Effect of Variety on Rehydration Characteristics of Dried Apples

The effect of dried apple varieties on their rehydration characteristics was investigated. Four varieties of apples, Champion, Cortland, Grey Reinette and Ligol, were taken into consideration. Rehydration properties and color of apples were investigated. In order to examine the influence of apple variety on its rehydration properties, the process of rehydration was modeled. The model parameters obtained for investigated apple varieties were compared. Apple cubes were dried in a tunnel dryer (air temperature 60 °C and air velocity 2 m/s) and next rehydrated in distilled water at temperature: 20, 45 and 70 °C. Mass, dry matter mass, volume and color attributes of apples (raw, dried and rehydrated) were measured. The process of rehydration was modeled using empirical (Peleg and Weibull models) and theoretical (the Fick’s second law) models. Results of the analysis showed that the apple variety affects values of mass and volume increase, dry matter decrease and color of the rehydrated apple. Discussed parameters were also affected by rehydration temperature. Fick’s second law model can be considered as the most appropriate. Apple variety and rehydration temperature influenced the values of the model’s constants. Obtained values enabled attempts of the explanation of the rehydration course. It can be stated that apple var. Champion showed a greater rate of water absorption during the entire process of rehydration than other investigated varieties.


Introduction
Rehydration belongs to one of the most significant quality properties of dehydrated foods. The quick and complete process of rehydration can lead to a reduction of labor costs and floor-space requirements and, very importantly, to improving the efficiency of production [1]. Moreover, some of the dried food products are consumed after their rehydrating (in milk or fruit juices). Therefore, a better understanding of the discussed process can cause the quality improvement of both dried and rehydrated products [2,3]. Rehydration is a complex process intended to restore the properties of the raw food product by contacting the dried product with liquid [4]. It can be assumed that during the described process, the following processes take place simultaneously: absorption of liquid by the dehydrated product, swelling of the rehydrated material and leaching of the solutes (vitamins, minerals, sugars, acids) from the product to the rehydrating medium. The kinetics of the mass transfer mechanisms depends on the rehydrating liquid [5,6].
Pre-drying treatments, drying and rehydration cause the changes in structure and composition of product tissue, which result in worsening of reconstitution characteristics. Rehydration can be, therefore, treated as a measure of the degree of alternations taking place during processing [7,8]. The effect of different parameters of pre-drying treatments, subsequent drying and rehydration on rehydration characteristics of food products has been widely investigated in the literature. Some examples are given below.
Golden Delicious, Granny Smith) based on the mass of fruit and also stated that one formula for investigated varieties could not be representative. Cruz et al. [34] studied the convective drying of apples from two varieties Golden Delicious and Granny Smith, and found that values of mass transfer properties such as moisture diffusion coefficient and moisture transfer coefficient were different for both varieties. Pissard et al. [35] determined the phenolic compounds and dry matter content in peel and flesh of twenty apple varieties. Both properties showed great variability among the varieties.
There is, however, little or no information about the effect of variety on the rehydration behavior of dried apples in the literature. Therefore, attempts were made to investigate the influence of apple variety on rehydration characteristics. The present study was conducted with the following objectives: 1.
To determine the effect of variety and rehydration temperature on the rehydration characteristics of dried apples; 2.
To fit the experimental rehydration data obtained to the Peleg model, Weibull model and Fick's second law model in order to: (i) estimate their suitability to describe the rehydration behavior of dried apples, (ii) obtain the values of models constants which have physical meaning and therefore can enable the explanation of the phenomena occurring during rehydration of different varieties of dried apples.

Materials and Methods
Four different varieties of apples, viz. Champion, Cortland, Grey Reinette and Ligol were procured from a local market in Warsaw, Poland. Homogenous fruits were chosen for each variety according to such maturity indicators as fruit appearance and size [28]. Champion belongs to a dessert variety but can also be used for cooking and processing. Its flesh is greenish-white with a cream undertone, medium loose, juicy, sweet, aromatic and tasty [36]. Cortland is a dessert variety. It has white, crispy, fine-grained, juicy, sweet, with medium contents of acids flesh. Cortland is aromatic and very tasty [36]. Grey Reinette has crispy, very juicy and green-yellow flesh. Its taste is acid; therefore, the variety is mostly used for cooking and processing [36]. Ligol belongs to a dessert variety. It has cream-colored, very juicy and tasty flesh [36]. Before the drying experiments, the apples were washed, hand peeled, and the outer cortex was cut into 10 ± 1 mm cubes. Drying was carried out on the same day in the tunnel dryer at the drying air temperature 60 • C and air velocity 2 m/s. The final moisture content of dried samples was ca. 9% w.b. (0.098 d.b.). Drying equipment and a method of conducting the experiments can be found in the paper by Kaleta and Górnicki [37]. The dried apples of the same variety obtained from the three independent experiments were mixed and then stored for further investigations in a sealed container for approx. seven days at 20 • C.
Dried apples were rehydrated in distilled water at temperature T r = 20, 45 and 70 • C. The temperature conditions were warranted with a water bath. The rehydration time amounted to 6 h at the water temperature 20 • C, 5 h at 45 • C and 4 h at 70 • C. Experiments were done in three repetitions. The water was not stirred, and its temperature was constant during the process of rehydration. The mass of each dried sample at the beginning of rehydration was 10 g. Mass of dried apple cubes to distilled water mass ratio amounted to 1:20. The WPE 300 scales (RADWAG, Radom, Poland) were used for the measurement of the sample mass (with 0.001 g accuracy). The change of dry matter of solid during rehydration was measured in accordance with AOAC standards [38]. The volume changes of dried apple cubes during rehydration were measured by the buoyancy method using petroleum benzine [39] with a relative error lower than 5%.
The color attributes of raw, dried and rehydrated apples were evaluated using a scanner (Canon CanoScan 5600F). Obtained color images were loaded into the sRGB color space. The mean brightness of pixels in each RGB channel of the image was used to express color parameters. The fresh, dried and rehydrated (color inside the cubes were additionally measured for the rehydrated apples (cubes were cut)) apple cubes were randomly positioned on the scanner platen. A total number of 20 images for each apple batch (different varieties and rehydration temperatures) were acquired. The ImageJ ver.47i software was used.
Two empirical models were adopted for describing the course of dried apple cubes rehydration, namely the Peleg model [40] and the Weibull model [41]. Such models were chosen because their constants have physical meaning.
Peleg model [40] is given by Equation (1): where M is the moisture content (dry basis), M 0 is the initial moisture content (dry basis), t is the time (h), k 1 is the Peleg rate constant (h/d.b.), and k 2 is the Peleg capacity constant (1/d.b.). When the rehydration process lasted long enough (t→∞) the equilibrium moisture content can be determined as follows: Constant k 1 informs about the rate of water absorption during the early stage of the rehydration; on the other hand, constant k 2 is related to the maximum capacity of water absorption [42,43]. The Peleg model has been used to describe the rehydration process of such dried products as carrots [44], mango [45] and potatoes [46].
The Weibull model is presented by the following equation: where M e is the moisture content at saturation (equilibrium moisture content, dry basis), α is the dimensionless shape parameter, and β is the scale parameter (h). Constant α represents product behavior during rehydration. The initial rate of the rehydration decreases with an increase in the α value. Constant β is related to the kinetics of the process and presents an inverse relation with the rehydration rate [43,47]. The Weibull model has been found to give satisfactory results in the descriptions of rehydration of such dried materials as ready-to-eat breakfast cereal [48], pumpkin [49] and Rosa rubiginosa fruits [43].
One theoretical model was also applied for describing the kinetics of rehydration. Different transport mechanisms take place during the discussed process, namely molecular diffusion, convection, hydraulic flow and capillary flow [50]. Theoretical models describing water absorption in foods are mostly based on the water diffusion through a porous medium; therefore, Fick's second law is frequently applied for mathematical modeling of rehydration. When following simplifying assumptions are considered: (1) the initial moisture content M 0 in the material is uniform, (2) the water diffusion coefficient is constant, (3) moisture gradient at the center of material equals zero, (4) shrinkage is negligible, (5) the sample surface reaches equilibrium moisture content M e instantaneously after immersion in rehydrating medium, (6) the process can be treated as isothermal, the Fick's second law describing the rehydration of cubes receives the following form [51,52]: where D is the water diffusion coefficient (m 2 /h), and L is the cube thickness (m). Ten terms of the series were taken for the calculations. Theoretical models based on Fick's second law of diffusion with given above simplifying assumptions have been successfully applied to different products such as carrots [53], dactyls [54] and soybeans [55].
The Levenberg-Marquardt nonlinear estimation method was applied to determine the model's constants while the significance of the influence of apple variety and the temperature of rehydrating water on the course of rehydration was determined with the use of the ANOVA technique applying the Levene test of homogeneity of variances. Homogenous groups were tested using Tukey's test HSD (α = 0.05). Calculations were conducted using the Statistica 12.5 application. The above-discussed Peleg model, Weibull model and Fick's second law model were chosen for describing the kinetics of dried apple cubes rehydration because their model constants have physical meaning, and obtained values of constants can be useful while discussing and explaining the course of different varieties of dried apple rehydration. Moreover, a comparison of the results obtained for three discussed models can give the answer, which of then can be treated as the most appropriate for describing the rehydration characteristics of dried apples.
The following statistical methods were used for finding the model suitability for the prediction of rehydration kinetics of dried apples: where M exp , i is the i-th experimentally observed moisture content (dry basis), M pre,i is the i-th predicted moisture content (dry basis), and N is the number of observations.
Lower SEE values indicate better fitness of the established model. Witrowa-Rajchert and Lewicki [56] and Rafiq et al. [18] used this statistical criterion for selecting the most suitable model to predict the rehydration kinetics.

•
Coefficient of determination R 2 The closer R 2 to 1, the greater is the relationship between experimental and predicted values. The coefficient has been applied by, e.g., Doymaz and Sahin [11] and Markowski et al. [46].

•
Root mean square error RMSE The lower the RMSE values, the better is the goodness of the fit. Such a criterion has been used by, e.g., Kaleta et al. [57] and Ricce et al. [44].

Results and Discussion
The results of the experiments are shown in Figure 1 where V is the volume (cm 3 ), V0 is the initial volume (cm 3 ) and equilibrium volume: According to the calculations, the Peleg model well described the mass gain, the dry matter loss, and the volume increase of dried apples during their rehydration, since the value of the coefficient of determination R 2 was within 0.9595 to 0.9883 for mass, 0.9150 to 0.9959 for dry matter and 0.9137 to 0.9896 for volume.
Statistical analysis of the influence of apple variety on the mass gain, the dry matter loss and the volume increase of dried apples during their rehydration at 20 °C (division into homogenous groups) are shown in Table 1. In this table, numbers mean average values from three repetitions of measurements of the current mass, dry matter and volume of the rehydrated dried material (with the standard deviation), whereas homogenous groups for each time of rehydration were determined with the same letters. The Peleg model took the following form: • for mass: where m is the mass (g), m 0 is the initial mass (g) and equilibrium mass: • for dry matter: where m d.m. is the dry matter (g), m d.m.0 is the initial dry matter (g) and equilibrium dry matter: • for volume: where V is the volume (cm 3 ), V 0 is the initial volume (cm 3 ) and equilibrium volume: According to the calculations, the Peleg model well described the mass gain, the dry matter loss, and the volume increase of dried apples during their rehydration, since the value of the coefficient of determination R 2 was within 0.9595 to 0.9883 for mass, 0.9150 to 0.9959 for dry matter and 0.9137 to 0.9896 for volume.
Statistical analysis of the influence of apple variety on the mass gain, the dry matter loss and the volume increase of dried apples during their rehydration at 20 • C (division into homogenous groups) are shown in Table 1. In this table, numbers mean average values from three repetitions of measurements of the current mass, dry matter and volume of the rehydrated dried material (with the standard deviation), whereas homogenous groups for each time of rehydration were determined with the same letters.
It can be noticed ( Figure 1a) that for all investigated apple varieties, water uptake increased with increasing rehydration time. The rate of the process was faster in the initial period and decreased up to the saturation level. Such a course of rehydration at the beginning could be explained by rapid filling up of capillaries and cavities near the surface with the water. The cell walls absorb water, soften, and then according to the natural cellular structure elasticity, the cells return to their original shape by drawing water into the inner cavities. In the further stage of the process, water absorption slows down because the rehydrated sample gets close to the state of equilibrium [58][59][60]. A similar character of mass changes during rehydration has been reported by, among others, Marabi et al. [61] for carrot, Markowski et al. [46] for potato and Maldonado et al. [4] for mango.
According to Table 1, the apple variety influenced the rehydration of the dried product. It can be observed that at the beginning of the process (0-1.5 h), the course of the dried Champion rehydration differed statistically significantly from the kinetics of dried Cortland, Gray Reinette and Ligol (the difference between the mass gain for these three varieties was at the same time statistically insignificant). The final mass was the greatest for the Cortland variety and the smallest for Ligol one, and the differences for all investigated apple varieties were statistically significant.
The results of the application of the Peleg model (Equations (8) and (9)) for approximating the mass gain during the rehydration of investigated varieties of dried apples are presented in Table 2. It could be noticed that apple variety had a statistically significant influence on the value of the equilibrium mass of the rehydrated sample. The highest value, 52.93 g, demonstrated Cortland variety rehydrated at 20 • C, the lowest 39.13 g Ligol one at 20 • C. The value of m e for the same apple variety depended in a statistically significant way on the temperature of rehydrating water. For the Ligol variety, the discussed value increased with increasing temperature, but for the Champion and Grey Reinette, m e value for 70 • C was lower than for 45 • C. This may be explained in such a way that higher temperature causes damage of cellular tissue and a decrease of permeability within the apple structure, and perhaps a loss of solids during rehydration. Similar trends for rehydration at higher temperatures have been noticed, among others, Femenia et al. [62] for broccoli stems, Garcia-Pascual et al. [41] for Boletus edulis mushroom and Maldonado et al. [4] for mangoes. The apple variety demonstrated a statistically significant influence on the value of constant k 1 . The highest value at 20 • C showed Cortland variety, the lowest one Champion variety. For Champion, Grey Reinette and Ligol varieties, the k 1 value decreased with increasing temperature. The results suggest that the rate of water absorption during the early stage of the rehydration at 20 • C was the highest for Champion and the lowest for Cortland ( Figure 1a) and, moreover, the discussed rate became higher at a higher temperature of rehydration. The achieved results confirm the statement that constant k 2 was related to the maximum capacity of water absorption [42,43]. The highest k 2 value was obtained for Ligol at 20 • C and the lowest for Cortland at 20 • C and the difference was statistically significant. Table 1. Average values of mass (g), dry matter (g) and volume (cm 3 ) of the rehydrated dried apples (with standard deviation) in the rehydration process at 20 • C.   (8) and (9)) for approximating the mass gain during the rehydration of different varieties of dried apples. It can be observed ( Figure 1b) that for all investigated apple varieties, solute loss increased with increasing rehydration time. The rate was faster at the beginning of the process and decreased up to the saturation level. The explanation of such a course of rehydration could be the following. At the beginning of the process, there was a high rate of mass transfer because of the high difference between the solid concentration in rehydrated dried apple and rehydrating water. In the further stage, the rate of mass transfer slowed down because both concentrations approached the state of equilibrium [60]. Similar rehydration kinetics had been observed by, among others, Górnicki [63] for parsley and apple var. Idared, Maté et al. [64] for potatoes and Stępień [65] for carrots.

Variety of Apple
According to Figure 1b and Table 1, it can be assumed that the apple variety had a statistically insignificant influence on the loss of dry matter. The same statement regards the equilibrium dry matter and Peleg capacity constant k 2 ( Table 3). The highest value m d.m.e = 3.387 g and k 2 = 0.1636 1/g reached Champion variety rehydrated at 70 • C, the lowest one m d.m.e = 2.329 g and k 2 = 0.1395 1/g Gray Reinette rehydrated at 45 • C, but the differences were statistically insignificant. As far as Peleg rate constant k 1 was concerned, the statistically significant influence of dried apple variety could be observed. For rehydration conducted at 20 • C, Gray Reinette showed the highest value of k 1 = 0.0814 h/g, whereas Ligol variety demonstrated the lowest value of k 1 = 0.0468 h/g. The obtained results suggest that the rate of dry matter loss during the early stage of the rehydration at 20 • C was the highest for Ligol and the lowest for Gray Reinette variety (Figure 1b). The value of k 1 for the same apple variety depended in a statistically significant way on the temperature of rehydrating water, and at 20 • C was higher than at 70 • C.  (10) and (11)) for approximating the dry matter loss during the rehydration of different varieties of dried apples. For all investigated apple varieties, the volume increased with increasing time of rehydration (Figure 1c). The fastest increase of volume took place in the initial period of rehydration; in the further stage of the process, water absorption slowed down because rehydrated samples approached the state of equilibrium. Fast water absorption at the beginning of the process was probably related to filling with water capillaries at the surface of a sample [66]. A similar rehydration behavior has been noticed by, among others, Bilbao-Săinz et al. [66] for apple var. Granny Smith, Maskan [67] for wheat and Witrowa-Rajchert [68] for apple var. Idared, carrots, parsley, potatoes and pumpkins. It can be stated that in the initial period of rehydration (0-0.5 h), the apple variety had a statistically insignificant influence on the increase of volume (Table 1). In the further stage (3-6 h), however, Gray Reinette showed the highest values of volume which differ statistically significant from volume values for Champion, Cortland and Ligol variety. Differences of volume values for these three apple varieties were statistically insignificant.

Variety of Apple
The results of the application of the Peleg model (Equations (12) and (13)) for approximating the volume increase during the rehydration of investigated varieties of dried apples are shown in Table 4. It can be admitted that apple variety had a statistically significant influence on the value of the equilibrium volume of the rehydrated sample. As far as rehydration at 20 • C is concerned, the highest value, 66.8 cm 3 , was obtained for Gray Reinette, the lowest one 49.4 cm 3 for Ligol. For Champion and Gray Reinette varieties, the V e value decreased with increasing rehydration temperature. The dependence of the V e on the temperature was statistically significant. The apple variety showed a statistically significant influence on the value of constant k 1 . The highest value at 20 • C demonstrated Cortland variety, the lowest one Ligol variety. Received results suggest that the rate of volume increase during the early period of the rehydration at 20 • C was the highest for Ligol and the lowest for Cortland. For Champion and Gray Reinette varieties, the k 1 value decreased with increasing temperature, whereas for the Ligol variety, k 1 at 45 • C was higher than at 20 • C and 70 • C. The dependence of the Peleg rate constant k 1 on the temperature was statistically significant. The Peleg capacity constant k 2 depends in a statistically significant way on apple variety and for Champion and Ligol on rehydration temperature. The highest value at 20 • C was obtained for Ligol, the lowest for Gray Reinette what was in agreement with the results achieved for the equilibrium volume of the rehydrated sample. Table 4. Results of the application of the Peleg model (Equations (12) and (13)) for approximating the volume increase during the rehydration of different varieties of dried apples. As it was told before, during the rehydration simultaneously took place absorption of liquid by the dried product, swelling of the rehydrated material and leaching of the solutes from the product to the rehydrating medium. Therefore, the value of the moisture content of the rehydrated product can be treated as a parameter that informs about the summary result of rehydration. An evaluation of the Peleg model (Equation (1)), Weibull model (Equation (3)) and Fick's second law model (Equation (4)) was applied in this work to describe the rehydration characteristics of investigated varieties of apples.

Variety of Apple
The calculations were carried out in the following way. The curve fitting computations with the drying time were carried on considered models. Then the regressions were undertaken to account for the effect of rehydrating water temperature T r on the model's constants/parameters. The effects of T r on the model's constants/parameters were also included in the models. The linear type of equations was examined. The constants/parameters combinations that gave the highest R 2 values were considered in the final model. Obtained equations were next used for determining the moisture content of investigated varieties of apples at any time during rehydration. The established models were validated by comparison of computed and measured moisture content in any particular rehydration run. Table 5 presents the coefficients of constant equations for the Peleg model (Equations (1) and (2)) and the results of statistical analyses on the rehydration modeling of different varieties of dried apples. The following linear type constant equations were examined:  (1) and (2)) and results of statistical analyses on the rehydration modeling of different varieties of dried apples. The R 2 values were greater than 0.9527, the RMSE ones were lower than 0.8473, and the SSE values were lower than 15.8500, so it can be admitted that the Peleg [5,45,70,71].

Variety of Apple
It turned out that the Peleg rate constant depended in a statistically significant manner on the apple variety. The apple var. Champion showed the lowest values of k 1 at the examined rehydration temperatures 20-70 • C. This suggests that the rate of water absorption in the early phase of the rehydration process was the fastest for the Champion variety. The highest value of k 1 at 20 • C was obtained for Gray Reinette, whereas Ligol showed the highest k 1 at 45 • C and 70 • C. The Peleg rate constant tended to decrease along with the rehydration temperature for investigated varieties, and statistically significant differences were found between data. This suggests a higher rate of water absorption at a higher rehydration temperature. Therefore, it could be stated that water transfer, related to the inverse of the constant k 1 , was promoted by the temperature increase. Similar behavior, as far as the dependence on the temperature was concerned, has been found, among others, for chickpeas [72], mangos [45] and Rosa rubiginosa fruits [43].
It resulted from the conducted investigations that the Peleg capacity constant was influenced in a statistically significant manner by the apple variety. The highest value of k 2 at 20 and 45 • C was demonstrated by apple var. Ligol, the lowest apple var. Grey Reinette, whereas at 70 • C Champion variety, showed the highest k 2 value and Ligol the lowest one. The Peleg capacity constant for apple var. Grey Reinette increased with increasing temperature, and the differences were statistically significant. The same tendency was observed for Champion, but the differences for the values of k 2 at 20 and 45 • C were statistically insignificant. Apple var. Ligol demonstrated the highest Peleg capacity constant at 20 • C, whereas the k 2 values at 45 and 70 • C were the same and lower than the value at 20 • C. The differences between the discussed constant at 20 • C and 45 • C was statistically significant. The Peleg capacity constant was related to equilibrium moisture content M e by Equation (2). According to this equation, a growing value of M e means a decreasing value of k 2 . Equilibrium moisture content was a characteristic parameter of each product. The maximum capacity of water absorption of biological material depends on the type of product, structure of its tissue and chemical composition of the cells and could be modified by thermal treatments. The value of M e (so consequently k 2 ) could change if the structure or other properties were modified by temperature during rehydration [47,58]. The effect of rehydration temperature on M e depended on the product. The results found in the literature indicate that equilibrium moisture content increased with increasing temperature [5,73], decreased with increasing rehydration temperature [42,72] or, in some cases, was independent of temperature [74,75]. Table 6 shows the coefficients of constant equations for the Weibull model (Equation (3)) and the results of statistical analyses on the rehydration modeling of different varieties of dried apples. The following linear-type constant equations were applied: As can be seen from the statistical analysis results, the R 2 values varied between 0.9580 and 0.9978, the RMSE ones fell within the range of 0.1602 to 0.8087, and the SSE values were between 0.3081 and 14.2117. It could be therefore accepted that the Weibull model showed a slightly better fit upon the experimental resulted than the Peleg model.   The same letters in the same column indicate homogenous groups (α < 0.05, Tukey's test HSD).
It resulted from the investigations that the dimensionless shape parameter α depended on the apple variety but in a statistically insignificant manner. The apple var. Cortland showed the highest value of α at rehydration temperature 20 • C and then next in the sequence were Grey Reinette, Champion and Ligol. The sequence from the highest value of α to the lowest at 45 • C was the following: Ligol, Grey Reinette and Champion. The apple var. Ligol and Grey Reinette demonstrated at 70 • C the same value of the dimensionless shape parameter, which was higher than α for Champion. As it was written, parameter α can be related to the rate of water absorption at the beginning of the rehydration. The lower the value of α, the faster was the rate of absorption. The obtained results were in good accordance with results obtained for Peleg rate constant k 1 , namely the process rate in the early phase of the rehydration was the fastest for Champion variety and the lowest for Ligol and Grey Reinette one at 45 and 70 • C. The dimensionless shape parameter tended to decrease with the rehydration temperature for apple var. Champion, whereas for Grey Reinette and Ligol, parameter α increased from 20 to 45 • C, and then decreased along with temperature, but the differences were statistically insignificant. A similar trend as for Champion was observed by Goula and Adamopoulos [47] for tomato, whereas Garcia-Pascual et al. [58] noticed for Morchella esculenta similar tendency as for Gray Reinette and Ligol. However, the dimensionless shape parameter had also been found to be independent of temperature [41,69].
It can be stated that the apple variety affects the value of the scale parameter β. Ligol showed the highest value of β at the rehydration temperatures 20 and 70 • C, whereas Champion the lowest value. The sequence at 45 • C was reversed, but at this temperature, the differences were statistically insignificant. According to Goula and Adamopoulos [47], parameter β represents the time needed to accomplish approx. 63% of rehydration. The high value of the scale parameter suggests a difficulty of the material to absorb water during the rehydration, resulting in a low process rate [43]. Therefore, it can be assumed that the rate of absorption during the entire process of rehydration at 20 and 70 • C was the highest for Champion and the lowest for Ligol. The values of parameter β decreased with increasing temperature for Grey Reinette (statistically significant differences), whereas Champion demonstrated the highest value of β at 45 • C and the lowest one at 70 • C. Ligol showed the highest β value at 20 • C and the lowest one at 45 • C, but the differences were statistically insignificant. The following behavior as far as the dependence of β on the temperature was concerned could be found in the literature: β value for pumpkin decreased when rehydration temperature increased [49], in case of Morchella esculenta, discussed value decreased along with temperature except at 70 • C, where β value increased [58], whereas for tomato scale parameter increased with increasing temperature [47]. Such a different effect of rehydration temperature on the value of the β parameter could be attributed to the different changes in the structure of material during the process of rehydration. Explanation of this phenomenon needs a deep understanding of the correlation between structure and mass transfer process during the rehydration.
The values of equilibrium moisture content M e , identified from the Weibull model, depended on apple variety, although the differences were statistically insignificant. The highest value of M e at rehydration temperature 20 • C showed apple var. Gray Reinette, whereas at 45 • C Champion and at 70 • C Ligol. The lowest M e value at temperature 20 • C demonstrates Champion, whereas at 45 • C Ligol and at 70 • C Champion. The values of equilibrium moisture content identified from the Weibull model and Peleg one were comparable. As far as the dependence on the temperature is concerned, the M e values for Gray Reinette decreased with increasing temperature, whereas apple var Champion shows the highest value of M e at 45 • C and the lowest at 70 • C. On the other hand, Ligol demonstrated the highest moisture equilibrium content at 20 • C and the lowest at 45 • C. The Weibull model, however, did not present statistically significant differences among temperatures for the M e values. Table 7 presents the results of statistical analyses on the rehydration modeling of different varieties of dried apples using Fick's second law model (Equation (4)). The R 2 were equal or greater than 0.9214 except for apple var. Champion at 70 • C (0.8965), the RMSEs were equal or lower than 0.0865, and the SSEs were equal or lower than 0.0642 except for Champion at 70 • C (0.0972). It can be, therefore, observed that Fick's second law model describes the experimental data adequately. Comparing the results obtained for the three discussed models, the diffusion model could be considered as the most appropriate. The values determined for D/L 2 range from 0.00772 to 0.06987 1/h and were found to be lower than the values reported in the literature for mushrooms: 1.764-10.84 1/h [41,58]. It should be underlined, however, that the values of the water diffusion coefficient reported in the literature for food materials were within the general range of 3.6·10 −10 m 2 /h to 3.6·10 −3 m 2 /h [76][77][78][79]. It turned out from the investigations that the values of D/L 2 depend on the apple variety, but the differences were statistically insignificant. The apple var. Champion demonstrated the highest values of D/L 2 at the examined rehydration temperatures 20-70 • C. The lowest value of the discussed parameter at 20 • C was obtained for Grey Reinette, whereas Ligol showed the lowest D/L 2 at 45 and 70 • C. The received results were in agreement with calculations obtained for the Peleg rate constant k 1 and confirm the statement that k 1 was related to the rate of mass transfer, and its reciprocal could be compared with a water diffusion coefficient. The values of D/L 2 increase with rehydration temperature, but the differences were statistically insignificant. The same dependence on temperature had been observed among others for amaranth grain [80], date palm fruits [54] and mango [4]. Cunningham et al. [81] observed, however, a positive effect of temperature on water absorption of potatoes until 60 • C, and then a negative effect was obtained. A similar tendency had been found by Garcia-Pascual et al. [58] for Morchella esculenta because the values of D/L 2 increased with temperature except at 70 • C, where this value decreased. Table 7. Results of statistical analyses on the rehydration modeling of different varieties of dried apples using Fisk's second law model (Equation (4)).  Table 8 presents the results of statistical analyses on the color changes of different varieties of raw, dried and dried apples during rehydration at different temperatures. The Gray Reinette variety (raw apple cubes) showed the lowest values of color attributes R and G (193.3 and 180.7, respectively), which differed statistically significant from discussed attributes for Champion, Cortland and Ligol. The differences between these three apple varieties were statistically insignificant.  4. The differences between apple varieties were statistically significant. The color of the rehydrated cubes of apples was measured in two places: at the surface of the side and in the center of the cube (cubes were cut). There was no effect of the place of the color test on the R channel values of the rehydrated apples, whereas values for channels G and B were greater at the center of the rehydrated apple cubes. The differences for Gray Reinette (T r = 20 • C-channel G) and Ligol (T r = 20 • C-channel B, T r 45 • C and 70 • C-channels G and B) were statistically significant. The resulted of the statistical analysis showed the influence of rehydration temperature on RGB channels. The values of each RGB channel increased with an increase of T r for rehydrated apple var. Ligol. The differences were statistically significant.

Variety of Apple
It turned out from the investigations that the values of RGB depend on the apple variety, and the differences were statistically significant. The apple var. Champion demonstrated the highest values of all RGB channels at the examined rehydration temperatures 20-70 • C. For apple var. Champion rehydrated at T r = 20 • C the values of R, G and B channels were higher than for other considered varieties.
Drying results in adverse changes that occur due to complex biochemical reactions and water loss and are dependent on the drying regime. Especially apples are exposed to undesirable quality changes due to the high content of water and sugars, particularly glucose and fructose, as well as the presence of pectins and malic acid [82]. The apple color change (especially the rapid increment in the initial stage of the drying process [83]) could be associated with the rapid synthesis of phenolic compounds and the non-enzymatic browning reactions [84]. Nadian et al. [83] stated as the color changes of pretreatment apples were visually different from the color changes of untreated slices at different drying times, and this difference could be related to the further progressing of chemical, biochemical and physical changes in untreated apple by stimulating most of the enzymatic and non-enzymatic reactions. Additionally, color change in the apple could have resulted from the decomposition of original pigments, the formation of brown pigments by enzymatic and non-enzymatic browning reactions and the formation of other undesirable pigments, wherein for pigments responsible for the original apple color is believed chlorophyll (green color), carotenoids, flavonoids (yellow color) and anthocyanins (red color) [85]. The Millard reaction during which interaction between reducing sugars and amino acids occurs is easily stimulated in wet products during thermal processing [86] and also be resulted from the product's structural shrinkage that subsequently increases the opacity of dehydrated samples [87,88]. The conducted research shows the influence of apple variety on both the color of the dried fruit and the color of the rehydrated dried material. Therefore, in order to obtain dried apples and rehydrated apple with desired (sensory attractive) color qualities, it should keep in mind the apple variety.

Conclusions
The following conclusions can be drawn from the conducted investigations.

1.
Apple variety and temperature of rehydrating water had a statistically significant influence on the value of the equilibrium mass of the rehydrated sample. The highest value demonstrated Cortland variety rehydrated at 20 • C, the lowest Ligol one at 20 • C. The rate of water absorption during the early stage of rehydration at 20 • C was the highest for Champion and the lowest for Cortland, and the discussed rate becomes higher at a higher rehydration temperature; 2.
The apple variety had a statistically insignificant influence on the loss of dry matter. The rate of dry matter loss during the early stage of the rehydration for some apple variety depended in a statistically significant way on the rehydration temperature, and at 20 • C was higher than at 70 • C; 3.
Apple variety and temperature of rehydrating water had a statistically significant influence on the value of the equilibrium volume of the rehydrated sample. The highest value demonstrated Gray Reinette at 45 • C, the lowest Champion at 70 • C; 4.
Comparing the results obtained for three considered models, namely Peleg model, Weibull model and Fick's second law model, the diffusion model can be considered as the most appropriate for describing the rehydration behavior of dried apples; 5.
The values of the water diffusion coefficient to the second power of the cube thickness ratio (D/L 2 ) depend on the apple variety, but the differences were statistically insignificant. Apple var. Champion demonstrated the highest values of D/L 2 at the rehydration temperatures of 20-70 • C. The lowest value of the discussed parameter at 20 • C was obtained for Gray Reinette, whereas Ligol showed the lowest D/L 2 at 45 and 70 • C. The values of D/L 2 increased with rehydration temperature, but the differences were statistically insignificant; 6.
Taking into account all the obtained results, it can be stated that apple var. Champion showed a greater rate of water absorption during the entire process of rehydration than other investigated varieties; therefore, it could easily apply for special purpose food products;

7.
The apple variety had a statistically significant influence on the color attribute B of raw apple. The highest value demonstrated Cortland, the lowest Gray Reinette one. The apple variety had a statistically significant influence on the color attribute of dried apple. The highest value demonstrated Champion, the lowest Gray Reinette and Ligol. Apple variety and temperature of rehydrating water had a statistically significant influence on the color attribute of the rehydrated apples.
Author Contributions: K.G., proposal of the research topic, data analysis, modeling, writing of the manuscript; A.C. experiments, data analysis; A.K. formal analysis, writing of the manuscript and critical revision of the manuscript. All authors have read and agreed to the published version of the manuscript.