# Influence of Different Hot Air Drying Temperatures on Drying Kinetics, Shrinkage, and Colour of Persimmon Slices

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Raw Materials

#### 2.2. Drying Experiments

_{t}/M

_{0}) vs. time (min), where M

_{t}was the moisture content (kg water/kg db) at a certain drying time and M

_{0}(kg water/kg db) was its initial value [9].

#### 2.3. Modelling of Drying Kinetics

_{t}/M

_{0}vs. time) at each investigated temperature. Nonlinear least square regression analysis was applied for the determination of the selected models’ parameters with the Levenberge–Marquardt procedure. For each model, the goodness of fit was assessed based upon the values of the following statistical parameters: the coefficient of determination (R

^{2}), the root mean square error (RMSE), and the reduced χ-square (χ

^{2}) [1,8,20,22].

_{R,exp,i}and M

_{R,pre,i}are experimental and predicted dimensionless moisture ratios, respectively, N is the number of observations, and z is the number of constants. The χ

^{2}is the mean square of the deviations between the experimental and calculated values for the models. The lower the value of χ

^{2}, the better the goodness of the fit. The RMSE explains the deviation between the predicted and experimental values and it is necessary to reach zero.

^{2}was used as the primary comparison criteria for choosing the best model to consider the variation in the drying curves of dried fruits [1]. Its value should be higher and close to one. In addition to R

^{2}, χ

^{2}and RMSE parameters were used to determine the quality of the fit [1,8,22]. The higher the value of R

^{2}, the lower the values of χ

^{2}and RMSE, which were chosen as the criteria for goodness of fit [1,8,19].

#### 2.4. Colour Evaluation

#### 2.5. Shrinkage Evaluation and Empirical Models

_{0}) was determined by using a digital Vernier caliper (0.01 mm accuracy), and it was calculated from diameter and thickness measurements for each slab (about 20 slices). The thickness and diameter dimensions were measured on the same slabs at specific times during drying tests, and the volume (V

_{t}) was calculated. Furthermore, the diameter and the thickness were measured at different sample positions to minimize the measurement error during drying, and their average values were estimated. The evaluation of shrinkage during drying was studied in terms of the mean volume shrinkage (V

_{t}/V

_{0}) reported as a function of the relative moisture ratio (M

_{t}/M

_{0}) [24].

#### 2.6. Statistical Analysis

## 3. Results and Discussion

#### 3.1. Drying Kinetics: Experiments and Empirical Models

_{t}/M

_{0}vs. drying time (min) are presented in Figure 2a–e. It was clear that the moisture content decreased with increased drying time. As shown in Figure 2, the changes in moisture content at all investigated temperatures were more evident in the first drying stage; while at the final stage these changes became very small.

^{2}), the reduced χ-square (χ

^{2}), and the root mean square error (RMSE) were used to describe the quality of the fit (Table 3). A good fitting among the experimental and theoretical data was connected to the highest R

^{2}value and the lowest χ

^{2}and RMSE values.

^{2}values of Enderson and Pabis, Page, Logarithmic, and Two term models were higher than 0.99, while χ

^{2}and RMSE ranged from 0.0001 to 0.0015 and 0.0069 to 0.0382, respectively.

_{1}and k

_{2}) had a value of 0.009 to 0.017 and these values increased with an increase in drying temperature.

^{2}values and the lowest χ

^{2}and RMSE values. On the other hand, the Two term model had the worst fitting for persimmon slabs dried in the range 45–65 °C.

#### 3.2. Colour Evaluation

#### 3.3. Shrinkage and Empirical Models

_{t}/V

_{0}) as a function of the moisture ratio (M

_{t}/M

_{0}) are presented in Figure 3a–e.

^{2}and RMSE) and the estimated model parameters are reported in Table 6 and Table 7, respectively.

^{2}values of the Linear, Quadratic, and Exponential models were all above 0.90. The estimations of statistical parameters demonstrated that R

^{2}and RMSE values ranged from 0.8992 to 0.99898, and 0.0103 to 0.1002, respectively (Table 6). The nonlinear model (Quadratic model) predicted the changes in the shrinkage of the persimmon slices significantly better than did the Linear and Exponential models for all drying conditions. Under the most ideal condition, the shrinkage is expressed as a linear function of the moisture ratio where a

_{1}and a

_{2}are coefficient and constant, respectively, of the model. On the contrary, in this study, the Linear model was found to be an inappropriate model for describing the persimmon shrinkage vs. moisture ratio at all investigated temperatures. Also, the volume ratio V

_{t}/V

_{0}and moisture ratio M

_{t}/M

_{0}had a poor exponential relationship for all hot air dried persimmon slabs, with the lowest value of R

^{2}(0.899) at 55 °C and the lowest value of the slope of this model, k, at 65 °C (Table 7).

^{2}values and the lowest RMSE values.

^{2}> 0.994) with the experimental data.

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**(

**a**) Whole persimmon fruit, cv. “Rojo Brillante”; (

**b**) Internal view of the persimmon fruit, cv. “Rojo Brillante”.

**Figure 2.**Experimental (symbols) and predicted (lines) drying curves in terms of moisture ratio (M

_{t}/M

_{0}) of persimmon samples at (

**a**) 45 °C, (

**b**) 50 °C, (

**c**) 55 °C, (

**d**) 60 °C, and (

**e**) 65 °C

**Figure 3.**Experimental data (symbols) and prediction (curves) of volume shrinkage in terms of volume ratio (V

_{t}/V

_{0}) of persimmon samples during drying at (

**a**) 45 °C, (

**b**) 50 °C, (

**c**) 55 °C, (

**d**) 60 °C, and (

**e**) 65 °C.

Model Name | Equation | Reference |
---|---|---|

Henderson and Pabis | $\frac{{M}_{t}}{{M}_{0}}=aexp\left(-kt\right)$ | Henderson and Pabis [19] (1961); Adiletta et al. [8] 2016 |

Page | $\frac{{M}_{t}}{{M}_{0}}=exp\left(-k{t}^{n}\right)$ | Doymaz [1] (2012); Adiletta et al. [8] 2016 |

Logarithmic | $\frac{{M}_{t}}{{M}_{0}}=aexp\left(-kt\right)+c$ | Yagcioglu et al. [20] (1999) |

Two term | $\frac{{M}_{t}}{{M}_{0}}={a}_{1}exp\left(-{k}_{1}t\right)+{a}_{2}exp\left(-{k}_{2}t\right)$ | Henderson [21] (1974); Adiletta et al. [22] 2018 |

Model Name | Equation | References |
---|---|---|

Linear | $\frac{{V}_{t}}{{V}_{0}}={a}_{1}+{a}_{2}\left(\frac{{M}_{t}}{{M}_{0}}\right)$ | Simal et al. [26] |

Quadratic | $\frac{{V}_{t}}{{V}_{0}}={a}_{1}+{a}_{2}\left(\frac{{M}_{t}}{{M}_{0}}\right)+{a}_{3}{\left(\frac{{M}_{t}}{{M}_{0}}\right)}^{2}$ | Mayor and Sereno [25] |

Exponential | $\frac{{V}_{t}}{{V}_{0}}={a}_{1}exp\left(k\frac{{M}_{t}}{{M}_{0}}\right)$ | Mayor and Sereno [25] |

**Table 3.**Statistical parameters (coefficient of determination R

^{2}, the root mean square error RMSE, the reduced χ-square χ

^{2}) of the drying models.

Model Name | Parameters | Temperatures (°C) | ||||
---|---|---|---|---|---|---|

45° | 50° | 55° | 60° | 65° | ||

Henderson and Pabis | R^{2} | 9.9 × 10^{−1} | 1.0 × 10^{0} | 1.0 × 10^{0} | 1.0 × 10^{0} | 1.0 × 10^{0} |

RMSE | 3.3 × 10^{−2} | 1.5 × 10^{−2} | 1.6 × 10^{−2} | 1.4 × 10^{−2} | 1.8 × 10^{−2} | |

χ^{2} | 1.1 × 10^{−3} | 3.0 × 10^{−4} | 3.0 × 10^{−4} | 2.0 × 10^{−4} | 3.0 × 10^{−4} | |

Page | R^{2} | 1.0 × 10^{0} | 1.0 × 10^{0} | 1.0 × 10^{0} | 1.0 × 10^{0} | 1.0 × 10^{0} |

RMSE | 2.3 × 10^{−2} | 9.3 × 10^{−3} | 1.2 × 10^{−2} | 6.9 × 10^{−3} | 7.1 × 10^{−3} | |

χ^{2} | 4.0 × 10^{−4} | 1.0 × 10^{−4} | 1.0 × 10^{−4} | 1.0 × 10^{−4} | 1.0 × 10^{−4} | |

Logarithmic | R^{2} | 9.9 × 10^{−1} | 1.0 × 10^{0} | 1.0 × 10^{0} | 1.0 × 10^{0} | 1.0 × 10^{0} |

RMSE | 2.8 × 10^{−2} | 1.1 × 10^{−2} | 1.4 × 10^{−2} | 1.5 × 10^{−2} | 1.9 × 10^{−2} | |

χ^{2} | 8.0 × 10^{−4} | 2.0 × 10^{−4} | 2.0 × 10^{−4} | 2.0 × 10^{−4} | 4.0 × 10^{−4} | |

Two term | R^{2} | 9.9 × 10^{−1} | 1.0 × 10^{0} | 1.0 × 10^{0} | 1.0 × 10^{0} | 1.0 × 10^{0} |

RMSE | 3.8 × 10^{−2} | 1.8 × 10^{−2} | 2.0 × 10^{−2} | 1.8 × 10^{−2} | 2.3 × 10^{−2} | |

χ^{2} | 1.5 × 10^{−3} | 4.0 × 10^{−4} | 4.0 × 10^{−4} | 3.0 × 10^{−4} | 5.0 × 10^{−4} |

**Table 4.**Model parameters (k, k

_{1}and k

_{2}, the drying constants; a, a

_{1}, a

_{2}, c, n, the drying coefficients) of the drying models.

Model Name | Parameters | Temperatures (°C) | ||||
---|---|---|---|---|---|---|

45° | 50° | 55° | 60° | 65° | ||

Henderson and Pabis | a | 1.0 × 10^{0} | 1.0 × 10^{0} | 1.0 × 10^{0} | 1.0 × 10^{0} | 1.0 × 10^{0} |

k | 9.2 × 10^{−3} | 9.7 × 10^{−3} | 1.4× 10^{−2} | 1.6 × 10^{−2} | 1.7 × 10^{−2} | |

Page | k | 3.2 × 10^{−3} | 6.0 × 10^{−3} | 8.0 × 10^{−3} | 8.8 × 10^{−3} | 6.7 × 10^{−2} |

n | 1.2 × 10^{0} | 1.1 × 10^{0} | 1.1 × 10^{0} | 1.1 × 10^{0} | 1.2 × 10^{0} | |

Logarithmic | a | 1.0 × 10^{0} | 1.0 × 10^{0} | 1.0 × 10^{0} | 1.0 × 10^{0} | 1.0 × 10^{0} |

k | 8.4 × 10^{−3} | 9.2 × 10^{−3} | 1.3 × 10^{−2} | 1.6 × 10^{−2} | 1.6 × 10^{−2} | |

c | −3.3 × 10^{−2} | −2.0 × 10^{−2} | −1.5 × 10^{−2} | −6.1 × 10^{−3} | −8.1 × 10^{−3} | |

Two term | a_{1} | 5.2 × 10^{−1} | 5.1 × 10^{−1} | 5.1 × 10^{−1} | 5.1 × 10^{−1} | 5.1 × 10^{−1} |

k_{1} | 9.2 × 10^{−3} | 9.7 × 10^{−3} | 1.4 × 10^{−2} | 1.6 × 10^{−2} | 1.7 × 10^{−2} | |

a_{2} | 5.0 × 10^{−1} | 5.0 × 10^{−1} | 5.0 × 10^{−1} | 4.9 × 10^{−1} | 4.9 × 10^{−1} | |

k_{2} | 9.2 × 10^{−3} | 9.7 × 10^{−3} | 1.4 × 10^{−2} | 1.6 × 10^{−2} | 1.7 × 10^{−2} |

**Table 5.**Colour parameters (lightness/darkness L*; redness/greenness a*; yellowness/blueness b*; Hue angle H°; total colour difference ΔE) for fresh and dried persimmon samples.

Sample | Drying Time (min) | L* | a* | b* | H° | ΔE |
---|---|---|---|---|---|---|

fresh persimmon | 71.7 ± 0.5 ^{a} | −1.6 ± 1.3 ^{a} | 46.4 ± 1.1 ^{a} | 92.0 ± 1.6 ^{c} | - | |

persimmon dried at 45 °C | 540 | 67.8 ± 1.8 ^{a} | 5.9 ± 1.5 ^{d} | 53.6 ± 2.0 ^{b} | 83.6 ± 0.0 ^{a} | 18.9 ± 1.1 ^{c} |

persimmon dried at 50 °C | 465 | 68.7 ± 2.4 ^{a} | 5.6 ± 0.3 ^{c,d} | 53.3 ± 1.1 ^{b} | 84.0 ± 0.4 ^{a} | 13.7 ± 0.7 ^{b} |

persimmon dried at 55 °C | 420 | 67.4 ± 2.5 ^{a} | 2.6 ± 1.1 ^{b} | 57.7 ± 2.4 ^{b} | 87.4 ± 1.1 ^{a,b} | 12.8 ± 1.0 ^{b} |

persimmon dried at 60 °C | 360 | 70.5 ± 1.9 ^{a} | 3.0 ± 0.9 ^{b,c} | 56.2 ± 1.1 ^{b} | 87.0 ± 1.0 ^{a,b} | 12.1 ± 0.7 ^{b} |

persimmon dried at 65 °C | 320 | 70.3 ± 0.8 ^{a} | 1.9 ± 0.8 ^{b} | 55.7 ± 4.0 | 88.0 ± 1.6 ^{b} | 9.2 ± 0.4 ^{a} |

Model Name | Parameters | Temperatures | ||||
---|---|---|---|---|---|---|

45 | 50 | 55 | 60 | 65 | ||

Linear | R^{2} | 1.0 × 10^{0} | 9.9 × 10^{−1} | 9.7 × 10^{−1} | 1.0 × 10^{0} | 9.9 × 10^{−1} |

RMSE | 2.0 × 10^{−2} | 3.0 × 10^{−2} | 5.2 × 10^{−2} | 1.3 × 10^{−2} | 2.9 × 10^{−2} | |

Quadratic | R^{2} | 1.0 × 10^{0} | 9.9 × 10^{−1} | 9.9 × 10^{−1} | 1.0 × 10^{0} | 1.0 × 10^{0} |

RMSE | 1.0 × 10^{−2} | 2.4 × 10^{−2} | 2.7 × 10^{−2} | 1.3 × 10^{−2} | 1.9 × 10^{−2} | |

Exponential | R^{2} | 9.7 × 10^{−1} | 9.8 × 10^{−1} | 9.0 × 10^{−1} | 9.8 × 10^{−1} | 9.5 × 10^{−1} |

RMSE | 4.9 × 10^{−2} | 4.4 × 10^{−2} | 1.0 × 10^{−1} | 5.7 × 10^{−2} | 6.7 × 10^{−2} |

**Table 7.**Model parameters (k, the shrinkage constant; a

_{1}, a

_{2}, a

_{3}, the shrinkage coefficients) of the shrinkage models.

Model Name | Parameters | Temperatures | ||||
---|---|---|---|---|---|---|

45 | 50 | 55 | 60 | 65 | ||

Linear | a_{1} | 1.6 × 10^{−1} | 1.8 × 10^{−1} | 2.3 × 10^{−1} | 1.6 × 10^{−1} | 2.6 × 10^{−1} |

a_{2} | 8.1 × 10^{−1} | 7.9 × 10^{−1} | 8.2 × 10^{−1} | 8.3 × 10^{−1} | 7.9 × 10^{−1} | |

Quadratic | a_{1} | 1.6 × 10^{−1} | 1.9 × 10^{−1} | 2.1 × 10^{−1} | 1.7 × 10^{−1} | 2.5 × 10^{−1} |

a_{2} | 6.5 × 10^{−1} | 6.0 × 10^{−1} | 1.2 × 10^{0} | 7.7 × 10^{−1} | 1.0 × 10^{0} | |

a_{3} | 1.8 × 10^{−1} | 2.1 × 10^{−1} | −4.5 × 10^{−1} | 6.1 × 10^{−2} | −2.4 × 10^{−1} | |

Exponential | a_{1} | 2.1 × 10^{−1} | 2.1 × 10^{−1} | 2.7 × 10^{−1} | 2.1 × 10^{−1} | 2.9 × 10^{−1} |

k | 1.6 × 10^{0} | 1.6 × 10^{0} | 1.3 × 10^{0} | 1.6 × 10^{0} | 1.3 × 10^{0} |

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**MDPI and ACS Style**

Senadeera, W.; Adiletta, G.; Önal, B.; Di Matteo, M.; Russo, P.
Influence of Different Hot Air Drying Temperatures on Drying Kinetics, Shrinkage, and Colour of Persimmon Slices. *Foods* **2020**, *9*, 101.
https://doi.org/10.3390/foods9010101

**AMA Style**

Senadeera W, Adiletta G, Önal B, Di Matteo M, Russo P.
Influence of Different Hot Air Drying Temperatures on Drying Kinetics, Shrinkage, and Colour of Persimmon Slices. *Foods*. 2020; 9(1):101.
https://doi.org/10.3390/foods9010101

**Chicago/Turabian Style**

Senadeera, Wijitha, Giuseppina Adiletta, Begüm Önal, Marisa Di Matteo, and Paola Russo.
2020. "Influence of Different Hot Air Drying Temperatures on Drying Kinetics, Shrinkage, and Colour of Persimmon Slices" *Foods* 9, no. 1: 101.
https://doi.org/10.3390/foods9010101