Dielectric properties of berries in the microwave range at variable temperature

1 Introduction

 Dielectric properties (DPs) are important parameters involved in the complex permittivity, ɛ, one relevant physical property of materials. DPs refer to both real and imaginary parts of the permittivity, known as dielectric constant (ɛ′) and dielectric loss factor (ɛ″), respectively. The equation for complex permittivity is [1]: ɛ = ɛ ′ - j ɛ ″(1)

where j is the imaginary unit, being j = ( - 1 ) .

 Physically, ɛ′ is related to the ability of the material to store energy, while ɛ″ is related to electromagnetic energy into heat, increasing the temperature of the material. Both ɛ′ and ɛ″ are affected by diverse factors: a) associated with the nature of the material, mainly composition, and b) related to the conditions of the application of the electromagentic energy, such as frequency [2]. Additionally, temperature and physical state of the material have effect on the DPs of the materials [3].

 Early, dielectric properties were studied for ceramic and dielectric materials, mainly in the electronics and communications fields. However, with the introduction of microwave ovens in 1960 and the potential application at industrial level of microwave treatments, dielectric properties of foods and biological products became valuable for agricultural products and foods [4]. There are numerous reports of these properties for different kind of foods, including fruits, vegetables, bread, nuts, coffee, meat, seafoods, milk, dairy products, eggs and purees [2], as well as for legumes [5, 6] and cereals [7, 8]. The objective of knowing the DPs is to predict the behavior of these foods when subjected to microwave heating for disinfestation, mold control, drying [2, 6], pasteurization or sterilization [9]. In addition, the knowledge of DPs is useful to relate them to other important characteristics in the materials, such as moisture content and density [5, 7].

 There are few reports of DPs for strawberry. Nelson et al. [10] measured strawberry with an open-ended coaxial probe with ɛ′ values of 73 at 915 MHz, and 71 for 2450 MHz, and ɛ″=14 for both frequencies at room temperature. Funebo and Ohlsson [11] measured the dielectric properties of strawberry at 2800 MHz, using a perturbation cavity, finding values of ɛ′=73 and ɛ″=15 for the berries with 10.1 kg_water/g_dry solids (or 91% of moisture content, w.b.) at 20°C. The potential of microwaves usage for strawberry drying [12–14], to avoid decay in fresh strawberries [15] and for continuous microwave pasteurization of strawberry puree [16] has been reported. Thus, it is important to know the DPs of other kind of berries in order to develop effective treatments based on microwave energy.

 In Mexico, the region known as “El Bajío” in Guanajuato, is distinguished in the country for the production of berries, especially, strawberries. Traditionally, strawberry is symbol of Irapuato (a city located in the region). Strawberries are commercialized fresh, and in diverse derivatives, such as jams, dried fruits, and crystallized fruits. The state of Guanajuato is an incipient exporter of blackberries and raspberries, with a growing market. The objective of this work was to analyze the DPs in the microwave range and physicochemical properties of raspberry, strawberry and blackberry produced in “El Bajío” (Guanajuato, Mexico).

3 Results

3.2 Dielectric constant

 Figure 1 shows the dielectric constant for the berries, which decreased with increasing frequency. At 0.5 GHz, ɛ′ values for all berries were around 77 diminishing to 28 at 25 GHz. With respect to temperature, no significant difference was observed between ɛ′ values at 20 and 40°C for blackberries and raspberries (p > 0.05), as it is shown in Fig. 1a and 1b. In the case of strawberries (Fig. 1), higher values for dielectric constant were found at the temperature of 20°C, at frequencies under 8 GHz (p < 0.05) in comparison with those measured at 40°C. The dielectric constant had higher values at 60°C only for raspberries (p < 0.05), shown in Fig. 1a.

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Fig. 1

Dielectric constant of a) blackberry, b) raspberry and c) strawberry from “El Bajío” region (Guanajuato, Mexico).

3.3 Dielectric loss factor

 The loss factor of the studied berries decreased from 0.5 to 2 GHz and then, increased with increasing frequency (Fig. 2). The loss factor was not affected by the temperature in the range from 0.5 to 2 GHz for the three studied berries (p > 0.05), but it decreased with increasing temperature from 5 to 20 GHz for all the samples (p < 0.05). Values for ɛ″ at 5 GHz are around 17.5–18.5 and increased to more than 31 at 20 GHz for the raspberries (Fig. 2b). Lower ɛ″ were observed for blackberry samples at these frequencies (Fig. 2a).

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Fig. 2

Dielectric loss factor of a) blackberry, b) raspberry and c) strawberry from “El Bajío” region (Guanajuato, Mexico).

 Moisture content of the three studied berries ranged between 88.15 and 90.50% (w.b.), being similar to the values reported by Funebo and Ohlsson [11] for strawberries (91% w.b.), Golding et al. [23] for raspberry after 2 days of storage (86.83% w.b., without treatment) and Acosta-Montoya et al. [24] for blackberries (85.1% for a maturity stage grade 3). Small differences may be due to variety and maturity stage. Also, the USDA [25] reports moisture content values from 85 to 90% for these berries. The quality of the studied raspberry fruits is similar that the reported by Golding et al. [23], who reported values of 9.8ºBx, 1.58% citric acid, and 240 mg anthocyanins/kg fresh berry for raspberries cv. ‘Maravilla’ from Australia. For blackberries from Costa Rica, Acosta-Montoya et al. [24] reported 5–7.7ºBx for TSS (lower than the analyzed in our study), and 1.03–8.3 mg cyanidin 3-glucoside equivalents/g (higher than the studied samples from Guanajuato, Mexico). Villa-Rojas et al. analyzed strawberries from Puebla, Mexico, and found 7.80ºBx (very similar to our data) and 0.66% of titratable acidity (lower than strawberries studied in this work). Differences are due to the variety, maturity stages and origin of the berries.

 Strawberries from “El Bajío” region, at 915 MHz and 20°C, had ɛ′=72.02 and ɛ″=12.19, values close to the early reports of Nelson et al. [10] (ɛ′=73 and ɛ″=14), and by Fubeno and Ohlsson [11], with values of ɛ′=73 and ɛ″=15.

 Dielectric constant at 2.45 GHz and 20°C was similar for blackberry and strawberry (p > 0.05), with values between 68.68 and 69.86. These values were significantly lower than the raspberries measurements, with an average of ɛ′=71 (p < 0.05). This result is related to higher titratable acidity in the raspberries. Decreasing of ɛ′ with respect to increasing frequency has been reported for other fruits, such as apples, cherries and oranges [27], mango [28], guava fruit, prickly pear and mamey sapote [21]. The behavior of ɛ′ for strawberries (decreasing with increasing temperature) was also observed in bananas measured at 2450 MHz by Sipahioglu and Barringer [29], with higher decreasing at higher temperatures, from 60 to 130°C.

 The “U” shape for dielectric loss factor when plotted versus frequency, was also reported for other fruits (guava fruit, prickly pear and mamey sapote [21]), and explained by Ryynänen [3], due to the influence of conductivity losses at low frequencies, but increasing ɛ″ at higher frequencies due to dipolar relaxations. Loss factor at 915 MHz from 20 to 60°C for blackberries were from 16.42 to 16.63, raspberries 16.39 to 16.90, and strawberries from 12.19 to 14.80. These berries’ values were higher than the reported for apples (8.5–10) [27] and prickly pears (8.2 to 10.8) [21], similar than mangoes (13.8 to 17.5) [28], but lower than cherries (16.4–20.4) and oranges (16.5 to 18.4) [27]. At 2450 MHz and 60°C, the ɛ″ values of berries were from 11.23 to 15.39, being higher than the reported for apples at same frequency and temperature, with values of 7 [29]. The results are related with higher moisture content of the berries (88 to 90%, w.b.) in comparison with the moisture content of the measured apples (84.89%).

 At 915 MHz, the penetration depth was about 2.5 and 3.6 cm, with a good penetration of the microwaves into the berries, taking account the small size of these fruits. With the d _p falling with increasing frequency, the effect of microwaves at 5800 MHz would be only on the surface of the berries, as the penetration reach only 0.27–0.42 cm inside the product.

 The penetration depth calculated for berries at 915 MHz at 20°C (2.7 cm for blackberry and raspberry, and 3.56 cm for strawberry) is very similar to the reported by cherry at same frequency and temperature, with a d _p value of 2.8 cm [27]. Both berries and cherries are red fruits highly appreciated for their sensory characteristics.

 These penetration depth results show that 915 and 2450 MHz frequencies are useful for microwave-based disinfestation and drying processes. For example, at 2450 MHz, a drying bed should not be higher than 1 cm for berries, in order to assure the penetration of the waves and provoke the evaporation of the moisture in the berries. Another case would be the continuous microwave pasteurization of berries’ purees at 915 MHz; the holding tube could be 5.2 cm of internal diameter to have effective microwave penetration and subsequent heating in blackberries and raspberries. Even a 6.28 cm diameter tube could be used for strawberry purees, as its penetration depth was deeper. Other applications, such as avoiding decay promoted by molds, could be carried out, as molds grow in the surface of the berries and the microwaves will easy penetrate the surface of the berries at high temperatures (40–60°C) in order to inactivate the microorganism.

 The presented dielectric properties and penetration depth values for berries from “El Bajío” contribute to the characterization of these emblematic crops in the region of Guanajuato, Mexico. Also, the results are important to develop new processes based on microwaves, which will enhance and preserve the valuable characteristics of these fruits.

Conflict of interest

The authors have no conflict of interest to report.