# Mass Transfer in Osmotic Dehydration of Kiwiberry: Experimental and Mathematical Modelling Studies

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Results and Discussion

#### 2.1. Weight Reduction

^{2}values, and low CRV, RMSE and χ

^{2}values (Table 3). The Peleg’s equation has two independent variables representing initial mass transfer rate (K

_{1}) and equilibrium moisture content (K

_{2}). The K

_{1}and K

_{2}values for the 50 °C process indicated both high transfer and water removal rates (Figure 2a,c). The K

_{1}values decreased with the increase of the temperature. There was no visible trend for the K

_{2}values. The usefulness of the Peleg’s model was also confirmed by Arballo et al. [18] when researchers were using this model for predicting the OD of different fruits.

#### 2.2. Water Loss

^{2}values, and low CRV, RMSE and χ

^{2}, which is expected for applicable models. High goodness of fit of this model for the OD was also reported by Yadav and Singh [1] and Cichowska et al. [21].

_{1}represents initial mass transfer rate and K

_{2}describes equilibrium moisture content. As it was aforementioned, low K

_{1}and K

_{2}values indicate both high mass transfer and high water removal rates [21,31]. Measured WL values suggest lower effectiveness of sucrose and maltitol, in comparison to xylitol carried out at 30 °C (Figure 1a,c). Statistical analysis has shown that these two osmotic agents belong to the same homogeneous group (Table 3). This could be explained by similar and high molecular weight of these solutions; such observations were also reported by Mendonça et al. [11]. Molecular weight could have also influenced the K

_{1}values for the OD at 30 °C; such phenomena were also reported by other researchers [28]. In addition, it could be explained by similar osmotic coefficient values, and should be further explored in the future experiments.

#### 2.3. Solid Gain

^{2}values, and low CRV, RMSE and χ

^{2}values. The usefulness of this model was also confirmed by Arballo et al. [15] and Cichowska et al. [21]. No visible trend was established for the K

_{1}values of SG for the “Geneva” cultivar. For the “Weiki” cultivar, there was a noticeable reduction in the K

_{1}value when the temperature was increased. The impact of the applied temperature on K

_{1}values was also reported by Ganjloo et al. [31]. This requires further analysis in future experiments.

## 3. Materials and Methods

#### 3.1. Sample Preparation

#### 3.2. Dehydration Procedure

#### 3.3. Analytical Methods

#### 3.3.1. Mathematical Modeling

^{2}) (Equation (11)), the reduced chi-squared statistic (χ

^{2}) (Equation (9)), the root mean square error (RMSE) (Equation (8)), and the coefficient of residual variation (CRV) (Equation (10)) were used to evaluate the goodness of fit of tested models:

^{2}values and the low χ

^{2}and RMSE values indicate that the model fits well to the experimental data. The values of CRV less than 20% indicate that the model can be used for predictions.

#### 3.3.2. Statistical Analysis

## 4. Conclusions

## Author Contributions

## Conflicts of Interest

## Nomenclature

OD | osmotic dehydration, |

WR | weight reduction, (%) |

WL | water loss, (g/g i.d.m.) |

SG | solid gain (g d.m./g i.d.m.) |

m | sample mass, (g) |

i.d.m. | initial dry matter, (g) |

d.m. | dry solids mass of material, (g) |

τ | time of osmotic dehydration, (min) |

K_{1} | parameter of Equation (7), (kg/kg) |

K_{2} | parameter of Equation (7), (kg/kg·h) |

K_{ω} | constant rate for water changes (4), (min^{−0.5}) |

K_{s} | constant rate for solutes changes (5), (min^{−0.5}) |

K_{m} | constant rate for solutes changes (6), (min^{−0.5}) |

Y | mean experimental value of WR, WL and SG respectively, (7) |

MR_{i,p} | predicted dimensionless moisture ratio, |

MR_{i,e} | experimental dimensionless moisture ratio, |

MR_{p} | experimental, mean dimensionless moisture ratio, |

N | number of observation, |

n | number of constants in the model equation, |

Subscripts | |

o | initial |

τ | time (min) |

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Sample Availability: Samples of the compounds from the polyols (xylitol, maltitol) are available from the authors. |

**Figure 1.**WR kinetics of the ‘Geneva’ cultivar dehydrated at (

**a**) 30 °C; and (

**b**) 50 °C in xylitol (▲—triangle), maltitol (■—square) and sucrose (●—circle). WR kinetics of the ‘Weiki’ cultivar dehydrated at (

**c**) 30 °C; and (

**d**) 50 °C in xylitol (▲—triangle), maltitol (■—square) and sucrose (●—circle). Dotted lines represent values obtained from the mathematical modelling.

**Figure 2.**WL kinetics of the ‘Geneva’ cultivar dehydrated at (

**a**) 30 °C; and (

**b**) 50 °C in xylitol (▲—triangle), maltitol (■—square) and sucrose (●—circle). WL kinetics of the ‘Weiki’ cultivar dehydrated at (

**c**) 30 °C; and (

**d**) 50 °C in xylitol (▲—triangle), maltitol (■—square) and sucrose (●—circle). Dotted lines represent values obtained from the mathematical modelling.

**Figure 3.**SG kinetics of the ‘Geneva’ cultivar dehydrated at (

**a**) 30 °C; and (

**b**) 50 °C in xylitol (▲—triangle), maltitol (■—square) and sucrose (●—circle). SG kinetics of. the ‘Weiki’ cultivar dehydrated at (

**c**) 30 °C and (

**d**) 50 °C in xylitol (▲—triangle), maltitol (■—square) and sucrose (●—circle). Dotted lines represent values obtained from the mathematical modelling.

Factor | p-Value | Contrast | +/− Limits | Difference | |
---|---|---|---|---|---|

Cultivar | Geneva ^{a} | <0.001 * | Geneva–Weiki | 0.006 | 0.034 * |

Weiki ^{b} | |||||

Temperature | 30 °C ^{a} | <0.001 * | 30 °C–50 °C | −0.044 | −0.005 * |

50 °C ^{b} | |||||

Time | 10 min ^{a} | <0.001 * | 10 min–60 min | 0.008 | −0.062 * |

10 min–30 min | 0.008 | −0.028 * | |||

10 min–180 min | 0.008 | −0.112 * | |||

30 min ^{b} | 60 min–30 min | 0.008 | 0.033 * | ||

1 h ^{c} | 60 min–180 min | 0.008 | −0.050 * | ||

3 h ^{d} | 30 min–180 min | 0.008 | −0.084 * | ||

Osmotic solution | Sucrose ^{a} | <0.001 * | Xylitol–Maltitol | 0.007 | 0.014 * |

Maltitol ^{a} | Xylitol–Sucrose | 0.007 | 0.019 * | ||

Xylitol ^{b} | Maltitol–Sucrose | 0.008 | 0.004 |

Interaction | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|

AB | AC | AD | BC | BD | CD | ABC | ABD | ACD | BCD | |

WR | 0.148 | 0.059 | 0.848 | <0.001 * | 0.311 | 0.098 | 0.938 | 0.026 | 0.465 | 0.022 * |

WL | 0.335 | 0.009 * | 0.304 | <0.001 * | 0.210 | <0.001 * | 0.492 | 0.339 | 0.074 | 0.002 * |

SG | 0.554 | 0.007 * | 0.019 * | <0.001 * | 0.388 | <0.001 * | 0.067 | 0.005 * | 0.1898 | 0.452 |

Cultivar | Temperature | Solution | Model | K_{1} | K_{2} | K_{m} | RMSE | χ^{2} | CRV (%) | R^{2} |
---|---|---|---|---|---|---|---|---|---|---|

Geneva | 30 °C | sucrose | Ade-Omowaye | - | - | 0.006 | 0.019 | 0.001 | 40.89 | 0.507 |

Peleg | 11.171 | −0.006 | - | 0.012 | 0.001 | 25.11 | 0.814 | |||

maltitol | Ade-Omowaye | - | - | - | - | - | - | - | ||

Peleg | 9.839 | −0.004 | - | 0.012 | 0.001 | 20.30 | 0.851 | |||

xylitol | Ade-Omowaye | - | - | - | - | - | - | - | ||

Peleg | 8.468 | 0.003 | - | 0.017 | 0.001 | 21.20 | 0.896 | |||

50 °C | sucrose | Ade-Omowaye | - | - | - | - | - | - | - | |

Peleg | 2.780 | 0.009 | - | 0.015 | 0.000 | 17.35 | 0.950 | |||

maltitol | Ade-Omowaye | - | - | - | - | - | - | - | ||

Peleg | 2.881 | 0.011 | - | 0.008 | 0.000 | 9.10 | 0.985 | |||

xylitol | Ade-Omowaye | - | - | - | - | - | - | - | ||

Peleg | 3.468 | 0.000 | - | 0.009 | 0.000 | 8.82 | 0.982 | |||

Weiki | 30 °C | sucrose | Ade-Omowaye | - | - | - | - | - | - | - |

Peleg | 12.525 | −0.009 | - | 0.011 | 0.000 | 49.16 | 0.763 | |||

maltitol | Ade-Omowaye | - | - | - | - | - | - | - | ||

Peleg | 14.953 | −0.004 | - | 0.006 | 0.000 | 27.75 | 0.886 | |||

xylitol | Ade-Omowaye | - | - | - | - | - | - | - | ||

Peleg | 9.001 | −0.008 | - | 0.013 | 0.000 | 29.75 | 0.838 | |||

50 °C | sucrose | Ade-Omowaye | - | - | - | - | - | - | - | |

Peleg | 1.193 | 0.001 | - | 0.006 | 0.000 | 10.73 | 0.989 | |||

maltitol | Ade-Omowaye | - | - | - | - | - | - | - | ||

Peleg | 2.776 | −0.002 | - | 0.007 | 0.000 | 10.75 | 0.986 | |||

xylitol | Ade-Omowaye | - | - | - | - | - | - | - | ||

Peleg | 2.834 | 0.002 | - | 0.004 | 0.000 | 7.26 | 0.993 |

**Table 4.**The influence of osmotic pre-treatment in different solutions, and time on WL (g/g i.d.m.).

Factor | p-Value | Contrast | +/− Limits | Difference | |
---|---|---|---|---|---|

Cultivar | Geneva ^{a} | 0.187 | Geneva–Weiki | −0.018 | 0.027 |

Weiki ^{a} | |||||

Temperature | 30 °C ^{a} | <0.001 * | 30 °C–50 °C | 0.027 | −0.312 * |

50 °C ^{b} | |||||

Time | 10 min ^{a} | <0.001 * | 10 min–60 min | 0.039 | −0.362 * |

10 min–30 min | 0.039 | −0.147 * | |||

10 min–180 min | 0.039 | −0.733 * | |||

30 min ^{b} | 60 min–30 min | 0.039 | 0.215 * | ||

1 h ^{c} | 60 min–180 min | 0.039 | −0.371 * | ||

3 h ^{d} | 30 min–180 min | 0.039 | −0.586 * | ||

Osmotic solution | Sucrose ^{a} | <0.001 * | Xylitol–Maltitol | 0.034 | 0.122 * |

Maltitol ^{a} | Xylitol–Sucrose | 0.034 | 0.151 * | ||

Xylitol ^{b} | Maltitol–Sucrose | 0.033 | 0.028 |

Cultivar | Temperature | Solution | Model | K_{1} | K_{2} | K_{ω} | RMSE | χ^{2} | CRV (%) | R^{2} |
---|---|---|---|---|---|---|---|---|---|---|

Geneva | 30 °C | sucrose | Ade-Omowaye | - | - | 0.043 | 0.119 | 0.016 | 35.91 | 0.538 |

Peleg | 1.711 | −0.028 | - | 0.056 | 0.003 | 16.91 | 0.897 | |||

maltitol | Ade-Omowaye | - | - | 0.052 | 0.098 | 0.010 | 25.01 | 0.735 | ||

Peleg | 1.520 | 0.012 | - | 0.037 | 0.001 | 9.51 | 0.961 | |||

xylitol | Ade-Omowaye | - | - | 0.079 | 0.081 | 0.008 | 17.87 | 0.948 | ||

Peleg | 1.448 | 0.013 | - | 0.082 | 0.009 | 11.83 | 0.959 | |||

50 °C | sucrose | Ade-Omowaye | - | - | 0.101 | 0.079 | 0.008 | 13.49 | 0.967 | |

Peleg | 0.402 | 0.100 | - | 0.077 | 0.007 | 13.06 | 0.969 | |||

maltitol | Ade-Omowaye | - | - | 0.099 | 0.029 | 0.001 | 5.02 | 0.995 | ||

Peleg | 0.484 | 0.102 | - | 0.054 | 0.004 | 9.22 | 0.982 | |||

xylitol | Ade-Omowaye | - | - | 0.118 | 0.082 | 0.008 | 11.64 | 0.969 | ||

Peleg | 0.507 | 0.036 | - | 0.056 | 0.004 | 7.93 | 0.986 | |||

Weiki | 30 °C | sucrose | Ade-Omowaye | - | - | 0.052 | 0.095 | 0.011 | 27.75 | 0.663 |

Peleg | 1.681 | 0.016 | - | 0.031 | 0.001 | 9.04 | 0.964 | |||

maltitol | Ade-Omowaye | - | - | 0.055 | 0.104 | 0.013 | 28.53 | 0.618 | ||

Peleg | 1.645 | 0.010 | - | 0.034 | 0.001 | 9.32 | 0.959 | |||

xylitol | Ade-Omowaye | - | - | 0.073 | 0.120 | 0.018 | 25.45 | 0.761 | ||

Peleg | 1.104 | −0.002 | - | 0.035 | 0.001 | 7.35 | 0.980 | |||

50 °C | sucrose | Ade-Omowaye | - | - | 0.099 | 0.045 | 0.002 | 7.57 | 0.986 | |

Peleg | 0.517 | 0.135 | - | 0.070 | 0.006 | 11.78 | 0.967 | |||

maltitol | Ade-Omowaye | - | - | 0.103 | 0.067 | 0.005 | 10.81 | 0.973 | ||

Peleg | 0.510 | 0.113 | - | 0.079 | 0.007 | 12.78 | 0.963 | |||

xylitol | Ade-Omowaye | - | - | 0.111 | 0.060 | 0.004 | 9.03 | 0.980 | ||

Peleg | 0.426 | 0.186 | - | 0.089 | 0.010 | 13.36 | 0.957 |

**Table 6.**The influence of osmotic pre-treatment in different solutions, and time on SG [g/g i.d.m.].

Factor | p-Value | Contrast | +/− Limits | Difference | |
---|---|---|---|---|---|

Cultivar | Geneva ^{a} | <0.001 * | Geneva–Weiki | 0.013 | −0.201 * |

Weiki ^{b} | |||||

Temperature | 30 °C ^{a} | <0.001 * | 30 °C–50 °C | 0.013 | −0.079 * |

50 °C ^{b} | |||||

Time | 10 min ^{a} | <0.001 * | 10 min–60 min | 0.018 | −0.056 * |

10 min–30 min | 0.018 | −0.003 | |||

10 min–180 min | 0.017 | −0.153 * | |||

30 min ^{a} | 60 min–30 min | 0.018 | 0.053 * | ||

60 min ^{b} | 60 min–180 min | 0.017 | −0.097 * | ||

180 min ^{c} | 30 min–180 min | 0.017 | −0.151 * | ||

Osmotic solution | Sucrose ^{a} | <0.001 * | Xylitol–Maltitol | 0.015 | 0.046 * |

Maltitol ^{a} | Xylitol–Sucrose | 0.015 | 0.045 * | ||

Xylitol ^{b} | Maltitol–Sucrose | 0.015 | −0.007 |

Cultivar | Temperature | Solution | Model | K_{1} | K_{2} | K_{s} | RMSE | χ^{2} | CRV (%) | R^{2} |
---|---|---|---|---|---|---|---|---|---|---|

Geneva | 30 °C | sucrose | Ade-Omowaye | - | - | 0.010 | 0.031 | 0.001 | 38.88 | 0.358 |

Peleg | 8.164 | −0.001 | - | 0.018 | 0.000 | 22.76 | 0.780 | |||

maltitol | Ade-Omowaye | - | - | 0.044 | 0.043 | 0.002 | 14.16 | 0.961 | ||

Peleg | 1.021 | 0.024 | - | 0.038 | 0.001 | 12.54 | 0.969 | |||

xylitol | Ade-Omowaye | - | - | 0.024 | 0.049 | 0.003 | 36.22 | 0.832 | ||

Peleg | −2.186 | 0.055 | - | 0.034 | 0.001 | 24.63 | 0.922 | |||

50 °C | sucrose | Ade-Omowaye | - | - | 0.023 | 0.023 | 0.001 | 16.42 | 0.940 | |

Peleg | 1.137 | 0.055 | - | 0.026 | 0.001 | 18.86 | 0.921 | |||

maltitol | Ade-Omowaye | - | - | 0.022 | 0.027 | 0.001 | 19.37 | 0.873 | ||

Peleg | 3.339 | 0.038 | - | 0.024 | 0.001 | 17.29 | 0.898 | |||

xylitol | Ade-Omowaye | - | - | 0.029 | 0.043 | 0.002 | 23.76 | 0.872 | ||

Peleg | 2.103 | 0.016 | - | 0.038 | 0.002 | 21.20 | 0.898 | |||

Weiki | 30 °C | sucrose | Ade-Omowaye | - | - | - | - | - | - | - |

Peleg | 3.101 | 0.000 | - | 0.010 | 0.000 | 4.05 | 0.988 | |||

maltitol | Ade-Omowaye | - | - | - | - | - | - | - | ||

Peleg | 2.947 | 0.000 | - | 0.021 | 0.000 | 8.45 | 0.952 | |||

xylitol | Ade-Omowaye | - | - | 0.036 | 0.093 | 0.010 | 37.56 | 0.208 | ||

Peleg | 2.782 | 0.003 | - | 0.035 | 0.001 | 14.11 | 0.888 | |||

50 °C | sucrose | Ade-Omowaye | - | - | 0.044 | 0.121 | 0.018 | 39.43 | 0.066 | |

Peleg | 2.266 | 0.002 | - | 0.029 | 0.001 | 9.63 | 0.944 | |||

maltitol | Ade-Omowaye | - | - | 0.044 | 0.099 | 0.012 | 33.64 | 0.431 | ||

Peleg | 2.244 | 0.012 | - | 0.051 | 0.003 | 17.36 | 0.848 | |||

xylitol | Ade-Omowaye | - | - | 0.052 | 0.101 | 0.012 | 29.18 | 0.626 | ||

Peleg | 1.871 | 0.032 | - | 0.078 | 0.007 | 22.59 | 0.776 |

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**MDPI and ACS Style**

Bialik, M.; Wiktor, A.; Latocha, P.; Gondek, E.
Mass Transfer in Osmotic Dehydration of Kiwiberry: Experimental and Mathematical Modelling Studies. *Molecules* **2018**, *23*, 1236.
https://doi.org/10.3390/molecules23051236

**AMA Style**

Bialik M, Wiktor A, Latocha P, Gondek E.
Mass Transfer in Osmotic Dehydration of Kiwiberry: Experimental and Mathematical Modelling Studies. *Molecules*. 2018; 23(5):1236.
https://doi.org/10.3390/molecules23051236

**Chicago/Turabian Style**

Bialik, Michał, Artur Wiktor, Piotr Latocha, and Ewa Gondek.
2018. "Mass Transfer in Osmotic Dehydration of Kiwiberry: Experimental and Mathematical Modelling Studies" *Molecules* 23, no. 5: 1236.
https://doi.org/10.3390/molecules23051236