Water-Sorption Isotherms and Air-Drying-Kinetics Modelling of Andean Tubers and Tuberous Roots

: In recent years, scientiﬁc research has focused on studying Andean roots and tubers due to their attractive agricultural and nutritional qualities; however, as they contain a high level of moisture, it is imperative to dry them to extend their useful life. Likewise, analysing food-drying kinetics and food stability (regarding water activity) is essential to control moisture removal and the marketing progress. The drying process carried out in this study (65 ◦ C for 8 h) showed three clear stages: adaptation, the drying period at a constant velocity, and a third stage with a gradual drop in the drying rate. The experimental data were satisfactorily adjusted to seven mathematical models, with the Page model highlighted since it presented higher coefﬁcient-of-determination values. Likewise, this model estimated that the mean-error and percentage-of-relative-mean-deviation values were less than 1. The isotherms showed a type-II sigmoidal shape, showing that the samples were hygroscopic due to the structural changes undergone by the matrix during the process. Finally, the GAB model showed a higher coefﬁcient of determination. All the Andean tubers and tuberous root ﬂours must be dried until reaching a humidity below 10 g water /g dry mass and stored in environments with a relative humidity lower than 60% to remain stable for longer.


Introduction
In recent years, scientific research has focused on studying underutilized autochthonous crops worldwide.Among these crops are the roots produced in the Andes mountain range.Numerous scientific articles report their peculiar cultivation properties, such as their high adaptability to temperature fluctuations and resistance to pests [1].There is also scientific evidence of the excellent nutritional qualities of these roots.For example, sweet potato (Ipomoea batatas (L.) Lam.) shows high values of protein, fibers, vitamin B, iron, calcium, and bioactive compounds [2].Mashua (Tropaeolum tuberosum Ruiz and Pavón) contains many glucosinolates, polyphenols, isothiocyanates, and anthocyanins that act against plagues and diseases.Also, this root is an excellent provider of vitamin C and provitamin A [3]. Zanahoria blanca (Arracacia xanthorrhiza Bancr.) has important values for thiamine, niacin, vitamin A, and ascorbic acid [4].Finally, oca (Oxalis tuberosa Molina) presents a high starch quantity (60% of the dry weight) [5], and it is a useful provider of protein, fructooligosaccharides, iron, and riboflavin [6].
Convection hot air drying is used mainly in industries to produce dried fruits and vegetables, even though it is not energy efficient and requires more time to reach a low level of moisture.The drying kinetics are essential to controlling the moisture removal progress and drying variables (the drying rate, moisture diffusivity, and activation energy) [7].An advantage is that this experiment can be conducted on a laboratory scale.Likewise, modelling the drying kinetics is necessary to optimize the process and propose improvements to the drier before it is built on a pilot scale.Food stability is essential in packaging, and a w is directly related to chemical and microbial changes.Some studies have demonstrated that an a w increase beyond 0.4 will induce a 50-100% increase in the degradation rate [8].In this sense, the water-sorption isotherms can predict the product's shelf life by modelling the possible moisture changes during storage.
The aims of the present work are (1) to determine the modelling of the corresponding drying kinetics and (2) to determine the water-sorption-isotherm modelling of sweet potato, mashua, zanahoria blanca, and three varieties of oca (white, yellow, and red).

Raw Materials and Sample Preparation
Sweet potato (I.batatas (L.) Lam.), mashua (T.tuberosum Ruiz & Pavón), zanahoria blanca (Arracacia xanthorrhiza Bancr.), and three varieties of Oca (O.tuberosa Molina) (white, yellow, and red) were purchased from a local market in Ambato, Ecuador.The roots were peeled and cut into slices (2 mm).Slices were pretreated in microwaves (750 W/20 s) and then submerged in water at 4 • C/20 s [9].This pretreatment was considered necessary because preliminary tests showed that these roots tend to brown due to enzymes and generate undesirable colors.The microwave energy ranges between 1.24 × 10 −6 and 1.24 × 10 −3 eV, and some studies have demonstrated that it does not affect molecular structure since it is lower than the ionization energies of biological compounds (13.6 eV), bond energies (2-5 eV), and van der Waals interactions (<2 eV) [10,11].Also, Shen et al. [12] demonstrated a decrease in the double-helix structure of potato starch after microwaving at 1000 W, and Lewandowicz et al. [13] showed crystallinity pattern changes after microwaving at 800 W. For this reason, pretreatment was carried out at a lower energy (750 W).

Determination of Drying Kinetics
Fresh-peeled slices (2 mm) were used to determine the initial water content (x w ).This determination was carried out in a Vaciotem vacuum oven (J.P. Selecta, Barcelona, Spain) set to 103 • C for 48 h.The slices were dried via convection in an air drier (model CD 160, Gander Mountain, Saint Paul, MN, USA) at 65 • C for 8 h, with the air velocity (2 m s −1 ) kept constant [14].The drying temperature was established based on preliminary tests and the results obtained in a study on similar roots grown in the same area (lower temperature for a long time/60 • C for 24 h) [15].
Samples were placed on a metallic mesh (450 × 450 mm), allowing a transversal airflow.Drying kinetics were determined via weighing in a precision analytical balance (Mettler Toledo, Greifensee, Switzerland).The weight was measured every 10 min during the first 2 h and, subsequently, every 30 min until the drying time was complete (8 h).These experiments were performed on 9 slices of each sample.The water content (x w ) was obtained through vacuum drying the pieces in a vacuum oven (Vaciotem, J.P. Selecta, Barcelona, Spain) at 103 • C for 48 h.

Drying Kinetics: Mathematical Modelling
Experimental data of drying kinetics were fitted to the models shown in Table 1.
where MR represents the amount of moisture remaining in the samples reported to the initial moisture content; t is the time (h); n is the drying exponent; and a, b, c, and k are the drying constants.

Determination of Water-Sorption Isotherms
The gravimetric method used saturated salt solutions to determine the equilibrium moisture content (Table 2) [23].The saline solutions used were of reagent grade, and the preparation method was adopted from W Spiess and Wolf [24].To inhibit microbial growth, thymol was added in a w ≥ 0.5.Water sorption experiments were carried out at 20 • C (±1 • C).The sorption isotherm is of particular importance in the determination of a drying endpoint, microbiological safety, and the prediction of shelf life; for this reason, the authors chose to experiment with the average annual temperature (20 ± 1 • C) [25] reported in the Andean area interested in the development of the technology, and where the flour obtained will be marketed (Ambato, Ecuador).Samples were weighed in a precision analytical balance (Mettler Toledo, Greifensee, Switzerland) at regular intervals until reaching constant weight (±0.0005 g), the moment at which it is considered that the moisture content of samples achieved the equilibrium (12 weeks).

Water-Sorption Isotherms: Mathematical Modelling
Experimental data were fitted to the models shown in Table 3.
Table 3. Equations used for modelling the sorption isotherms.

Statistical Analysis
The goodness of the fit was evaluated based on the coefficient of determination (r 2 ), root-mean-square error (RMSE), and mean relative percentage deviation (MRPD).
Statgraphics Centurion XVII Software, version 17.2.04(Statgraphics Technologies, Inc., The Plains, VA, USA) was used in the analyses.

Drying Kinetics
Figure 1a shows the experimental drying kinetic curves.A sudden decrease in humidity is evident in the first 4 h of drying.A trend change is observed, since the food has transferred the most significant amount of free water.Figure 1b represents the drying-rate curve.An adaptation period is observed in all samples in the first 30 min, in which the interface temperature increased to reach the drying conditions.Subsequently, the constant velocity period was marked for 30 min.In this phase, the samples lose moisture at 1054 ± 249 g water /h × m 2 until reaching the critical humidity.This phase depends directly on the product, temperature, relative humidity of the air, flow direction, and food thickness [28].The third stage showed a gradual drop in the drying rate, because the superficial layer of water in the food had evaporated entirely.In this period, the drying rate completely decays (18 ± 9 g water /h × m 2 ).

Statistical Analysis
The goodness of the fit was evaluated based on the coefficient of determination (r 2 ), root-mean-square error (RMSE), and mean relative percentage deviation (MRPD).Statgraphics Centurion XVII Software, version 17.2.04(Statgraphics Technologies, Inc., The Plains, VA, USA) was used in the analyses.

Drying Kinetics
Figure 1a shows the experimental drying kinetic curves.A sudden decrease in humidity is evident in the first 4 h of drying.A trend change is observed, since the food has transferred the most significant amount of free water.Figure 1b represents the drying-rate curve.An adaptation period is observed in all samples in the first 30 min, in which the interface temperature increased to reach the drying conditions.Subsequently, the constant velocity period was marked for 30 min.In this phase, the samples lose moisture at 1054 ± 249 gwater/h × m 2 until reaching the critical humidity.This phase depends directly on the product, temperature, relative humidity of the air, flow direction, and food thickness [28].The third stage showed a gradual drop in the drying rate, because the superficial layer of water in the food had evaporated entirely.In this period, the drying rate completely decays (18 ± 9 gwater/h × m 2 ).Drying Kinetics: Mathematical Modelling The coefficient-of-determination values (r 2 ) were higher in the Page model (Table 4).Likewise, the RMSE and MRPD were less than 1 in this model.The parameter k represents the movement of moisture inside the food and the transfer to the surface of the air; therefore, higher values represent a faster drying process [29].The Fick model yielded effective diffusivity values from 2.22 to 2.92 × 10 −7 m 2 /s; this value in food oscillates between 1 × 10 −6 and 1 × 10 -11 m 2 /s [30].The variation in the diffusivity depends on the drying conditions (the temperature, pressure, and velocity) and the matrix (its structure, size, and composition) [31].Drying Kinetics: Mathematical Modelling The coefficient-of-determination values (r 2 ) were higher in the Page model (Table 4).Likewise, the RMSE and MRPD were less than 1 in this model.The parameter k represents the movement of moisture inside the food and the transfer to the surface of the air; therefore, higher values represent a faster drying process [29].The Fick model yielded effective diffusivity values from 2.22 to 2.92 × 10 −7 m 2 /s; this value in food oscillates between 1 × 10 −6 and 1 × 10 -11 m 2 /s [30].The variation in the diffusivity depends on the drying conditions (the temperature, pressure, and velocity) and the matrix (its structure, size, and composition) [31].Water-sorption isotherms.Mathematical modelling The BET model was correctly adjusted up to an aw of 0.57, while the GAB model was adjusted in the entire evaluated range; likewise, the GAB model presented a higher r 2 .Similar results were observed in sweet potato flour (Ipomoea batata L.) [34].The parameters are reported in Table 5.

Table 1 .
Equations used for modelling the drying kinetics.

Table 2 .
Saturated salt solutions are used in the determination of water-sorption isotherms.

Table 4 .
Parameters obtained in the drying-kinetics mathematical modelling.