# Thermal and Dielectric Properties of Wolfberries as Affected by Moisture Content and Temperature Associated with Radio Frequency and Microwave Dehydrations

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

^{2}= 0.977 − 0.997) were best for fitting the dielectric constant and loss factor at four representative frequencies of 27, 40, 915, and 2450 MHz, respectively. The penetration depth increased with the decreased frequency, temperature, and moisture content, and was greater at RF frequencies than MW range, making the RF heating more effective for drying bulk wolfberries. These findings offered essential data before optimizing RF or MW dehydration protocols for wolfberries via computer simulation.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Sample Preparation

^{3}) and placed on the metal tray of a heat pump dryer (WRH-100TB1, Guangdong Weierxin Industrial Co., LTD., Guangzhou, China). The temperature and relative humidity were 60 °C and 20%, respectively, in heat pump drying. The sample weight loss was determined every half hour by taking the tray out of the drying cavity and weighing it using an electronic balance (LT1002B, Changshu Tianliang Instrument co., LTD., Changshu, China) with an accuracy of 0.01 g. The sample MC was estimated according to the original mass, initial MC, and the mass after drying [39]. The drying procedure was finished when the required MC level of wolfberries s was achieved. The dried wolfberries were transferred from the drying chamber to the desiccator immediately for cooling, which can prevent the samples from absorbing moisture in the air. The final and actual MC levels of the samples were 75.1 ± 1.3%, 59.8 ± 1.8%, 45.3 ± 1.4%, 30.3 ± 1.1%, and 15.2 ± 1.2% (w.b.), which were determined according to the AOAC Official Method 934.06 [37].

#### 2.2. Measurements of True Density

_{7}H

_{8}) [25]. For each MC level, 3.325 ± 0.052 g wolfberries were randomly chosen and weighed (w, g) as an experimental group in triplicate. After that, the samples were placed into a Lee’s pycnometer with C

_{7}H

_{8}, and the volumes (V, cm

^{3}) that were occupied by the wolfberries were estimated. The equation to determine true density (ρ, g/cm

^{3}) can be expressed as:

#### 2.3. Measurement of Thermal Properties

#### 2.4. Measurement of Dielectric Properties

_{0–9}are regression coefficients. M and T represent MC and temperature, respectively. According to results of the analysis of variance (ANOVA), the term was removed when the corresponding p > 0.05. After ignoring the insignificant terms, the final regression equations were established again.

_{p}, m) is defined as the distance where the power decreases to 1/e (e ≈ 2.718) of its amplitude entering the surface [27]. The equation to determine the penetration depth is described as:

^{8}m/s) and f is the frequency (MHz).

#### 2.5. Statistical Analysis

## 3. Results and Discussion

^{3}when the MC was raised from 15.2% to 75.1% (w.b.). This agreed with the trends that were reported by Zhu et al. [29], in which the true density of the chestnut kernel was reduced from 1430 to 1126 kg/m

^{3}as the MC was raised from 10 to 60% (w.b.). The possible reason for this phenomenon could be that the increasing rate in wolfberries volume might be higher than that in weight due to the raised moisture [25]. Meanwhile, the true density (1.193 ± 0.019 g/cm

^{3}) of wolfberries with an MC of 15.2% was significantly greater than the value (0.947 ± 0.004 or 1.147 ± 0.012 g/cm

^{3}) of the sample with an MC of 75.1% or 45.3 ± 1.4%. Since significant differences (p < 0.05) were observed among wolfberries at various moisture levels, the true density of the samples should be maintained for the determination of TPs and DPs.

#### 3.1. Thermal Properties of Wolfberries

#### 3.2. Dielectric Properties of Wolfberries

#### 3.2.1. Frequency-Dependent DPs

#### 3.2.2. Moisture Content- and Temperature-Dependent DPs

#### 3.2.3. Regression Models

^{2}) approached 1. The R

^{2}values of the fitted polynomial models of DPs for wolfberries were 0.977–0.997, indicating that these models could be capable of precisely predicting their DPs under given temperature and MC levels at four frequencies. Zhou et al. [28] also indicated that the R

^{2}of quadratic and cubic polynomial models had competent ability to fit the data of DPs in kiwifruits with different MC levels and temperatures. To determine whether independent variables had a significant effect on DPs and models, the results of the ANOVA are listed in Table 3 and Table 4. Due to the significance level of 0.0001 (p < 0.0001), it also shown that the equations fitted the experimental data well. For all models of DPs for wolfberries, the linear term of M had very strong effect on these models (p < 0.0001). Thus, these models could be used to describe the moisture- and temperature-dependent DPs of wolfberries in future computer simulations at the four specific frequencies (27, 40, 915, and 2450 MHz).

#### 3.3. Penetration Depth

_{p}that was estimated from the measured DPs of wolfberries at five MC levels, four temperatures, and four frequencies are listed in Table 5. With decreasing MC, temperature, and frequency, the d

_{p}of electromagnetic waves into the sample increased. For instance, the d

_{p}decreased from 30.74 cm to 4.50 cm at 65 °C and 27 MHz when the moisture content of wolfberries increased from 15.1% to 75.1% w.b. Similar trends of d

_{p}as influenced by these parameters have been found in previous studies [28,51]. Meanwhile, when the frequency decreased from MW frequency (2450 MHz) to RF frequency (27 MHz), the d

_{p}of wolfberries with a moisture content of 30.3% (w.b.) increased from 0.61 cm to 22.71 cm at 25 °C. Li et al. indicated that the volume heating uniformity of the sample was better during RF heating since the penetration depth of RF waves in the sample was greater than that of MW [26]. Therefore, RF drying would be used to improve heating efficiency in the future for designing drying beds or protocols for wolfberries with a large volume and high throughput.

## 4. Conclusions

^{2}= 0.977–0.997) were best for fitting DPs at four frequencies of 27, 40, 915, and 2450 MHz, respectively. The penetration depth increased with decreasing moisture content, temperature, and one at RF range was greater than that at MW frequencies, making the RF energy more effective for drying bulk wolfberries. Further studies would be focused on optimizing the efficacious dielectric drying protocols for wolfberries using an appropriate sample thickness.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Moisture content and temperature-dependent specific heat capacity (

**a**) and thermal conductivity (

**b**) of wolfberries.

**Figure 2.**Frequency-dependent dielectric constant (ε′) of wolfberries with a moisture content of 15.2% (

**a**) and 75.1% (w.b.) (

**b**).

**Figure 3.**Frequency-dependent dielectric loss factor (ε″) of wolfberries with a moisture content of 15.2% (

**a**) and 75.1% (w.b.) (

**b**).

**Figure 4.**Moisture- and temperature-dependent dielectric constant (ε′) of wolfberries at 27 (

**a**), 40 (

**b**), 915 (

**c**), and 2450 MHz (

**d**).

**Figure 5.**Moisture- and temperature-dependent dielectric loss factor (ε″) of wolfberries at 27 (

**a**), 40 (

**b**), 915 (

**c**), and 2450 MHz (

**d**).

Moisture Content (w.b.) | True Density (g/cm^{3}) |
---|---|

15.2 ± 1.2% | 1.193 ± 0.019 a * |

30.3 ± 1.1% | 1.166 ± 0.004 ab |

45.3 ± 1.4% | 1.147 ± 0.012 b |

59.8 ± 1.8% | 1.126 ± 0.042 b |

75.1 ± 1.3% | 0.947 ± 0.004 c |

**Table 2.**Regression equations of the dielectric properties of wolfberries at four representative frequencies as a function of moisture content (M, % w.b.) and temperature (T, °C).

Frequency (MHz) | Dielectric Properties | Equations |
---|---|---|

27 | ε′ = 20.64 + 0.16T − 19.81M + 0.82TM + 330.70M^{2} − 1.77M^{2}T − 227.30M^{3} | (4) |

ε″ = 212.80 − 2.44T − 1295.00M + 13.38TM + 1962.00M^{2} | (5) | |

40 | ε′ = 25.10 − 0.14T − 82.66M + 0.83TM + 495.85M^{2}−1.77M^{2}T−356.02M^{3} | (6) |

ε″ = 151.70 − 1.71T − 901.23M + 9.39TM + 1369.00M^{2} | (7) | |

915 | ε′ = −3.72 + 72.69M + 0.93TM−1.57M^{2}T + 66.77M^{3} | (8) |

ε″ = 1.54 − 0.04T + 54.95M + 0.33TM − 36.79M^{2} | (9) | |

2450 | ε′ = 30.99−276.90M + 0.91TM + 770.70M^{2}−1.67M^{2}T−438.21M^{3} | (10) |

ε″ = −5.99 + 0.05T + 78.81M − 52.21M^{2} | (11) |

**Table 3.**Analysis of variance of regressed models of Equations (4), (6), (8), and (10) for wolfberries at four frequencies relevant to dehydration.

Variance and R ^{2} | 27 MHz (Equation (4)) | 40 MHz (Equation (6)) | 915 MHz (Equation (8)) | 2450 MHz (Equation (10)) | ||||
---|---|---|---|---|---|---|---|---|

F-Value | p-Value | F-Value | p-Value | F-Value | p-Value | F-Value | p-Value | |

T | 7.246 | 0.0226 | 13.608 | 0.0042 | 0.995 | 0.3420 | 0.737 | 0.4109 |

M | 215.363 | <0.0001 | 581.503 | <0.0001 | 169.904 | <0.0001 | 119.065 | <0.0001 |

TM | 73.438 | <0.0001 | 160.598 | <0.0001 | 14.337 | 0.0036 | 5.007 | 0.0492 |

T^{2} | 0.001 | 0.9799 | 0.157 | 0.7004 | 0.063 | 0.8069 | 0.019 | 0.8922 |

M^{2} | 41.620 | <0.0001 | 116.886 | <0.0001 | 0.693 | 0.4247 | 25.166 | 0.0005 |

T^{2}M | 0.123 | 0.7335 | 0.0001 | 0.9905 | 0.041 | 0.8444 | 0.001 | 0.9765 |

TM^{2} | 12.091 | 0.0059 | 27.172 | 0.0004 | 6.431 | 0.0296 | 6.215 | 0.0318 |

T^{3} | 0.125 | 0.7307 | 0.183 | 0.6776 | 0.013 | 0.9122 | 0.020 | 0.8896 |

M^{3} | 9.251 | 0.0124 | 51.168 | <0.0001 | 25.777 | 0.0005 | 11.137 | 0.0075 |

Model | 191.722 | <0.0001 | 420.048 | <0.0001 | 91.154 | <0.0001 | 68.785 | <0.0001 |

R^{2} | 0.994 | 0.997 | 0.988 | 0.984 |

**Table 4.**Analysis of variance of regressed models of Equations (5), (7), (9), and (11) for wolfberries at four frequencies relevant to dehydration.

Variance and R ^{2} | 27 MHz (Equation (5)) | 40 MHz (Equation (7)) | 915 MHz (Equation (9)) | 2450 MHz (Equation (11)) | ||||
---|---|---|---|---|---|---|---|---|

F-Value | p-Value | F-Value | p-Value | F-Value | p-Value | F-Value | p-Value | |

T | 55.004 | <0.0001 | 117.475 | <0.0001 | 59.110 | <0.0001 | 17.160 | 0.0010 |

M | 789.362 | <0.0001 | 1199.657 | <0.0001 | 751.532 | <0.0001 | 532.508 | <0.0001 |

TM | 73.609 | <0.0001 | 73.709 | <0.0001 | 25.173 | 0.0002 | 0.277 | 0.6070 |

T^{2} | 0.077 | 0.7860 | 0.071 | 0.7938 | 0.050 | 0.8266 | 0.005 | 0.9459 |

M^{2} | 99.675 | <0.0001 | 98.608 | <0.0001 | 20.259 | 0.0005 | 45.142 | <0.0001 |

Model | 297.693 | <0.0001 | 297.904 | <0.0001 | 171.225 | <0.0001 | 119.018 | <0.0001 |

R^{2} | 0.991 | 0.991 | 0.984 | 0.977 |

**Table 5.**Penetration depth of electromagnetic waves into wolfberries at different frequencies, moisture contents, and temperatures (T, °C).

Moisture Content (% w.b.) | T (°C) | Penetration Depth (cm) | |||
---|---|---|---|---|---|

27 MHz | 40 MHz | 915 MHz | 2450 MHz | ||

15.1 | 25 | 38.84 ± 0.73 | 30.68 ± 0.59 | 2.16 ± 0.01 | 0.85 ± 0.00 |

45 | 34.36 ± 0.75 | 27.64 ± 0.42 | 2.13 ± 0.01 | 0.81 ± 0.02 | |

65 | 30.74 ± 0.87 | 25.21 ± 0.71 | 2.06 ± 0.01 | 0.79 ± 0.02 | |

85 | 25.51 ± 0.75 | 20.92 ± 0.57 | 1.99 ± 0.01 | 0.75 ± 0.01 | |

30.3 | 25 | 22.71 ± 1.38 | 18.55 ± 1.15 | 1.74 ± 0.12 | 0.61 ± 0.04 |

45 | 20.44 ± 0.24 | 16.83 ± 0.11 | 1.70 ± 0.06 | 0.60 ± 0.02 | |

65 | 18.70 ± 0.31 | 15.49 ± 0.26 | 1.56 ± 0.01 | 0.53 ± 0.00 | |

85 | 16.43 ± 0.12 | 13.73 ± 0.10 | 1.51 ± 0.00 | 0.51 ± 0.00 | |

45.3 | 25 | 11.75 ± 0.19 | 9.85 ± 0.16 | 1.33 ± 0.05 | 0.46 ± 0.02 |

45 | 9.60 ± 0.06 | 8.03 ± 0.04 | 1.31 ± 0.03 | 0.43 ± 0.01 | |

65 | 8.26 ± 0.01 | 6.87 ± 0.03 | 1.28 ± 0.02 | 0.42 ± 0.01 | |

85 | 7.52 ± 0.09 | 6.25 ± 0.09 | 1.26 ± 0.01 | 0.40 ± 0.00 | |

59.8 | 25 | 9.86 ± 0.02 | 8.37 ± 0.02 | 1.65 ± 0.02 | 0.59 ± 0.01 |

45 | 7.57 ± 0.09 | 6.32 ± 0.08 | 1.48 ± 0.01 | 0.56 ± 0.01 | |

65 | 5.97 ± 0.07 | 4.94 ± 0.06 | 1.31 ± 0.01 | 0.53 ± 0.00 | |

85 | 5.36 ± 0.18 | 4.42 ± 0.15 | 1.20 ± 0.04 | 0.48 ± 0.01 | |

75.1 | 25 | 5.80 ± 0.03 | 4.80 ± 0.02 | 1.69 ± 0.01 | 0.63 ± 0.00 |

45 | 4.97 ± 0.01 | 4.10 ± 0.01 | 1.45 ± 0.01 | 0.61 ± 0.00 | |

65 | 4.50 ± 0.02 | 3.69 ± 0.01 | 1.24 ± 0.01 | 0.56 ± 0.01 | |

85 | 4.09 ± 0.03 | 3.34 ± 0.03 | 1.06 ± 0.03 | 0.50 ± 0.01 |

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**MDPI and ACS Style**

Bai, S.; Liu, L.; Yu, H.; Guan, X.; Li, R.; Hou, L.; Ling, B.; Wang, S.
Thermal and Dielectric Properties of Wolfberries as Affected by Moisture Content and Temperature Associated with Radio Frequency and Microwave Dehydrations. *Foods* **2022**, *11*, 3796.
https://doi.org/10.3390/foods11233796

**AMA Style**

Bai S, Liu L, Yu H, Guan X, Li R, Hou L, Ling B, Wang S.
Thermal and Dielectric Properties of Wolfberries as Affected by Moisture Content and Temperature Associated with Radio Frequency and Microwave Dehydrations. *Foods*. 2022; 11(23):3796.
https://doi.org/10.3390/foods11233796

**Chicago/Turabian Style**

Bai, Shunqin, Li Liu, Haibo Yu, Xiangyu Guan, Rui Li, Lixia Hou, Bo Ling, and Shaojin Wang.
2022. "Thermal and Dielectric Properties of Wolfberries as Affected by Moisture Content and Temperature Associated with Radio Frequency and Microwave Dehydrations" *Foods* 11, no. 23: 3796.
https://doi.org/10.3390/foods11233796