Mathematical Modelling of Blanch-Assisted Drying of Pomegranate ( Punica granatum ) Arils in a Hot-Air Drier

: The e ﬀ ect of blanching conditions on the hot-air drying kinetics of three pomegranates (cvs. “Acco”, “Herskawitz” and “Wonderful”) were assessed. Water blanching conditions considered were 90 ◦ C for 30 s, 90 ◦ C for 60 s, 100 ◦ C for 30 s and 100 ◦ C for 60 s. The drying experiments were carried out at 60 ◦ C, 19.6% relative humidity and at a constant air velocity of 1.0 m s − 1 . The experimental curves were ﬁtted to seven di ﬀ erent drying models. For the Acco cultivar, the drying behaviour was best predicted by the Logarithmic and Page model for blanched (R 2 ranging between 0.9966 and 0.9989) and unblanched (R 2 = 0.9918) samples, respectively. Furthermore, for the Herskawitz cultivar, Logarithm, Page and Midili models were most suitable for predicting drying behaviour of both blanched and unblanched samples. Also, for the Wonderful cultivar, Logarithm and Midili models were most accurate for predicting the drying behaviour for both blanched and unblanched samples amongst other models. The blanched samples dried faster with shorter drying times: “Acco” (7 h), “Herskawitz” (8 h), and “Wonderful” (7 h), compared to the unblanched samples, which dried after 15, 20 and 11 h, respectively. E ﬀ ective di ﬀ usion coe ﬃ cient of moisture in pomegranate arils ranged from 4.81 × 10 − 9 and 1.11 × 10 − 8 m 2 s − 1 for the Acco cultivar, for the Herskawitz cultivar; 3.29 × 10 − 9 and 1.01 × 10 − 8 m 2 s − 1 and for the Wonderful cultivar; 5.83 × 10 − 9 and 1.09 × 10 − 8 m 2 s − 1 . Overall, blanching resulted in low energy consumption during drying of pomegranate arils. In addition, the Logarithmic model generally showed an appropriate model for blanched samples regardless of cultivar. For unblanched samples, the Page model was more appropriate for “Acco” and “Herskawitz”, while the Midili model was appropriate for “Wonderful”. Therefore, this study provided science-based and practical drying conditions for the investigated pomegranate cultivars.


Introduction
Pomegranate (Punica granatum) fruit consumption has continued to gain global interest among consumers due to its rich nutritional properties and high content of polyphenols [1,2]. It is a good source of phenolic compounds including flavonoids (anthocyanins and flavonols), condensed tannins (proanthocyanidins) and hydrolysable tannins (ellagitannins and gallotannins) [3]. However, pomegranates arils are highly perishable, with a shelf life of 5 to 8 days [4]. This limits pomegranate consumption and availability during the off-season. Drying is one of the oldest methods used to preserve food commodities [5]. Drying has been shown to preserve and add value to pomegranates Goyal et al. [28] reported that Logarithmic model best described the drying kinetics in comparison to other models investigated.
Several types of hot air drying have been implemented to dry agricultural crops, the design and operation of such dryers have been challenging due to the complexity of the parameters that govern the drying process and the factors affecting the quality of the product. One of the most important factors to be measured in dryer design is the drying rate for the prediction of drying time. Hence, investigating the appropriate model suitable for the modelling and prediction of the drying process is crucial. Since cultivar and nature of pre-treatment may affect the drying process, it is necessary to establish the appropriate drying model as a function of cultivar and pre-treatment. Therefore, the aims of this study were two-fold, first, to investigate the effect of different blanching conditions on thin-layer drying kinetics of three pomegranate cultivars, and second, to determine the mathematical model that best describes the characteristics of the drying process. In addition, effective diffusivity coefficients for the investigated cultivars were determined.

Plant Material and Sample Processing
Three pomegranate cultivars, "Acco", "Herskawitz" and "Wonderful", classified as sweet, sour and sweet-sour, respectively, were investigated. The fruit was harvested at commercial harvest (13 • Brix) between February and April in the 2018 harvest season from a local orchard in Wellington, South Africa (33 • 01 00" S, 18 • 58 59" E). Fruit was sorted for uniformity in size, shape, and colour and transported in an air-conditioned vehicle to the Postharvest Technology Laboratory at Stellenbosch University. The arils were manually separated from the fruits and used for processing. Immediately before the blanching process, 10 g of pomegranate arils per cultivar were taken for initial moisture content determination [9,29] with slight modification. The initial moisture content of the fresh arils was: 56.67%, 54.95% and 78.51% (w.b) for "Acco", "Herskawitz" and "Wonderful", respectively.

Oven Drying Procedure
Blanching of fresh arils was carried out in a water bath in batches. Samples were blanched at 90 • C and 100 • C, each for 30 s and 60 s. The unblanched sample was used as the control. Blanched arils were dipped in iced water 0 • C for 3 min to halt the continuous heating process and carefully drained before weighing. The process was carried out in triplicates for each treatment. Samples (60 g) were weighed before being subjected to drying in an oven (Model nr. 072160, Prolab Instruments, Sep Sci., South Africa) set at a temperature of 60 • C, 19.6% relative humidity and 1.0 m s −1 constant air velocity. The ambient air was used at 20 ± 0.3 • C and 80%-88% RH. Weight loss was recorded every 60 min until the desired moisture content between 10% ± 0.2%, wet basis (w.b.) was reached [8,9] with slight modification. A schematic view of a laboratory hot-air convective drying system is illustrated in Figure 1.

Mathematical Modelling
To find the most suitable model, seven models were examined ( Table 1). The selected mathematical models best describe drying mechanisms of food material and provide the required temperature and moisture information for proper control of the process [8]. Midili MR = a.exp(-kt n ) + bt [34] In these models, the moisture ratio was simplified to Equation (1) according to [35]:

Mathematical Modelling
To find the most suitable model, seven models were examined ( Table 1). The selected mathematical models best describe drying mechanisms of food material and provide the required temperature and moisture information for proper control of the process [8]. In these models, the moisture ratio was simplified to Equation (1) according to [35]: where M t is the instantaneous moisture content at time t (h), and M 0 is the initial moisture content.

Drying Rate (DR)
The drying rate at a particular time was calculated by Sarpong et al. [36] in Equation (2): where t 1 and t 2 are the drying times (min) at different times during drying; M t1 and M t2 are the moisture content of samples (g min −1 ).

Effective Moisture Diffusivity Determination
Fick's second law of diffusion is used to describe the drying process usually controlled by internal diffusion for most biological materials during the falling rate period [36] and shown in Equation (3): The effective moisture diffusivity (D eff ) (m 2 s −1 ) was calculated from the diffusion equation (Equation (3)) for the geometry on the assumption of unstable moisture diffusivity, spherical coordinate movement of moisture, constant temperature and diffusion coefficients and negligible shrinkage during the process of drying is given as the following [37]: where D eff is the effective moisture diffusivity (m 2 s −1 ), t is the time (h), R denotes the radius of the aril, assumed spherical and constant during the drying period, and n is a positive integer. In the case of longer drying periods, the above equation can be simplified to the only first term of series, without much affecting the accuracy of the prediction [8,37,38]: From Equation (5), a plot of ln(MR) versus drying time gives a straight line with a slope (K) of:

Statistical Analysis of the Models
Data was processed with STATISTICA (Statistica 13.0, StatSoft Inc., Tulsa, OK, USA) and presented as means ± standard error. All analysis was done in triplicate. Factorial analysis of variance (ANOVA) in order to observe if the mean values were statistically different and the Fisher's LSD test at a level of significance of 95%. The moisture ratio curves obtained were fitted with seven mathematical models in order to describe the drying characteristics of blanched and unblanched pomegranate arils. Multiple regression analysis was performed using MATLAB software. The experimental data were evaluated with the coefficient of determination (R 2 ) and the root mean square error (RMSE). The higher the R 2 values, and the lower the RMSE values, the better the model of best fit [30].
MR exp,i is the ith experimentally determined moisture ratio, MR pre,i is the ith predicted moisture ratio value, N is the number of observations and z, the number of drying constants. Figure 2 shows a pictorial representation of the trend of pomegranate arils before and after processing. At the end of drying, blanched samples became stickier while the unblanched appeared easily separated from each other, which informs part of the textural properties during crushing and grinding [39].

Moisture Ratio
MRexp,i is the ith experimentally determined moisture ratio, MRpre,i is the ith predicted moisture ratio value, N is the number of observations and z, the number of drying constants. Figure 2 shows a pictorial representation of the trend of pomegranate arils before and after processing. At the end of drying, blanched samples became stickier while the unblanched appeared easily separated from each other, which informs part of the textural properties during crushing and grinding [39]. Also, blanched samples showed glistering dark-purple colour as a result of the occurrence of Maillard reactions during drying [40], while unblanched arils appeared pale. Amongst the investigated cultivars, the order of average drying time blanched sample (100 °C for 60 s) and unblanched sample (control) was observed in the order of cultivar "Herskawitz" (600 min) > "Acco" (420 min) > "Wonderful" (300 min) regardless of blanching condition (Figure 3).

Acco
Herskawitz Also, blanched samples showed glistering dark-purple colour as a result of the occurrence of Maillard reactions during drying [40], while unblanched arils appeared pale. Amongst the investigated cultivars, the order of average drying time blanched sample (100 • C for 60 s) and unblanched sample (control) was observed in the order of cultivar "Herskawitz" (600 min) > "Acco" (420 min) > "Wonderful" (300 min) regardless of blanching condition (Figure 3).
Moisture ratio (MR) decreased rapidly with drying time for "Acco", "Herskawitz" and "Wonderful" dried pomegranate arils. The drying curves showed the same trend regardless of blanching conditions. For instance, moisture content decreased, and the desired moisture was reached faster in blanched samples (420-480 min) than in the unblanched (660-1200 min), regardless of blanching condition ( Figure 4). This amounted to approximately 53%, 60% and 36% reduction in drying time for "Acco", "Herskawitz" and "Wonderful", respectively.
Also, blanched samples showed glistering dark-purple colour as a result of the occurrence of Maillard reactions during drying [40], while unblanched arils appeared pale. Amongst the investigated cultivars, the order of average drying time blanched sample (100 °C for 60 s) and unblanched sample (control) was observed in the order of cultivar "Herskawitz" (600 min) > "Acco" (420 min) > "Wonderful" (300 min) regardless of blanching condition (Figure 3).

Drying Rate
The variation in drying rate with drying time obtained from Equation (2) is shown in Figure 5 for "Acco", "Herskawitz" and "Wonderful", respectively. The variation in drying rate with drying time obtained from Equation (2) is shown in Figure 5 for "Acco", "Herskawitz" and "Wonderful", respectively.   In the early stages, drying rate increased rapidly, reaching a maximum value, then a progressive decrease with drying time was observed. Drying rates for both blanched and unblanched samples followed a pattern of falling rate period, which is considered as a phenomenon of diffusion-control. A similar trend was observed in the studies by Minaei et al. [8] for pomegranate arils; Wang et al. [30] and Kaya et al. [41] in apples. During the falling rate period, the highest drying rates were found in the blanched samples ranging from (0.358 to 0.398 g min −1 ; 0.274 to 0.363 g min −1 and 0.333 to 0.382 g min −1 ) for "Acco", "Herskawitz" and "Wonderful", respectively, while all unblanched samples had the lowest drying rate (ranging from 0.214 to 0.311 g min −1 ) for the three cultivars. The rates of drying for all blanched arils were higher than the unblanched pomegranate arils for "Acco", "Herskawitz" and "Wonderful". Also, the differences in drying were highest at the early stage of drying when the greater amount of water in the sample is evaporated and at the later stage, the differences in the amount of moisture evaporation in the sample is gradually lower ( Figure 5). The higher drying rate is ascribed to the microstructural differences between the blanched and unblanched pomegranate arils. Microstructural differences between fresh apple pomace and the pre-treated apple pomace were reported by Wang et al. [30]. This is due to the porous structure and shrinkage of arils during blanching as a result of wide spaces between neighbouring cells [42,43].

Moisture Diffusion
An isothermal temperature at 60 • C was maintained during the drying process. There were variations in Deff for all the blanching conditions regardless of the cultivars Table 2. Deff values were within the range of 4.81 × 10 −9 and 1.11 × 10 −8 m 2 s −1 for the Acco cultivar, for the Herskawitz cultivar; 3.29 × 10 −9 and 1.01 × 10 −8 m 2 s −1 and for the Wonderful cultivar; 5.83 × 10 −9 and 1.09 × 10 −8 m 2 s −1 . The highest Deff was recorded for samples blanched at 90 • C for 60 s for Acco and Herskawitz cultivars, while (100 • C for 60 s) for the Wonderful cultivar. However, control samples for all cultivars had the lowest Deff values.
As observed in Figure 4, blanching condition lowered drying time. These results suggested the positive impact of blanching by lowering the drying time of pomegranate arils, regardless of the cultivar. Results from this study correspond with findings by Karaaslan et al. [29], who reported the shortest drying time for pre-treated samples of pomegranate aril under vacuum dryer. A 20% reduction in drying time for banana under a relative humidity-convective air dryer was also reported by Sarpong et al. [36]. Variability in blanching conditions with a similar drying curve indicated that increased temperature or duration during blanching had no distinct differences on the drying kinetics of dried pomegranate arils. This result also agreed with the study by Sarpong et al. [36], who reported no significant effect on the drying kinetics of dried banana as a result of similar drying curves for all treatments.
Moisture diffusion and drying rate phenomena are dependent on temperature and product composition [8]. It is thus logical to attribute the observed differences in moisture diffusion and drying time to initial moisture content in the investigated Acco (56.67%), Herskawitz (54.95%) and Wonderful (78.51%) pomegranate cultivars. Generally, higher values were found in the blanched samples, which is connected to the rapid removal of moisture and faster drying of the samples. Deff values reported in this study were close to the range previously reported for pomegranate arils, with Deff values of 0.74 × 10 −10 to 5.25 × 10 −10 m 2 s −1 and 3.05 × 10 −10 to 3.43 × 10 −10 m 2 s −1 for vacuum and microwave dried arils, respectively [8]. High Deff values among the blanching conditions indicated that moisture movement in pomegranate arils was in liquid form, a notion reported by Sarpong et al. [36] for banana slices.

Fitting of Drying Curve
The R 2 and RMSE were used to determine the goodness of fit model as shown in Tables 3-5.   (Table 5).
From the tables, it was observed that Logarithmic, Page and Midili amongst other models considered for best fit represented the drying characteristics of both blanched and unblanched pomegranate arils for each analysis based on blanching condition and cultivar. The suitability of Logarithmic, Page and Midili models described the observed conformity between R 2 and RMSE values according to Wang et al. [30], the higher the R 2 values and the lower the RMSE values, the better the model of best fit. This is also similar to the observations reported for drying of pre-treated and untreated pumpkin [44].

Conclusions
The effect of blanching on the drying of "Acco", "Herskawitz" and "Wonderful" pomegranate arils in a hot-air dryer was investigated. The blanched samples dried faster with a shorter drying time: "Acco" (7 h), "Herskawitz" (8 h) and "Wonderful" (7 h), compared to the unblanched samples which dried after 15, 20 and 11 h, respectively. The trend of blanching showed a falling rate as observed against time. Blanched samples had a higher drying rate than the unblanched samples. The lowest moisture diffusion was obtained as 4.81 × 10 −9 , 3.29 × 10 −9 and 5.83 × 10 −9 m 2 s −1 for Acco, Herskawitz and Wonderful cultivars, respectively, while the maximum values were 1.34 × 10 −8 , 1.19 × 10 −8 and 1.29 × 10 −8 m 2 s −1 in the same order of cultivar. The suitability of seven mathematical models to describe the drying behaviour of pomegranate arils was investigated. The models that had the best fit with the highest values of R 2 and lowest values RMSE in Acco cultivar were the Logarithmic model for all blanched samples and the Page model for unblanched samples. The best-fit models in Herskawitz cultivar were Logarithmic, Page and Midili models amongst the blanched samples and Page model for unblanched sample. Wonderful cultivar had the best fit for Logarithmic and Midili models amongst the blanched samples and Midili model for the unblanched sample. Thus, Logarithmic, Page and Midili models were identified as being more suitable for describing the pomegranate aril drying process for the blanching conditions considered.