# Kinetic Model of Moisture Loss and Polyphenol Degradation during Heat Pump Drying of Soursop Fruit (Annona muricata L.)

^{1}

^{2}

^{3}

^{4}

^{*}

## Abstract

**:**

^{2}), Chi–square value (X

^{2}), etc.). The loss of moisture in the material is described in accordance with Fick’s diffusion law. Value of moisture rate (MR), and effective moisture diffusivities (D

_{eff}) have been identified. Experimental results show that MR value depends on the time and drying temperature, D

_{eff}increases when increasing the drying temperature from 20–50 °C with values of 1.24 × 10

^{−9}, 1.85 × 10

^{−8}, 7.69 × 10

^{−8}, and 5.54 × 10

^{−7}m/s

^{2}. The Singh et al. model is the best option to describe the moisture of the sliced soursop drying process at 30 °C (R

^{2}= 0.97815). The largest TPC decomposition occurs at a temperature of 50 °C. The ability to decompose TPC is proportional to the drying temperature. The TPC decomposition dynamic model follows a first–order reaction when drying at 20 °C with a determinant coefficient R

^{2}= 0.9693.

## 1. Introduction

^{2}> 0.96) [11]. As reported by Zhou et al., polyphenol degradation during bean drying follows a first–order dynamic model with R

^{2}= 0.91 when drying at 80 °C by hot air [12]. The report of Si Tan et al. showed the compatibility of experimental data with Page model (R

^{2}> 0.93) when investigating moisture loss during heat pump drying of tomato slices [13]. There have been many studies on the kinetic model of moisture loss and polyphenol degradation in various materials in the past. However, there have been no studies on polyphenol degradation kinetics and moisture loss kinetics in soursop slices. The twelve models represent three common groups of models including: theoretical, semi–theoretical and experimental groups of models which this study applied to the heat pump drying process of soursop slices. Simultaneous investigation between moisture loss efficiency and TPC degradation in the heat pump drying process thus serves as the basis for the selection of drying conditions to satisfy the concurrency between drying efficiency and post–drying product quality. This is different from previous studies. On the other hand, most of the previous studies have applied the convection, microwave and vacuum drying processes to investigate the drying kinetics of some foods such as lemons and limes [14], apples [15], and mushrooms [16]. However, the heat pump drying method is a method rarely applied in previous studies, especially for soursop raw materials. On the other hand, due to the influence of the structure and conditions of the soursop growing area in each country being different, the resulting properties of the raw materials are also different. The mechanism/degree of polyphenol degradation and the mechanism/degree of moisture loss over time in soursop in Vietnam were also affected. However, there have not been any studies to comprehensively evaluate the effect of heat pump drying on the efficiency of moisture removal and TPC degradation before this. The study was carried out on a device with a maximum drying capacity of 25 kg of soursop and the characteristic parameters stated in this study.

## 2. Materials and Methods

#### 2.1. Materials

#### 2.2. Chemicals and Agents

_{2}CO

_{3}which were purchased from Shantou City, Guangdong Province, China (purity 99.8%), MB90 moisture drying scale (Ohaus Corporation, Waukegan, IL, USA).

^{3}with dimensions of length × width × height, respectively (110 × 80 × 55 cm). The device is designed with a maximum drying temperature range of 20–50 °C. The allowable wind speed range for equipment operation is 40–60 Hz. Wind is blown horizontally from left to right. A drying chamber contains 20 drying trays and the distance between the drying trays is 5 cm.

#### 2.3. Processing

#### 2.4. Determination of Total Polyphenol Content (TPC)

_{2}CO

_{3}solution is added, and left for 60 min in the dark. The sample is measured for absorbance at 765 nm.

#### 2.5. Determination of Moisture Content (MC)

#### 2.6. Mathematical Model of Kinetic Loss Moisture

^{2}) is used to choose the best equation describing the experimental data of the drying process. In addition to the coefficient of determination, Chi–square value (X

^{2}) is used to determine the degree of compatibility with 7 types of experimental models. The rate constant (k) of the process is determined by a nonlinear regression equation based on experimental values based on the graph of moisture function and t.

_{pre,i}is the value predicted A

_{i}by the fitted model at time i, A

_{exp,i}is the value of A at time i [19].

_{exp,i}is the ith dimensionless experimental moisture rate, MR

_{pre,i}is the dimensionless predicted moisture rate, N and n represent the total value of the experimental data and the total the number of predicted moisture rate, respectively [20].

^{2}/s) is expressed as D

_{0}, E

_{a}represents the activation energy (KJ/moL), and R = 8.314 KJ/moL represents the ideal gas constant, and T is the absolute temperature (K). Activation energy (E

_{a}) and constant D

_{0}were determined based on the graph of ln(D

_{eff}) vs. 1/T after linearizing Equation (5) [21]. MC

_{t}, MC

_{0}, MC

_{e}are the variables corresponding to the MC at a particular time, the initial MC and the equilibrium MC [14].

#### 2.7. Mathematical Model of Kinetic Polyphenol Degradation

_{A}: concentration of nutrient A at any time t, k: reaction rate constant.

#### 2.8. Statistical Analysis

## 3. Result and Discussion

#### 3.1. Variation of Total Polyphenol Content during Heat Pump Drying of Soursop Fruit

#### 3.2. Kinetics of Moisture Loss during Heat Pump Drying

_{2}O.g

^{−1}.min

^{−1}) when investigating 4 temperature levels from 20–50 °C. Continuing to increase the drying time (>50 min), the DR was decreased rapidly (Figure 3). There is a large difference in MC inside and outside the material when drying at high temperature (50 °C), the MC in the material is quickly released. Continuing to increase the drying time at the same temperature, the MC difference between the raw materials and the drying medium decreases, resulting in a significantly reduced DR. On the other hand, in the early stages of the drying process, the MC on the product surface and its exposure to dry air is very large and there is no interference between this contact [24]. Therefore, a large loss of MC in the early stages is obvious [48]. During this drying period, the DR was continuously reduced until the balance between MC on the surface of the material and the air. The next drying time (from 75 to 220 min at a temperature of 50 °C), the MC on the surface of the material was gradually exhausted. Phase 2 of the drying process then begins to take place, the MC of the material is diffused within the internal material before moving out of the material surface. This interpretation is the same for the 20 °C, 30 °C and 40 °C temperature levels. However, this process often happens quickly, making it difficult to detect. In general, the higher the temperature, the greater the MR in the early stages of the drying process. The general trend for the temperature levels is a gradual decrease in DR with drying time. However, in the first time, the higher the DR, the lower the DR in the next time and quickly achieve a constant MC of the sample. This is evident during the drying process at a temperature of 30–50 °C. At the same time, in the first stage of the drying process, the higher the temperature, the higher the drying rate, and vice versa in the later stage of the drying process. At low drying temperature (20 °C), the MR of the material is very slow at all time points. The time for the MR to reach a constant state at 20 °C is 590 min. The gradual increase in the drying temperature leads to a decrease in time. The drying process at 50 °C takes about 250 min for the DR to reach a constant state.

^{2}) and Chi–square (X

^{2}) values are shown in Table 2. The fit of the classical models to the soursop drying curve is based on the R

^{2}value. The higher the R

^{2}value, the better the fit of the drying curve for the models. At different temperatures shows compatibility with different models. R

^{2}value > 0.9 in the Newton/Lewis (1), Page (2), and Henderson and Pabis (3) models at drying temperature ranges. However, R

^{2}> 0.9 is found in some models, such as the two–term (6) model at 40–50 °C, the Wang and Singh model (7) at 20, 30 and 50 °C and the Weibull model (8) at 30 and 50 °C. Based on the average of the statistical parameters (SP), the highest SP and the lowest Chi–square appear in the Singh et al., (11) model. This finding is suggested that the Singh et al., model best represents the heat pump drying of soursop slices. Moreover, recent studies also show that the Singh et al., model is effective in simulating the drying process of fruits. Therefore, this model was selected in the present study to represent the drying characteristics of soursop slices.

_{eff}) at the temperatures of 20, 30, 40, and 50 °C are 1.24 × 10

^{−9}, 1.85 × 10

^{−8}, 7.69 × 10

^{−8}, and 5.54 × 10

^{−7}m/s

^{2}, respectively. The results are consistent with a report by T.T.Y. Nhi et al., on an increase in the D

_{eff}value with the increasing drying temperature of soursop leaves [34]. Ln(D

_{eff}) is the inverse function of the absolute value of the drying temperature which is shown in Figure 4.

_{eff}is a straight line, representing the dependence of Arrhenius. The D

_{eff}values show that they fit perfectly in the linear regression. The results are similar to a previous report, where the logarithm of D

_{eff}was also used to demonstrate a linear relationship with [RT]

^{−1}[8]. According to the results shown in Figure 4, R

^{2}value = 0.9887. In addition, the E

_{a}of moisture diffusion during the drying of soursop was estimated to be 155.8 kJ/mol. R

^{2}, Chi–square, and k values are three values used as the basis for choosing a model that is suitable for experimental data in the 12 models that are applied in this work. The SP value is the average value of all R

^{2}values at the investigated temperatures. The SP value in the model by Singh et al., reached the highest value (SP = 0.97492). Based on R

^{2}reaching the highest value and Chi–square reaching the lowest value, the Singh et al., model is the model of choice. The drying process at 30 °C showed that the moisture diffusion rate constant k increased by 36 times compared with the heat pump drying process at 20 °C and the k constant was only 1.789–2.02 times lower than the temperature 40–50 °C. On the other hand, the R

^{2}value in the drying condition at 30 °C reached the highest value (R

^{2}= 0.97815) and the Chi–square value reached the second lowest value only after the 20 °C temperature (Chi–square = 0.00204). This result clearly shows that the drying efficiency at 30 °C helps to optimize the drying process at 20, 40, and 50 °C in terms of energy used because it does not need too much energy to create the ambient temperature. At the same time, the low difference in efficiency when drying at 30–50 °C is indicated by the diffusion coefficient k (Table 3). Therefore, this model can be applied to describe the heat pump drying kinetics during the drying of soursop slices.

#### 3.3. Polyphenol Degradation Kinetics during Heat Pump Drying

^{2}value and k value are two factors to be considered to select an appropriate model that describes the TPC degradation process during heat pump drying of soursop slices. The SP value is the average of the R

^{2}values at the investigated temperatures. The SP value in the first–order kinetic model reached the highest value (SP = 0.9405) (Table 4). At the drying temperature condition of 20 °C, the R

^{2}value reached the highest value (R

^{2}= 0.9693). At the same time, the decomposition rate constant reached the lowest value (k = 0.0013). Therefore, the first–order reaction model was used to predict the residual TPC in the feedstock with the decomposition rate constant k = 0.0013 when drying the soursop slices at 20 °C. The lower the decomposition rate constant, the lower the TPC loss during heat pump drying. This helps to store maximum nutritional content after processing dried products from soursop slices. The equation to predict the remaining TPC in the raw materials is:

_{t}= C

_{0}× e

^{−0.0013t}

_{t}: TPC at any time during the drying process, C

_{0}: the original TPC of the material, t: the time to perform the drying process at any time. Some previous reports have shown the reduction in polyphenols during the drying process of cocoa, and the author also shows that the kinetic model of TPC degradation of cocoa during drying follows a first–order reaction [3]. In the report of Jaiswal et al., it was shown that TPC in cabbage is affected by temperature during drying and the study data follows a first–order response with coefficient of determination (R

^{2}> 0.94) [49].

## 4. Conclusions

^{2}= 0.97815) at the drying temperature of 30 °C. At this condition, it takes 375 min to dry the material and retain maximum TPC, while at the same time economically optimizing the production process. In addition, the study identified a first–order response model that predicted TPC degradation during the drying of soursop (R

^{2}= 0.9693). The result is an important contribution to the field of food drying, especially fruit and vegetables, in predicting the TPC remaining in the dried product when similar studies on the model are found. The kinetics of nutrient breakdown have not been focused on.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- González, E.M.; Fernández, A.E.L.; Sáyago-Ayerdi, S.G.; Estrada, R.M.V.; Vallejo, L.G.Z. In vitro antioxidant capacity of crude extracts and acetogenin fraction of soursop fruit pulp. Pharm. Anal. Acta
**2017**, 8, 6. [Google Scholar] - Badrie, N.; Schauss, A.G. Soursop (Annona muricata L.): Composition, nutritional value, medicinal uses, and toxicology. Bioact. Foods Promot. Health
**2010**, 39, 621–643. [Google Scholar] - Alean, J.; Chejne, F.; Rojano, B. Degradation of polyphenols during the cocoa drying process. J. Food Eng.
**2016**, 189, 99–105. [Google Scholar] [CrossRef] - Dao, T.P.; Vu, D.N.; Nguyen, D.V.; Pham, V.T.; Tran, T.Y.N. Study of jelly drying cashew apples (Anacardium occidentale L.) processing. Food Sci. Nutr.
**2021**, 10, 363–373. [Google Scholar] [CrossRef] - Tran, N.Y.; Nhan, N.P.; Thanh, V.T.; Chinh, N.D.; Tri, D.L.; Nguyen, D.V.; Vy, T.A.; Truc, T.T.; Thinh, P.V. Effect of storage condition on color, vitamin C content, polyphenol content and antioxidant activity in fresh soursop pulp (Annona muricata L.). IOP Conf. Ser. Mater. Sci. Eng.
**2020**, 736, 22065. [Google Scholar] [CrossRef] - Garau, M.C.; Simal, S.; Rossello, C.; Femenia, A. Effect of air-drying temperature on physico-chemical properties of dietary fibre and antioxidant capacity of orange (Citrus aurantium v. Canoneta) by-products. Food Chem.
**2007**, 104, 1014–1024. [Google Scholar] [CrossRef] - Roman, M.C.; Fabani, M.P.; Luna, L.C.; Feresin, G.E.; Mazza, G.; Rodriguez, R. Convective drying of yellow discarded onion (Angaco INTA): Modelling of moisture loss kinetics and effect on phenolic compounds. Inf. Process. Agric.
**2020**, 7, 333–341. [Google Scholar] [CrossRef] - Tran, N.Y.; Nhan, N.P.; Thanh, V.T.; Nguyen, D.V.; Thinh, P.V.; Vy, T.A.; Lam, T.D.; Truc, T.T. Effects of drying conditions on total phenolic content and other parameters of soursop jelly (Annona muricata L.). IOP Conf. Ser. Mater. Sci. Eng.
**2020**, 736, 022064. [Google Scholar] [CrossRef] - Jimenez, V.M.; Gruschwitz, M.; Schweiggert, R.M.; Carle, R.; Esquivel, P. Identification of phenolic compounds in soursop (Annona muricata) pulp by high-performance liquid chromatography with diode array and electrospray ionization mass spectrometric detection. Food Res. Int.
**2014**, 65, 42–46. [Google Scholar] [CrossRef] - De Andrade, J.M.M.; Fasolo, D. Polyphenol antioxidants from natural sources and contribution to health promotion. Polyphen. Hum. Health Dis.
**2014**, 20, 253–265. [Google Scholar] - Kyi, T.M.; Daud, W.R.W.; Mohammad, A.B.; Samsudin, M.W.; Kadhum, A.A.H.; Talib, M.Z.M. The kinetics of polyphenol degradation during the drying of Malaysian cocoa beans. Int. J. Food Sci. Technol.
**2005**, 40, 323–331. [Google Scholar] [CrossRef] - Zhou, L.; Cao, Z.; Bi, J.; Yi, J.; Chen, Q.; Wu, X.; Zhou, M. Degradation kinetics of total phenolic compounds, capsaicinoids and antioxidant activity in red pepper during hot air and infrared drying process. Int. J. Food Sci. Technol.
**2016**, 51, 842–853. [Google Scholar] [CrossRef] - Tan, S.; Miao, Y.; Xiang, H.; Tan, W.; Li, W. Effects of air-impingement jet drying on drying kinetics and quality retention of tomato slices. Food Sci. Biotechnol.
**2021**, 30, 691–699. [Google Scholar] [CrossRef] - Salehi, F.; Kashaninejad, M. Modeling of moisture loss kinetics and color changes in the surface of lemon slice during the combined infrared-vacuum drying. Inf. Process. Agric.
**2018**, 5, 516–523. [Google Scholar] [CrossRef] - Srikiatden, J.; Roberts, J.S. Moisture loss kinetics of apple during convective hot air and isothermal drying. Int. J. Food Prop.
**2005**, 8, 493–512. [Google Scholar] [CrossRef][Green Version] - Rodriguez, R.; Lombrana, J.I.; Kamel, M.; de Elvira, C. Kinetic and quality study of mushroom drying under microwave and vacuum. Dry. Technol.
**2005**, 23, 2197–2213. [Google Scholar] [CrossRef][Green Version] - Dao, T.P.; Nguyen, D.V.; Tran, T.Y.; Pham, T.N.; Nguyen, P.T.; Bach, L.G.; Nguyen, V.H.; Do, V.Q.; Nguyen, V.M.; Tran, T.T. Effects of tannin, ascorbic acid, and total phenolic contents of cashew (Anacardium occidentale L.) apples blanched with saline solution. Food Res.
**2021**, 5, 409–416. [Google Scholar] [CrossRef] - Olalusi, A.P.; Erinle, O. Influence of drying temperature and pretreatment on the drying characteristics and quality of dried cashew (Anacardium occidentale L.) apple slices. Croat. J. Food Sci. Technol.
**2019**, 11, 97–103. [Google Scholar] [CrossRef] - Di Bucchianico, A. Coefficient of determination (R
^{2}). Encycl. Stat. Qual. Reliab.**2008**, 1. [Google Scholar] [CrossRef] - Zarein, M.; Samadi, S.H.; Ghobadian, B. Investigation of microwave dryer effect on energy efficiency during drying of apple slices. J. Saudi Soc. Agric. Sci.
**2015**, 14, 41–47. [Google Scholar] [CrossRef][Green Version] - Guo, H.L.; Chen, Y.; Xu, W.; Xu, M.T.; Sun, Y.; Wang, X.C.; Wang, X.Y.; Luo, J.; Zhang, H.; Xiong, Y.K. Assessment of drying kinetics, textural and aroma attributes of mentha haplocalyx leaves during the hot air thin-layer drying process. Foods
**2022**, 11, 784. [Google Scholar] [CrossRef] [PubMed] - Hii, C.L.; Law, C.L.; Suzannah, S. Drying kinetics of the individual layer of cocoa beans during heat pump drying. J. Food Eng.
**2012**, 108, 276–282. [Google Scholar] [CrossRef] - Mishra, A.; Sharma, N. Mathematical modelling and tray drying kinetics of loquat (Eriobotrya japonica). J. Dairy Food Sci.
**2014**, 9, 272–284. [Google Scholar] [CrossRef] - Page, G.E. Factors Influencing the Maximum Rates of Air Drying Shelled Corn in Thin Layers; Purdue University: West Lafayette, India, 1949. [Google Scholar]
- Doymaz, I. Sun drying of figs: An experimental study. J. Food Eng.
**2005**, 71, 403–407. [Google Scholar] [CrossRef] - Midilli, A.; Kucuk, H. Mathematical modeling of thin layer drying of pistachio by using solar energy. Energy Convers. Manag.
**2003**, 44, 1111–1122. [Google Scholar] [CrossRef] - Toğrul, İ.T.; Pehlivan, D. Mathematical modelling of solar drying of apricots in thin layers. J. Food Eng.
**2002**, 55, 209–216. [Google Scholar] [CrossRef] - Henderson, S.M. Progress in developing the thin layer drying equation. Trans. ASAE
**1974**, 17, 1167–1168. [Google Scholar] [CrossRef] - Murthy, D.N.P.; Xie, M.; Jiang, R. Weibull Models; John Wiley & Sons.: Hoboken, NJ, USA, 2004. [Google Scholar]
- Akpinar, E.; Midilli, A.; Bicer, Y. Single layer drying behaviour of potato slices in a convective cyclone dryer and mathematical modeling. Energy Convers. Manag.
**2003**, 44, 1689–1705. [Google Scholar] [CrossRef] - Singh, F.; Katiyar, V.K.; Singh, B.P. Mathematical modeling to study drying characteristic of apple and potato. J. Food Sci. Technol.
**2014**, 52, 5442–5455. [Google Scholar] [CrossRef][Green Version] - Barroca, M.J.; Guiné, R. Study of drying kinetics of quince. In Proceedings of the International Conference of Agricultural Engineering CIGR-AgEng2012, Valencia, Spain, 8–12 July 2012. [Google Scholar]
- Dadali, G.; Demirhan, E.; Özbek, B. Color change kinetics of spinach undergoing microwave drying. Dry. Technol.
**2007**, 25, 1713–1723. [Google Scholar] [CrossRef] - Nhi, T.T.; Thinh, P.V.; Vu, N.D.; Bay, N.T.; Tho, N.T.; Quyen, N.N.; Truc, T.T. Kinetic model of moisture diffusivity in soursop leaves (Annona muricata L.) by convection drying. IOP Conf. Ser. Mater. Sci. Eng.
**2020**, 991, 012107. [Google Scholar] [CrossRef] - McSweeney, M.; Seetharaman, K. State of polyphenols in the drying process of fruits and vegetables. Crit. Rev. Food Sci. Nutr.
**2015**, 55, 660–669. [Google Scholar] [CrossRef] - Vauzour, D.; Rodriguez-Mateos, A.; Corona, G.; Oruna-Concha, M.J.; Spencer, J.P.E. Polyphenols and human health: Prevention of disease and mechanisms of action. Nutrients
**2010**, 2, 1106–1131. [Google Scholar] [CrossRef] - Billaud, C.; Maraschin, C.; Chow, Y.; Chériot, S.; Peyrat-Maillard, M.; Nicolas, J. Maillard reaction products as ‘natural antibrowning’ agents in fruit and vegetable technology. Mol. Nutr. Food Res.
**2005**, 49, 656–662. [Google Scholar] [CrossRef] - Abbaspour-Gilandeh, Y.; Jahanbakhshi, A.; Kaveh, M. Prediction kinetic, energy and exergy of quince under hot air dryer using ANNs and ANFIS. Food Sci. Nutr.
**2020**, 8, 594–611. [Google Scholar] [CrossRef][Green Version] - Lopez-Nicolás, J.M.; García-Carmona, F. Enzymatic and nonenzymatic degradation of polyphenols. In Fruit and Vegetables Phytochemicals; Wiley-Blackwell Publishing: Ames, IA, USA, 2010; Volume 4, pp. 101–103. [Google Scholar]
- Sánchez-Ferrer, Á.; Rodríguez-López, J.N.; García-Cánovas, F.; García-Carmona, F. Tyrosinase: A comprehensive review of its mechanism. Biochim. Biophys. Acta (BBA)-Protein Struct. Mol. Enzymol.
**1995**, 1247, 1–11. [Google Scholar] [CrossRef] - Baysal, T.; Demirdöven, A. Lipoxygenase in fruits and vegetables: A review. Enzym. Microb. Technol.
**2007**, 40, 491–496. [Google Scholar] [CrossRef] - Eskin, N.A.M.; Grossman, S.; Pinsky, A.; Whitaker, J.R. Biochemistry of lipoxygenase in relation to food quality. Crit. Rev. Food Sci. Nutr.
**1977**, 9, 1–40. [Google Scholar] [CrossRef] - Zielinska, M.; Michalska, A. Microwave-assisted drying of blueberry (Vaccinium corymbosum L.) fruits: Drying kinetics, polyphenols, anthocyanins, antioxidant capacity, colour and texture. Food Chem.
**2016**, 212, 671–680. [Google Scholar] [CrossRef] - Ong, S.P.; Law, C.L. Drying kinetics and antioxidant phytochemicals retention of salak fruit under different drying and pretreatment conditions. Dry. Technol.
**2011**, 29, 429–441. [Google Scholar] [CrossRef] - Pal, U.S.; Khan, M.K.; Mohanty, S.N. Heat pump drying of green sweet pepper. Dry. Technol.
**2008**, 26, 1584–1590. [Google Scholar] [CrossRef] - Zheng, D.-J.; Cheng, Y.-Q.; Liu, H.-J.; Li, L.-T. Investigation of EHD-enhanced water evaporation and a novel empirical model. Int. J. Food Eng.
**2011**, 7, 11. [Google Scholar] [CrossRef] - Chong, C.H.; Law, C.L.; Cloke, M.; Hii, C.L.; Abdullah, L.C.; Daud, W.R.W. Drying kinetics and product quality of dried Chempedak. J. Food Eng.
**2008**, 88, 522–527. [Google Scholar] [CrossRef] - Taşeri, L.; Aktaş, M.; Şevik, S.; Gülcü, M.; Seckin, G.U.; Aktekeli, B. Determination of drying kinetics and quality parameters of grape pomace dried with a heat pump dryer. Food Chem.
**2018**, 260, 152–159. [Google Scholar] [CrossRef] - Jaiswal, A.K.; Abu-Ghannam, N. Degradation kinetic modelling of color, texture, polyphenols and antioxidant capacity of York cabbage after microwave processing. Food Res. Int.
**2013**, 53, 125–133. [Google Scholar] [CrossRef]

No. | Models | Equations | References |
---|---|---|---|

01 | Newton/Lewis | $MR={e}^{-kt}$ | [23] |

02 | Page | $MR={e}^{-k{t}^{n}}$ | [24] |

03 | Henderson and Pabis | $MR=a.{e}^{-kt}$ | [25] |

04 | Midilli | $MR=a.{e}^{-k{t}^{n}}+bt$ | [26] |

05 | Logarithmic | $MR=a.{e}^{-kt}+c$ | [27] |

06 | Two–term | $MR=a.{e}^{-{k}_{1}t}+b.{e}^{-{k}_{2}t}$ | [28] |

07 | Wang and Singh | $MR=1+at+b{t}^{2}$ | [25] |

08 | Weibull | $MR=\alpha -b{e}^{-{k}_{0}{t}^{n}}$ | [29] |

09 | Quadratic | $MR=\mathrm{a}+\mathrm{bx}+c{x}^{2}$ | [14] |

10 | Verma | $MR=a.{e}^{\left(-kt\right)}+\left(1-a\right).{e}^{\left(-gt\right)}$ | [30] |

11 | Singh et al. | $MR={e}^{\left(-\mathrm{kt}\right)}-akt$ | [31] |

12 | Vega–Lemus | $MR={\left(a+kt\right)}^{2}$ | [32] |

No. | Models | Value | 20 °C | 30 °C | 40 °C | 50 °C | Statistical Parameters |
---|---|---|---|---|---|---|---|

1 | Newton/Lewis | R^{2} | 0.89208 | 0.97000 | 0.96904 | 0.97000 | 0.95028 |

Chi–square | 0.00813 | 0.00200 | 0.00232 | 0.00200 | 0.00361 | ||

2 | Page | R^{2} | 0.94867 | 0.99181 | 0.97365 | 0.98440 | 0.97463 |

Chi–square | 0.00387 | 0.00076 | 0.00198 | 0.00147 | 0.00202 | ||

3 | Henderson and Pabis | R^{2} | 0.89392 | 0.97900 | 0.96887 | 0.98000 | 0.95545 |

Chi–square | 0.00800 | 0.00100 | 0.00234 | 0.00100 | 0.00309 | ||

4 | Midilli | R^{2} | −2.35181 | −0.58374 | −0.07385 | −0.26511 | No Fit |

Chi–square | 0.25263 | 0.14768 | 0.08057 | 0.11913 | 0.15000 | ||

5 | Logarithmic | R^{2} | 0.03077 | 0.11210 | 0.96852 | 0.19080 | 0.32555 |

Chi–square | 0.07305 | 0.08270 | 0.00236 | 0.07610 | 0.05855 | ||

6 | Two–term | R^{2} | −3.87070 | −0.71132 | 0.96767 | 0.97848 | No Fit |

Chi–square | 0.36711 | 0.15958 | 0.00243 | 0.00203 | 0.13279 | ||

7 | Wang and Singh | R^{2} | 0.97837 | 0.98679 | 0.85974 | 0.95500 | 0.94498 |

Chi–square | 0.00163 | 0.00123 | 0.01052 | 0.00400 | 0.00435 | ||

8 | Weibull | R^{2} | 0.00049 | 0.99311 | 0.22060 | 0.98396 | 0.54954 |

Chi–square | 0.07500 | 0.00064 | 0.05848 | 0.00151 | 0.03391 | ||

9 | Quadratic | R^{2} | 0.98747 | 0.98642 | 0.90858 | 0.95836 | 0.96021 |

Chi–square | 0.00094 | 0.00127 | 0.00686 | 0.00392 | 0.00325 | ||

10 | Verma | R^{2} | 0.88846 | 0.98146 | 0.96767 | 0.98641 | 0.95600 |

Chi–square | 0.00841 | 0.00173 | 0.00243 | 0.00128 | 0.00346 | ||

11 | Singh et al. | R^{2} | 0.97642 | 0.97815 | 0.96845 | 0.97666 | 0.97492 |

Chi–square | 0.00178 | 0.00204 | 0.00237 | 0.0022 | 0.00210 | ||

12 | Vega–Lemus | R^{2} | 0.94195 | 0.98635 | 0.88407 | 0.9513 | 0.94092 |

Chi–square | 0.00438 | 0.00127 | 0.0087 | 0.0045 | 0.00471 |

Temp (°C) | Model Parameters | |||
---|---|---|---|---|

k | a | R^{2} | Chi–Square | |

20 | 0.00017 | 9.39003 | 0.97642 | 0.00178 |

30 | 0.00613 | 0.0171 | 0.97815 | 0.00204 |

40 | 0.01238 | 0.00172 | 0.96845 | 0.00237 |

50 | 0.01096 | 0.00862 | 0.97666 | 0.00220 |

Models | Temp (°C) | k (min^{−1}) | C_{0} | Chi–Square | A (%) | R^{2} | Statistical Parameters |
---|---|---|---|---|---|---|---|

Kinetic order 0 | 20 | 0.0255 | 23.3770 | 0.2491 | 0.0126 | 0.9576 | 0.9106 |

30 | 0.0323 | 22.1740 | 0.6539 | 0.0686 | 0.9326 | ||

40 | 0.0286 | 21.1730 | 1.2253 | 0.1044 | 0.8521 | ||

50 | 0.0335 | 22.0920 | 1.0000 | 0.0689 | 0.9000 | ||

Kinetic order 1 | 20 | 0.0013 | 23.6590 | 0.1803 | 0.0007 | 0.9693 | 0.9405 |

30 | 0.0019 | 22.7560 | 0.3776 | 0.0442 | 0.9611 | ||

40 | 0.0017 | 21.7390 | 0.8719 | 0.0804 | 0.8948 | ||

50 | 0.0020 | 22.7430 | 0.6620 | 0.0415 | 0.9370 |

_{0}and C

_{0}of the model.

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Vu, N.D.; Tran, N.T.Y.; Le, T.D.; Phan, N.T.M.; Doan, P.L.A.; Huynh, L.B.; Dao, P.T.
Kinetic Model of Moisture Loss and Polyphenol Degradation during Heat Pump Drying of Soursop Fruit (*Annona muricata* L.). *Processes* **2022**, *10*, 2082.
https://doi.org/10.3390/pr10102082

**AMA Style**

Vu ND, Tran NTY, Le TD, Phan NTM, Doan PLA, Huynh LB, Dao PT.
Kinetic Model of Moisture Loss and Polyphenol Degradation during Heat Pump Drying of Soursop Fruit (*Annona muricata* L.). *Processes*. 2022; 10(10):2082.
https://doi.org/10.3390/pr10102082

**Chicago/Turabian Style**

Vu, Ngoc Duc, Nhi Thi Yen Tran, Truong Dang Le, Nguyet Thi Minh Phan, Phu Le An Doan, Long Bao Huynh, and Phat Tan Dao.
2022. "Kinetic Model of Moisture Loss and Polyphenol Degradation during Heat Pump Drying of Soursop Fruit (*Annona muricata* L.)" *Processes* 10, no. 10: 2082.
https://doi.org/10.3390/pr10102082