# Effect of Drying on Lettuce Leaves Using Indirect Solar Dryer Assisted with Photovoltaic Cells and Thermal Energy Storage

^{1}

^{2}

^{*}

## Abstract

**:**

^{−1}, and process time ~10.0 h. Fifteen drying models were adjusted to the experimental data obtained; three models with maximum values of coefficient of determination (R

^{2})—Page, Midilli, and Kucuk, and Weibull Distribution, whose values of R

^{2}≥ 0.998, and other statistical parameters, χ

^{2}, SSE, and RMSE values closer to zero were chosen. The initial browning index BI = 120.5 ± 0.7 decreased compared to the dry sample BI = 78.99 ± 0.5, with chromatic coordinate degradations a* and b*; but not the luminosity L*; where ΔE = 8.26; whose meaning is that the dry sample is a “more opaque brownish color” due to the difference in the chroma ΔC = 6.65, and with a change from the yellow-green to yellow-red zone, and a difference in hue angle, Δh° = 14.27, between the fresh and the dried sample. D

_{eff}values for shredded lettuce leaves were 1.8 × 10

^{−9}m

^{2}s

^{−1}for values ≤ 52 °C.

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Material

#### 2.2. Solar Drying Equipment

#### 2.3. Experimental Procedures

^{−1}; (d) inlet drying air temperature ≤ 60 °C; the drying process was conducted using the pilot solar dryer in the beginning summer in the southern hemisphere, December 2016–January 2017, with air temperatures in the environment between 17.0 and 23.0 °C over a one-day drying cycle, under relative humidity between 60.5 and 82.7%, with solar radiation changing between 8.25 and 8.74 kWh/m

^{2}in Antofagasta, Chile. In each of the drying chambers of the equipment, 350 to 440 g in weight of fresh shredded lettuce leaves were placed and uniformly distributed in the three trays at the beginning of the drying process, and the thickness of the thin layer was less than 10 mm. Every 20 min during the drying period, the weight of the three trays in each drying chamber was determined using a digital balance (0.05 g precision) (Radwag, WLC model 20/A2, Radom, Poland) coupled to them. The drying process was continued until the moisture content remained constant.

#### 2.4. Drying Curves

#### 2.5. Calculations for Determining the Drying Curves and Drying Rate

_{o}), both given in grams, which is known as moisture ratio ($\frac{M}{{M}_{o}}$) versus time. The moisture content (g water/g dry solids) was determined using the following equation:

_{o}: the initial weight of sample (g); W: amount of evaporated water (g); W

_{1}: the dry matter content of the sample (g). The moisture ratio (MR) was simplified to ($\frac{M}{{M}_{o}}$), being M

_{o}initial moisture content in the initial time = 0 in place of $\frac{\left(M-{M}_{e}\right)}{\left({M}_{o}-{M}_{e}\right)}$, for mathematical modeling of the solar drying curves due to the continuous fluctuation of the relative humidity of the drying air during the solar drying process [21].

#### 2.6. Modeling of Drying Curves

#### 2.7. Color Analysis

#### 2.8. Calculation of Effective Moisture Diffusivity

_{eff}is the effective diffusivity (m

^{2}·s

^{−1}), L is the half-thickness of the lettuce leaves (L = 0.00075 m), and n is a positive integer, also called the Fourier’s series number. Simplified by taking the first term of the series solution:

_{eff}value was calculated from Equation (11) as follows Equation (12):

#### 2.9. Statistical Analysis

^{2}, SSE, RMSE and, χ

^{2}, were used to determine the goodness of fit of the drying curves of the fifteen models studied. The determination coefficient (R

^{2}) was the primary criterion for selecting the most suitable equation to describe the drying curves of shredded lettuce leaves in the solar dryer [40]. In addition, other statistical parameters were used to compare the goodness of fit of the drying models with the experimental data, these being the standard error of estimated (SEE), which provides information on the long-term performance of the correlations by allowing a comparison of the actual deviation between predicted and measured values term by term; the root mean square error (RMSE) which provides information on the short term performance and, reduced the Chi-square (χ

^{2}) is the mean square of the deviations between the experimental and predicted moisture levels. The closest values to 1.0 for R

^{2}and those closest to zero for SSE, RMSE, and χ

^{2}are commonly regarded as the optimal criterion to evaluate the goodness of fit of the models used [28,41,42]. The Equations (13)–(16) for these statistical parameters are:

_{exp,i}stands for the experimental moisture ratio found in any measurement; MR

_{pre,i}predicted moisture ratio for this measurement; N, the total number of observations; n, number of constants [40,42].

^{2}≥ 0.998; χ

^{2}≤ 0.00025, SSE ≤ 0.00020, and RSME ≤ 0.0140.

## 3. Results and Discussion

#### 3.1. Drying Characteristics

#### 3.1.1. Drying Curve

#### 3.1.2. Drying Rate Curve

_{o}) of 17.16 g water/g dry solid, until reaching a moisture value of 16.45 g water/g dry solid at 60 min into the process where it arrives at an average drying rate of 0.0467 g water/g dry solid * min. At this stage, the air temperature reached mean values of 35.2 and 32.2 °C, chamber 1 and 2, respectively (Figure 2). From there the period of constant drying rate began to reach 280 min, remaining practically constant with average values of 0.0486 g water/g dry solid * min, and a mean value at the end of this stage for moisture content of 6.06 g water/g dry solid; this point in the curve is called critical moisture (M

_{crít.}), this trajectory passed during 220 min; that is, 3 h and 40 min. It is at this point that the falling rate period begins, and the drying rate will progressively fall until equilibrium, reaching average values of 0.00012 g water/g dry solid * min and a final moisture, called equilibrium moisture (M

_{eq}), with average values of 0.11 g water/g dry solid (Figure 3).

#### 3.2. Modeling of Drying Curves Statistical Parameters

^{2}, SSE, RMSE and R

^{2}, which were used to determine the goodness of fit of the drying curves of the fifteen models studied [40,42]. The criteria used for selecting the best fitting model was based primarily on the coefficient of determination (R

^{2}) with values closer to 1.0, and values closer to zero for χ

^{2}, SSE, and RMSE. Thus, the best fit model, according to the thermal history displayed in the process drying curve for the group of the three models derived from Newton’s law of cooling, Newton, Page, and Modified Page, was the Page model with values to R

^{2}, χ

^{2}, SSE, and RMSE of 0.9989, 1.49 × 10

^{−4}, 1.40 × 10

^{−4}, and 0.01182, respectively. The values of the kinetic constant (k), and the empirical parameter (n) were: 1.53 × 10

^{−5}min

^{−1}, and 1.98128, respectively. Amongst the tested models for the group of the nine models derived from Fick’s second law of diffusion, Henderson and Pabis, Modified Henderson and Pabis, Logarithm, Approach of diffusion, Midilli and Kucuk, Two-Term, Two-Term Exponential, Aghbashlo, and Verma models, the one with the best fit was that Midilli and Kucuk model with values to R

^{2}, χ2, SSE, and RMSE of 0.9988, 1.70 × 10

^{−4}, 1.48 × 10

^{−4}, and 0.01217, respectively; with empirical constants a, b, and n of, 1.00374, −1.92 × 10

^{−5}, 1.91162 and the kinetic constant (k) of 2.22 × 10

^{−5}min

^{−1}, respectively.

^{2}, χ

^{2}, SSE, and RMSE of 0.9985, 2.15 × 10

^{−4}, 1.87 × 10

^{−4}, and 0.01368, respectively; being the empirical constants a, b, and n of 1.01587, 0.00075, 1.88817 and the kinetic constant (k) of 2.60 × 10

^{−5}min

^{−1}, respectively (Table 2).

#### 3.3. Model Validation

^{1.98128})

^{1.91162}) + (−0.0000192 t)

^{1.88817})

#### 3.4. Chromatic Coordinates

#### 3.5. Effective Moisture Diffusivity (D_{eff})

_{eff}values of shredded lettuce leaves obtained from Equation (15) is shown in Figure 7 in which the ln (MR) is related to the drying time in order to obtain the slope K and from there perform the D

_{eff}determination.

_{eff}value for shredded lettuce leaves of 1.8 × 10

^{−9}m

^{2}·s

^{−1}was reached for temperature values ≤ 52 °C. D

_{eff}values for lettuce leaves has not been found in the literature, but the following values have been reported for other vegetable leaves in thin-layer drying for vegetable waste (as a mixture of lettuce and cauliflower leaves) from the wholesale market for a temperature range of 50–150 °C, D

_{eff}values varied from 6.03 × 10

^{−9}to 3.15 × 10

^{−8}m

^{2}s

^{−1}[19], demonstrating that D

_{eff}values are higher with increasing temperature. In the present solar dryer indirect, although the shredded lettuce leaves were subjected to a constant airspeed (1 m·s

^{−1}), its temperature throughout the drying process was rising, starting at 25 °C until reaching a maximum of 51.7 and ending at 41 °C, so that the value of the D

_{eff}is the result of a mean value obtained by fitting the function shown in Figure 7 to a straight line.

_{eff}values correspond to similar values obtained for other green leaves vegetables, herbs, and aromatic plants, for example, the thin-layer drying behavior of mint leaves for a temperature range of 35–60 °C, the D

_{eff}varied from 3.07 × 10

^{−9}to 1.94 × 10

^{−8}m

^{2}s

^{−1}and increased with the air temperature [54,55]. In another study on the thin layer drying of mint leaves [55,56], D

_{eff}values between 1.23 × 10

^{−10}and 2.66 × 10

^{−10}m

^{2}s

^{−1}were reported for a temperature range of 45 to 65 °C. Doymaz et al. [56,57] determined that the D

_{eff}values for 50, 60 and 70 °C were 6.69 × 10

^{−10}; 9.205 × 10

^{−10}, 1.434 × 10

^{−9}m

^{2}s

^{−1}for dill leaves, and 9.0 × 10

^{−10}, 1.36 × 10

^{−9}, 2.35 × 10

^{−9}m

^{2}s

^{−1}for parsley leaves, respectively.

## 4. Conclusions

## Supplementary Materials

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Schematic representation of the indirect solar dryer assisted with photovoltaic cells and with the thermal energy storage unit. (1) Three photovoltaic cells, (2) voltage controller, (3) electrical switches board, (4) battery, (5) heat exchanger air-water, (6) digital balance, (7) drying chamber # 2, (8) window for entry and exit of air dryer, (9) drying chamber # 1; (10) digital balance, (11) (12) solar collectors for water (U-pipe), (13) hydro-pneumatic tank water with inner membrane for thermal energy storage (with external insulation), (14) water pump, (15) variable speed drive for airflow, (16) water pump, (17) variable speed fan.

**Figure 2.**Relationship between the moisture ratio and the drying time and the air temperature versus drying time for the two drying chambers and heat exchanger outlet (mean values of the three runs performed).

**Figure 5.**Validation of experimental and predicted moisture ratio values from the Midilli and Kucuk model.

**Figure 6.**Validation of experimental and predicted moisture ratio values from the Weibull Distribution model.

N° | Model Name | Model | References |
---|---|---|---|

Models derived from Newton’s law of cooling | |||

1 | Newton | MR = exp (−k t) | [23] |

2 | Page | MR = exp (−k t ^{n}) | [24] |

3 | Modified Page I | MR = exp (−k t)^{n} | [25] |

Models derived from Fick’s second law of diffusion | |||

4 | Henderson and Pabis | MR = a exp (−k t) | [26] |

5 | Modified Henderson and Pabis. | MR = a exp (−k t) + b exp (−g t) + c exp (−h t) | [27] |

6 | Logarithmic | MR = a exp (−k t) + c | [28] |

7 | Approximation of diffusion | MR = a exp (−k t) + (1−a) exp (−k b t) | [28] |

8 | Midilli and Kucuk | MR = a exp (–k t ^{n}) + b t | [29] |

9 | Two Term | MR = a exp (−k_{0} t)+ b exp (−k_{1} t) | [30] |

10 | Two Term exponential | MR = a exp (−k t) + (1−a) exp (−k a t) | [31] |

11 | Aghbashlo Model | MR = exp (−(k_{1} t)/(1 + k_{2} t)) | [32] |

12 | Verma Model | MR = a exp(−k t) + (1−a) exp(−g t) | [33] |

Empirical models | |||

13 | Wang and Sing | MR = 1 + a t + b t^{2} | [34] |

14 | Thompson | MR = exp ((−a −(a^{2} + 4 b t)^{0.5})/2b) | [35] |

15 | Weibull Distribution | MR = a − b exp (− k t ^{n}) | [36] |

^{−1}), n and a: empirical parameters (dimensionless); t: drying time (min); b, c, g, h, k

_{o}, k

_{1}, and k

_{2}: empirical constants in the drying models [37].

**Table 2.**Statistical results from modeling the moisture content and drying time for shredded lettuce leaves.

N° | Models | Coefficients | R^{2} | χ2 | SSE | RMSE | |||||
---|---|---|---|---|---|---|---|---|---|---|---|

1 | Newton | k = 3.85 × 10^{−3} | 0.8995 | 1.32 × 10^{−2} | 1.28 × 10^{−2} | 0.11302 | |||||

2 | Page | k = 1.53 × 10^{−5} | n = 1.98128 | 0.9989 | 1.49 × 10^{−4} | 1.40 × 10^{−4} | 0.01182 | ||||

3 | Modified Page | k = 9.61 × 10^{−3} | n = 0.40023 | 0.8995 | 1.37 × 10^{−2} | 1.28 × 10^{−2} | 0.11203 | ||||

4 | Henderson and Pabis | a = 1.20453 | k = 4.58 × 10^{−3} | 0.9385 | 8.36 × 10^{−3} | 7.82 × 10^{−3} | 0.08842 | ||||

5 | Modified Henderson & Pabis | a = 0.26382 | b = 0.26382 | c = 0.67678 | k = 4.56 × 10^{−3} | g = 4.56 × 10^{−3} | h = 4.58 × 10^{−3} | 0.9385 | 9.70 × 10^{−3} | 7.82 × 10^{−3} | 0.08842 |

6 | Logarithm | a = 1.60883 | c = −0.48434 | k = 2.27 × 10^{−3} | 0.9781 | 3.08 × 10^{−3} | 2.79 × 10^{−3} | 0.05277 | |||

7 | Approach of diffusion | a = −119.017 | b = 0.98918 | k = 9.31 × 10^{−3} | 0.9908 | 1.29 × 10^{−3} | 1.17 × 10^{−3} | 0.03414 | |||

8 | Midilli and Kucuk | a = 1.00374 | b = −1.92 × 10^{−5} | n = 1.91162 | k = 2.22 × 10^{−5} | 0.9988 | 1.70 × 10^{−4} | 1.48 × 10^{−4} | 0.01217 | ||

9 | Two Term | a = 12.7062 | b = −11.7499 | k = 8.93 × 10^{−3} | k_{1} = 9.99 × 10^{−3} | 0.9915 | 1.24 × 10^{−3} | 1.08 × 10^{−3} | 0.03284 | ||

10 | Two Term Exponential | a = 2.23266 | k = 6.67 × 10^{−3} | 0.9868 | 1.85 × 10^{−3} | 1.67 × 10^{−3} | 0.04093 | ||||

11 | Aghbashlo | k_{1} = 1.85 × 10^{−3} | k_{2} = −1.66 × 10^{−3} | 0.9928 | 9.80 × 10^{−4} | 9.17 × 10^{−4} | 0.03028 | ||||

12 | Verma | a = 14.6651 | k = 8.05 × 10^{−4} | g = 6.71 × 10^{−4} | 0.9650 | 4.93 × 10^{−3} | 4.45 × 10^{−3} | 0.06671 | |||

13 | Wang and Sing | a = −2.64 × 10^{−3} | b = 1.42 × 10^{−6} | 0.9678 | 4.37 × 10^{−3} | 4.09 × 10^{−3} | 0.06396 | ||||

14 | Thompson | a = −180.062 | b = 0.41438 | 0.9378 | 2.76 × 10^{−2} | 2.58 × 10^{−2} | 0.16060 | ||||

15 | Weibull Distribution | a = 1.01587 | b = 0.00746 | k = 2.60 × 10^{−5} | n = 1.88817 | 0.9985 | 2.15 × 10^{−4} | 1.87 × 10^{−4} | 0.01368 |

**Table 3.**Chromatic Coordinates of Lettuce in Fresh (n = 10) and after Drying process (n = 20). Color Difference (ΔE), Ratio of redness over yellowness (R), and Browning Index (BI) (n = 3), fresh and after the drying process.

Chromatic Coordinates and Others Parameters | Samples | |
---|---|---|

Fresh | Dried | |

L* | 27.97 ± 0.05 ^{a} | 28.92 ± 0.71 ^{a} |

a* | −4.5 ± 0.07 ^{a} | 0.8 ± 0.13 ^{b} |

b* | 22.27 ± 0.10 ^{a} | 16.5 ± 0.32 ^{b} |

ΔE | - | 8.26 ± 0.18 |

R =$\frac{{\mathit{a}}^{\mathbf{*}}}{{\mathit{b}}^{\mathbf{*}}}$ | −0.20 ± 0.00 ^{a} | 0.05 ± 0.01 ^{b} |

h° | 101.43 ± 0.15 ^{a} | 87.16 ± 0.41 ^{b} |

C | 22.72 ± 0.11 ^{a} | 16.07 ± 0.32 ^{b} |

BI | 120.50 ± 0.70 ^{a} | 78.99 ± 0.50 ^{b} |

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**MDPI and ACS Style**

Cerezal Mezquita, P.; Álvarez López, A.; Bugueño Muñoz, W.
Effect of Drying on Lettuce Leaves Using Indirect Solar Dryer Assisted with Photovoltaic Cells and Thermal Energy Storage. *Processes* **2020**, *8*, 168.
https://doi.org/10.3390/pr8020168

**AMA Style**

Cerezal Mezquita P, Álvarez López A, Bugueño Muñoz W.
Effect of Drying on Lettuce Leaves Using Indirect Solar Dryer Assisted with Photovoltaic Cells and Thermal Energy Storage. *Processes*. 2020; 8(2):168.
https://doi.org/10.3390/pr8020168

**Chicago/Turabian Style**

Cerezal Mezquita, Pedro, Aldo Álvarez López, and Waldo Bugueño Muñoz.
2020. "Effect of Drying on Lettuce Leaves Using Indirect Solar Dryer Assisted with Photovoltaic Cells and Thermal Energy Storage" *Processes* 8, no. 2: 168.
https://doi.org/10.3390/pr8020168