({\text{ε}}_{\text{r}}^{{\prime }}\). This observation could mean that more accurate and repeatable results can be obtained for the dielectric constant when the cavity perturbation technique is employed, but it could also imply that the execution of the cavity perturbation technique was not accurate enough to this type of product (which would result in the same erroneous value for the dielectric constant). Nevertheless, the results obtained by cavity perturbation gave coherent values, even if the comparation with the literature is not possible for the exact same foods. So, the hypothesis that the cavity gives accurate results seem more plausible.
Concerning the use of OECP or cavity perturbation, the most suitable measurement technique for a certain product depends on the frequency of interest, the nature (physical and electrical) of the dielectric material to be measured, and the degree of accuracy required (S.O. Nelson 2006). Lau et al. (2020) affirmed that the open-ended coaxial probe may have reduced accuracy for measurements below 200 MHz and for materials with low values for dielectric constant and loss factor. Table 4 shows the results found in the literature for the dielectric properties of corn starch, curry, paprika, semi-skimmed milk powder, dried chives, rice grain, and wheat grain.
Table 4
Scientific articles found in the literature reporting the dielectric properties of the same products that were used in this work.
PRODUCT | LITERATURE |
Corn starcha | Technique: OECP1 Frequency: 2450 MHz Sample conditions: 30°C and 1% MC2 \({\text{ε}}_{\text{r}}^{{\prime }}\) = 2.74 \({\text{ε}}_{\text{r}}^{\text{''}}\) = 0.14 |
Curryb | Technique: LCR meter and liquid test fixture Frequency: 1–30 MHz (radio frequency) Sample conditions: 23°C and 8.3% MC \({\text{ε}}_{\text{r}}^{{\prime }}\) between 2–3 \({\text{ε}}_{\text{r}}^{\text{''}}\text{ }\)between 0-0.3 |
Paprikab | Technique: LCR meter and liquid test fixture Frequency: 1–30 MHz (radio frequency) Sample conditions: 23°C and 12.3% MC \({\text{ε}}_{\text{r}}^{{\prime }}\) between 4 to 5 \({\text{ε}}_{\text{r}}^{\text{''}}\) between 0 to 0.3 |
Semi-skimmed milk powderc | Technique: OECP1 Frequency: 1 MHz to 3 GHz Sample conditions: 20°C and 3.65% MC \({\text{ε}}_{\text{r}}^{{\prime }}\) around 2.2 \({\text{ε}}_{\text{r}}^{\text{''}}\) close to 0 |
Dried chives | Not found |
Rice grainde | Technique: X-band and K-band MW measurement system Frequency: 11 and 22 GHz Sample conditions: 24°C, 11.5% MC2 Density = 0.443 g/cm3 \({\text{ε}}_{\text{r}}^{{\prime }}\)= 1.76 \({\text{ε}}_{\text{r}}^{\text{''}}\)= 0.10 | Technique: coaxial air-line system Frequency: 2450 MHz Sample conditions: 24°C, 11% MC2 \({\text{ε}}_{\text{r}}^{{\prime }}\) around 2.2 \({\text{ε}}_{\text{r}}^{\text{''}}\) around 0.25 |
Wheat grainf | Technique: power signal generator Frequency: 2450 MHz Sample conditions: bulk density of 0.6 to 0.9 g/cm3, 10.4% MC2 \({\text{ε}}_{\text{r}}^{{\prime }}\)= 2.55–2.90 (depending on the bulk density) \({\text{ε}}_{\text{r}}^{\text{''}}\)= 0.26–0.30 (depending on the bulk density) | Technique: power signal generator Frequency: 2450 MHz Sample conditions: bulk density of 0.6 to 0.9 g/cm3, 10.4% MC2 \({\text{ε}}_{\text{r}}^{{\prime }}\) = 2.55–2.90 (depending on the bulk density) \({\text{ε}}_{\text{r}}^{\text{''}}\) = 0.26–0.30 (depending on the bulk density) |
a(Ndife et al. 1998) |
b(Ozturk et al. 2018) |
c(Lau et al. 2020) |
d(You and Nelson 1988) |
e(Noh and Nelson 1989) |
f(Sokhansanj and Nelson 1988) |
1OECP = open-ended coaxial probe |
2MC = moisture content |
Errors in the measurement of the dielectric constant through cavity perturbation technique are mostly associated with inaccuracies in determining of the frequency shift and volume ratio. If these values are properly identified, the measurement error of the dielectric constant can be kept close to 2%. For the measurements of this study, occasionally there were no frequencies corresponding to a S11 value of 50% reflection of incident power (or -3 db), and in this case the corresponding frequency values closest to the 50% reflection were chosen. This decision caused a difference in the calculated loss factor, estimated in around 0.18 for paprika powder (above or below the reported loss value). The precision of loss factor values is constrained by the frequency shift error and especially the quality factor change error, being very difficult to control. This quality factor change error deteriorates the measurement accuracy of dielectric loss because of the combination of various factors, such as homogeneity of the specimen, coupling condition, specimen holes, and uncertainty. This inaccuracy is extremely hard to estimate. The variation of data reported by the literature is very wide (Risman & Bengtsson, 1971; Dube et al., 1988; Sheen, 2005). The dielectric loss factors for vegetable powders, for instance, were very low due to the small amount of water in these products. For broccoli powder and onion powder, the \({\text{ε}}_{\text{r}}^{\text{''}}\) values were not shown by the authors because they were too low, and the instrument could not give stable values (Ozturk et al. 2016).
According to Sheen (2009), the cavity perturbation technique is good for measurement of the real part of permittivity but is not adequate for extremely low loss factors. Moreover, P. Risman, (2009) reported that a maximum of 2 mm in diameter is necessary for lossy materials at 2450 MHz and using a TM010 circular cavity, otherwise the quality factor will be too low or the attenuation in transmission will be too high, reducing the resolution and allowing weak non-modal field signs to interfere in the main mode. The experimental approach of the present work was to abstract these considerations, and the appropriate diameter of the tube was chosen based on the consideration of minimum perturbation inside the cavity.