Mathematical modeling and quality parameters of Salicornia fruticosa dried by convective drying

Abstract

The effect of convective drying at 50, 60 and 70 °C on the drying kinetics and quality parameters of Salicornia fruticosa was investigated. To estimate the equilibrium moisture content a desorption isotherm was performed using five empirical models: Halsey, Caurie, Henderson, Smith and Oswin. The experimental data was also fitted to different drying kinetic models (Logarithmic, Two-Terms, Midilli–Kucuk and Exponential Two-Terms). A numerical simulation using the Finite Volume Method allowed us to describe the evolution of temperature and moisture content distributions during drying. The Henderson model was found to be the most suitable for predicting the equilibrium moisture content of S. fruticosa, with values of X_we in the drying process of 1.51; 1.54 and 1.36 g water/g d.m for 50, 60 and 70 °C, respectively. A good agreement was found between the numerical and experimental results of temperature and moisture during Salicornia drying. The Midilli–Kucuk model presented the best fitting to the drying curves. The effects of drying on S. fruticosa were significant in two quality parameters. Antioxidant capacity decreased in ca. 45% and lightness (> L*) significantly increased at a drying temperature of 70 °C, compared to the fresh samples. The optimum drying temperature where drying time and nutrients loss was minimum was 70 °C. These results can be used to estimate the best drying conditions for producing dehydrated Salicornia. The use of halophytes as sustainable crops is promising, and the vision of their commercial production must be evaluated and considered, given water scarcity in many areas of the planet.

Electronic supplementary material

The online version of this article (10.1007/s13197-020-04556-6) contains supplementary material, which is available to authorized users.

Introduction

The global trends in the last decades have been focused to the consumption of healthy foods, prevailing products that can supply relevant benefits to human health, minimally processed or preferably fresh. Apart from the traditional vegetal sources rich in phytochemicals, minerals, fibers among others, new alternatives of fresh vegetables are being explored. Halophytes are edible salt-resistant plants that grow near the coasts adapted to salinity stress. Their salt tolerance makes these plants an economic vegetable source that can be considered as a sustainable crop in the current scenario of increased soil salinization and growing scarcity of fresh water (Ventura and Sagi 2013). Among halophytes, plants from the genus Salicornia belonging to Amaranthaceae family, grow approximately 10–40 cm high with a stem color deep green and changes to red in the fall (Rhee et al. 2009).

Also commonly known as pickleweed, glasswort, sea beans or sea asparagus with a geographical distribution spanning four continents such as North America, Asia, Africa and Europe (Patel 2016).

Several studies have been carried out on the nutritional and chemical characterization of phenolic compounds and antioxidant activity of different halophytic species (Salicornia herbacea, S. bigelovii, S. persica and S. fruticosa) growing in saline areas (Lu et al. 2010; Ventura et al. 2011). Salicornia species have shown to be a promising functional food given their high nutritional value in terms of mineral compounds, including Mg, Na, Ca, Fe and K, and many bioactive compounds, such as phytosterols, polysaccharides and phenolic compounds, particularly flavonoids and phenolic acids (Jang et al. 2007; Ventura et al. 2011).

Dehydration as a preservation method is one of the most used techniques in the food industry. Drying decreases the water activity (a_w) of the food matrix by removing water down to a level where biochemical and microbial reactions associated with deterioration are minimal. Hot air drying involves heat and mass transfer processes, which occur simultaneously (Afolabi et al. 2015) and it is also dependent on factors such as the geometry and properties of the food matrix and drying conditions such as temperature, relative humidity, drying rate and time of exposure (Tzempelikos et al. 2015). Mathematical modeling of food drying processes considers the transfer of heat and mass, the interaction air-food and the loss of moisture from the food by convection and evaporation. To study these parameters, several mathematical models are developed to simulate drying kinetics and optimize the drying process. These models derive from Fick’s second law, which explains the transport of water inside the product due to diffusion (Tzempelikos et al. 2015). Models that can predict mass transfer during drying are applied to simulate drying curves under different conditions. In general, the diversity of mathematical models has allowed the description of the transport phenomena immersed in the drying process. The success of this approach will depend on the resolution of complex mathematical equations, considering body geometry, initial boundary conditions and the physical problem. If the food product has small dimensions and the thermophysical properties favor the speed of heat transmission by diffusion, a simplified mathematical model can be used without considering heat transport by diffusion (Cengel 2003), similar to the study reported in Youcef-Ali et al. (2001).

Little attention has been paid to S. fruticosa, commonly found in Chile, and there have been no reports on the characterization of S. fruticosa nutrient composition, antioxidant capacity or its use in the food industry. Given the potential of S. fruticosa as a vegetable food source, the objectives of this work were (a) to determinate the chemical composition and quality parameters; (b) to study the drying kinetics; (c) to estimate empirical mathematical models; and (d) to solve a numerical simulation with the Finite Volume Method. All objectives aim to estimate the optimal convective drying conditions of S. fruticosa as an alternative process with special attention to the salt of salicornia that might serve as a potential natural food condiment.

Materials and methods

All reagents were purchased from Sigma–Aldrich Company Ltd. (St. Louis, MO, USA) and Merck KgaA, (Darmstadt, Germany) with analytical grade.

Plant material and growing conditions

Salicornia fruticosa plants were collected from the Arrayán Bay (La Serena, Chile; 29°43′57,54″S, 71°19′29, 08″W). The bay has an average temperature of 8 to 22 °C, an annual precipitation of 77.0 mm and a relative humidity of 82%. Plants were maintained refrigerated at 4 °C until use.

Determination of chemical composition, water activity and pH

The methodologies described by the Association of Official Analytical Chemists (AOAC) were used. Moisture content, crude protein, lipid content, crude fiber and crude ash content were determined by the AOAC methods number 934.06, 960.52, 960.39, 962.09 and 923.03, respectively (AOAC 1990). Water activity was measured by using a water activity measuring system at 25 °C (4TE, Aqua Lab, METER Group, Inc., USA) and the pH was determined by using a pHmeter (Thermo Scientific, Orion Star A211, USA). All measurements were carried out in triplicate.

Drying experiments

Drying of S. fruticosa was carried out in a convective dryer (Model UF 110. Shwabach FRG, Memmert, Germany) at a constant temperature of 50, 60 and 70 °C under a relative humidity outlet of 55.0 ± 1.5% measured with a digital hygro-thermometer (Extech Instrument Inc.) and at an air velocity of 1.5 ± 0.2 m/s. Air velocity was measured perpendicular to the S. fruticosa stems with an omnidirectional anemometer (451112, Extech Instrument Inc.). The average load density for each drying experiment was 0.32 ± 0.03 kg/m² and the mass of S. fruticosa was continuously monitored and recorded by 5 min intervals until constant weight (equilibrium condition) was achieved. Temperature was measured with T-type thermocouples (0.3 mm in diameter) located in the inner-center of S. fruticosa (in triplicate). The experiments were carried out to each temperature using three baskets in which the sample consisting of three cylinders of Salicornia were arranged. The dimensions of cylinders (height/diameter expressed as mm ± DS) were of an average height of 314 ± 4 mm and an average diameter 46 ± 4 mm.

Determination of equilibrium moisture content

The methodology recommended by Greenspan (1977) was used to determinate the equilibrium moisture content of S. fruticosa, and the desorption isotherm were determined at 50 °C, 60 °C and 70 °C. To carry them out, a known mass of sample (in triplicate) was brought to an equilibrium with an atmosphere produced by a saturated salt solution having a known water activity. Saturated solutions utilized were of lithium chloride (LiCl), potassium carbonate (K₂CO₃), sodium chloride (NaCl) and potassium nitrate (KNO₃). To inhibit the growth of fungi in the container with KNO₃, a thymol (2-Isopropyl- 5-methylphenol) solution was used. Once equilibrium was reached, the moisture content was determined. The mathematical models used to predict equilibrium moisture content of S. fruticosa were Halsey, Caurie, Henderson, Smith and Oswin, corresponding to Eqs. (1)–(5)

$$X_{\mathit{we}}={\left(\frac{A}{ln\left(\frac{1}{a_w}\right)}\right)}^{\frac{1}{B}}$$ 1

$$X_{\mathit{we}}=exp\left(a_{w}ln(r)-\frac{1}{4.5X_{\mathit{ws}}}\right)$$ 2

$$X_{\mathit{we}}=0.01{\left(\frac{-log\left(1-a_w\right)}{{10}^f}log\right)}^{\frac{1}{n}}$$ 3

$$X_{\mathit{we}}=B+Alog\left(1-a_w\right)$$ 4

$$X_{\mathit{we}}=A{\left(\frac{a_w}{1-a_w}\right)}^B$$ 5

Empirical models

To find a suitable empirical model, the moisture content (Mt) at different times (min) was converted to moisture ratio (MR) using the following Eq. (6):

$$MR=\frac{M_t-M_e}{M_o-M_e}$$ 6

where M_t is the moisture content at time (t), M_o the initial moisture content and M_e the equilibrium moisture content (kg water/kg d.m.). Moisture values are the average of three sets of experiments as described above. Experimental drying curves were fitted to four thin layer-drying empirical models, namely: Logarithmic, Two-Terms, Midilli–Kucuk and Exponential Two-Terms (Midilli et al. 2002; Toğrul and Pehlivan 2003). Mathematical expressions of the empirical models are presented in Table 3. Using the mathematical expression of Eq. (1), the dependent variable and MR were calculated. The goodness of fit for each model was evaluated based on the statistical parameters R² and χ² calculated as described below in the section statistical analysis.

Table 3.

Kinetic parameters for the four models at different drying temperatures

Model/equation	Parameters	50 °C	60 °C	70 °C
Logarithmic $\text{MR}=a{e}^{-kt}+c$	a	1.19 ± 0.06a	1.20 ± 0.03a	1.30 ± 0.01b
	k	7.79 × 10−5 ± 5.64 × 10−6a	1.00 × 10−4 ± 0.00b	1.00 × 10−4 ± 0.00b
	c	− 0.22 ± 0.05a	-0.23 ± 0.02a	− 0.34 ± 0.01b
Two-terms $MR=a{e}^{(-k1t)}+b{e}^{(-k2t)}$	a	0.51 ± 8.81 × 10−3a	0.51 ± 3.65 × 10−3a	0.52 ± 7.04 × 10−3a
	k1	1.00 × 10−4 ± 0.00a	2.00 × 10−4 ± 0.00b	3.00 × 10−4 ± 0.00c
	b	0.51 ± 0.01a	0.51 ± 3.65 × 10−3a	0.52 ± 0.00a
	k2	1.00 × 10−4 ± 0.00a	2.00 × 10−4 ± 0.00b	3.00 × 10−4 ± 0.00c
Midilli–Kucuk $\text{MR}=a{e}^{-ktn}+bt$	a	0.99 ± 0.01a	1.01 ± 0.00b	1.01 ± 2.48 × 10−3ab
	k	2.00 × 10−4 ± 1.00  × 10−4a	3.98  × 10−4 ± 7.64  × 10−6a	3.67  × 10−4 ± 1.53 × 10−4a
	b	− 6.15  × 10−6 ± 7.08  × 10−7a	− 9.52 × 10−6 ± 2.82 × 10−8a	− 1.44 × 10−5 ± 8.98 × 10−7a
	n	0.93 ± 0.06a	0.892 ± 0.008b	0.94 ± 0.04c
Exponential two terms $\text{MR}=a{e}^{-kt}+\left(1-a\right)e^{-kat}$	a	1.22 ± 0.04a	1.42 ± 0.37a	1.00 ± 0.00a
	k	1.00 × 10−4 ± 0.00a	2.67 × 10−4 ± 5.77 × 10−5b	2.33  × 10−4 ± 5.7 × 10−5b

Values represent the mean ± SD of three replicates (n = 3). Different lowercase letters in same row indicate that values are significantly different (p < 0.05)

Mathematical model

Temperature predictions over time were made using the energy equation, with the transient term and the heat entering the sample by convection as shown in Eq. (7), where A_s and V are the surface area and volume of the sample, calculated considering an approximated cylindrical geometry with averaged diameter and length; h is the convective heat transfer coefficient between the air and the sample, $\overline{C_p}$ and $\overline{\rho }$ are the specific heat and density of the sample respectively, averaged in their respective drying temperature range. The heat transport by diffusion in the sample is neglected considering the condition that Biot number (Bi) ≪ 1 (Cengel 2003). In this case, the Bi for each drying temperature was between 0.05 and 0.06 approximately.

$$\overline{\rho }{\overline{C}}_p\frac{\mathit{dT}}{\mathit{dt}}=h\frac{A_s}{V}\left(T_{\infty }(t)-T\right)$$ 7

$$\frac{\mathit{dT}}{\mathit{dt}}=A-BT$$ 8

$$A=\frac{h{A}_s}{\overline{\rho }{\overline{C}}_{p}V}{T}_{\infty }(t)B=\frac{h{A}_s}{\overline{\rho }{\overline{C}}_{p}V}$$ 9

The air temperature $T_{\infty }\left(t\right)$ during drying was measured experimentally in time. Since air temperature presents high variations, its adjustment to a mathematical function for numerical integration is difficult, thus, a numerical solution was used discretizing the temporal derivative. Equations (8) and (9) show the energy equation as a linear equation, with temperature as a dependent variable, where $T_{\infty }\left(t\right)$ is considered a known value.

The first time step is carried out discretizing the temporal derivative with a forward Euler scheme, with an implicit formulation (Versteeg and Malalasekera 2007), as shown in Eq. (10). The temperature of the second-time step can be calculated directly from Eq. (11), knowing the initial temperature (measured experimentally).

$$\frac{\partial T}{\partial t}=\frac{T^{t+\mathrm{\Delta }t}-T^t}{\mathrm{\Delta }t}=A-B{T}^{t+\mathrm{\Delta }t}$$ 10

$$T^{t+\mathrm{\Delta }t}=\frac{A\mathrm{\Delta }t+T^t}{1+B\mathrm{\Delta }t}$$ 11

Temperatures from the second time step onwards were calculated using the Adams–Moulton scheme (Moukalled et al. 2015), once the temperature is known at the initial time and at the first time step. The temperature can be calculated directly, as shown in Eqs. (12) and (13).

$$\frac{\partial T}{\partial t}=\frac{3T^t-4T^{t-\mathrm{\Delta }t}+T^{t-2\mathrm{\Delta }t}}{2\mathrm{\Delta }t}=A-B{T}^t$$ 12

$$T^t=\frac{2A\mathrm{\Delta }t+4T^{t-\mathrm{\Delta }t}-T^{t-2\mathrm{\Delta }t}}{3+2B\mathrm{\Delta }t}$$ 13

The convective heat transfer coefficient was calculated with the equations reported in Youcef-Ali et al. (2001), used for drying with forced convection (Eq. (14)).

$$h=\frac{Nu{k}_f}{L_c}Nu=0.37R{e}^{0.6}Re=\frac{{\rho }_f{v}_{f}Lc}{{\mu }_f}$$ 14

where Nu is the Nusselt number, Re is the Reynolds number and ${\text{v}}_{\text{f}}$ is the air velocity, considered constant. The density ${\rho }_{\text{f}}$, dynamic viscosity ${\mu }_{\text{f}}$ and thermal conductivity of air ${\text{k}}_{\text{f}}$ were calculated using the thermo library (Bell 2016). The average values in the respective temperature range of each process were used.

The numerical solution was implemented in a computer code in Python language, in the Jupyter Notebook web application. The calculations were made in an Intel Core i5-6200U CPU @2.3 GHz personal computer, with 4 GB of RAM.

Quality parameters

Mineral analysis

The mineral content (Ca, Mg, Na, K, Fe and Cu) of S. fruticosa samples was measured using atomic absorption spectroscopy (PinAAcle 900F FL HSN, Perkin Elmer Inc., Massachusetts, USA with WinLab32 software). An acid digestion of 0.5 g fresh and dry sample was performed by adding 8 ml of HNO₃ (65% v/v) and heating to 80 °C until the removal of red NO₂ fumes resulted in a clarified solution. After cooling the solution, 3 ml of HClO₄ (70% v/v) were added and the sample was again heated to a slight reduction in volume. The sample was cooled, and 15 ml of deionized water were added to the solution. Finally, the solution was filtered to remove remaining solids and completed to a volume according the dilution factor required for further analysis. All determinations were done in triplicate.

Determination of total antioxidant capacity by DPPH assay

The antioxidant capacity was measured using the 2,2’-diphenyl-1-picryhydrazyl free radical scavenging (DPPH) method (Brand-Williams et al. 1995). A solution of 50 μM DPPH in aqueous methanol (80%) was mixed for 20 min. Then, 0.1 ml of 50 μM DPPH or S. fruticosa extract was mixed with 3.9 ml of DPPH solution and incubated for 30 min in darkness. DPPH was measured spectrophotometrically at 517 nm. Total DPPH was calculated from a calibration curve (y = -0.0003x + 0.51; R² = 0.984) of the synthetic antioxidant Trolox at concentrations between 0.1 to 1.0 mM. The antioxidant capacity determined by DPPH assay was expressed in μmol Trolox equivalents per g FW (μmol TE/g f.m.). All measurements were carried out in triplicate.

Color measurement

The color of S. fruticosa samples was measured after drying at different temperatures with a colorimeter (HunterLab, Model MiniScan XE Plus, 45/O, Hunter Associates Laboratory, Reston, VA, USA). A black ceramic cell with a diameter just close to the nose cone of the colorimeter was filled with the S. fruticosa sample and placed above the light source; the L*, a* and b* color values were recorded. The reading was performed on the external surface of the sample, and the mean of nine readings at random locations on the S. fruticosa sample was used and results were averaged. Before the color measurements, the instrument was calibrated using a standard white plate (x = 82.43, y = 84.55, z = 99.39) and a standard black plate (x = 0, y = 0, z = 0). The Hunter L*, a* and b* values correspond to lightness, greenness (−a) or redness (+a), and blueness (−b) or yellowness (+b), respectively. The overall color difference was indicated by ∆E and determined by the formula shown in Eq. (15):

$$\mathrm{\Delta }\text{E}=\sqrt{{\left({\text{a}}^{\ast }-{\text{a}}_{\text{o}}\right)}^2+{\left({\text{b}}^{\ast }-{\text{b}}_{\text{o}}\right)}^2+{\left({\text{L}}^{\ast }-{\text{L}}_{\text{o}}\right)}^2}$$ 15

where L*, a* and b* were the values of the samples, while L_o, a_o and b_o were the color values of the reference or control.

Statistical analysis

The fit quality of the experimental data to the proposed models were evaluated using: coefficient of determination R², Eq. (16) and Chi square, χ², Eq. (17). These parameters can be calculated as follows:

$$R^2=\sum _{i=1}^N\frac{{\left(M{R}_{cal,i}-{\overline{\mathit{MR}}}_{\mathit{exp}}\right)}^2}{{\left(M{R}_{exp,i}-{\overline{\mathit{MR}}}_{\mathit{exp}}\right)}^2}$$ 16

$${\chi }^2=\frac{{\sum }_{i=1}^N{\left(M{R}_{exp,i}-M{R}_{calc,i}\right)}^2}{N-m}$$ 17

where MR_exp and ${\overline{\mathit{MR}}}_{\mathit{exp}}$ are the experimental and average moisture ratio; MR_cal is the calculated moisture ratio; N is number of observations; m is number of constants. The best model describing the drying characteristics was chosen as the one with the highest coefficient of determination and the least reduced Chi square.

An analysis of variance (ANOVA) was performed using Statgraphics Centurion XVI (Statistical Graphics Corp., Herndon, USA) to detect significant differences among treatments. Significance testing was performed by Fisher’s test; differences were statistically significant when p < 0.05.

Results and discussion

Chemical composition, water activity and pH

The chemical composition of fresh S. fruticosa is summarized in Table 1. The moisture of the fresh sample was 87.81 ± 0.66% with a pH value equal 5.59 ± 0.01 and a_w equal 0.971 ± 0.003 (f.m).

Table 1.

Proximal composition and a_w of wild S. fruticosa plants grown in La Serena, Chile

Parameter	Value
Proteins (g/100 g of dry sample)	12.11 ± 0.55
Lipids (g/100 g of dry sample)	3.43 ± 0.03
Ash (g/100 g of dry sample)	37.71 ± 0.08
Crude Fiber (g/100 g of dry sample)	10.94 ± 0.62
Total Carbohydrates (g/100 g of dry sample)	46.48 ± 0.03
aw (Water activity)	0.359 ± 0.053 (50 °C)
	0.264 ± 0.006 (60 °C)
	0.335 ± 0.053 (70 °C)

As in similar plants of succulent stem, carbohydrate was the most abundant nutrient in S. fruticosa, followed by ash. The biochemical composition obtained in this research was similar to that reported for the Salicornia genus (Barreira et al. 2017; Lu et al. 2010), except from the lipid content, which was slightly higher than the content reported by Riquelme et al. (2016) in Sarcocornia neei plants grown in Valparaíso, Chile. One of the mayor characteristics of halophytes is their tolerance to saline stress, and Salicornia species are highly salt tolerant (Ventura et al. 2011). Due to the exposure to stress conditions in its natural coastal ecosystem, the wild halophyte plants can present a high amount of fiber, which can cause an increase of lignin and other structural carbohydrates as a defense mechanism against salt stress (Moura et al. 2010). As expected, the water activity decreased in dried samples compared to the fresh samples, ensuring the microbiological safety (a_w < 0.6) of dehydrated Salicornia.

Desorption isotherm and drying curves

The moisture desorption isotherms have a fundamental influence in the dehydration process and the storage stability of the dried products. Sorption isotherms mathematically describe the relationship between a_w and X_we in a food product (Dalgıç et al. 2012). The nature of this relationship depends on the interaction between water and other ingredients (Fabra et al. 2009). The empirical parameters of the different models for desorption isotherms at 20 °C for Salicornia samples at different drying temperatures (50, 60 and 70 °C) are shown in Table 2. The criteria to evaluate the quality of fit considered R² values over 0.98 and χ² values lower than 0.005 when comparing the results obtained on all the mathematical models used (Lahsasni et al. 2004). The results showed that the desorption isotherm at 60 °C had the lowest value of χ², indicating a better fit quality at this temperature compared to all other temperatures. According to the statistical tests applied, the Henderson model gave a closest fit to the experimental data and equilibrium moisture content (X_we) (Table 2). The equilibrium moisture content in the drying process were X_we (50 °C) = 1.51; X_we (60 °C) = 1.54; and X_we (70 °C) = 1.36 g water/g d.m., respectively.

Table 2.

Mathematical model constants and statistic parameters determined by each desorption isotherm at 20 °C

Drying temperature of S. fruticosa	Model	Model parameters	Coefficient of determination (R2)	Reduced Chi square (χ2)
50 °C	Halsey	A = 0.047 B = − 7.97	0.993	0.029
	Caurie	r = 0.56	0.984	0.031
		Xws = − 0.38
	Henderson	f = 11.92 n = − 5.88	0.927	0.012
	Smith	A = 0.60 B = 1.92	0.999	0.302
	Oswin	A = 1.36 B = − 0.1	0.964	0.343
60 °C	Halsey	A = 236.17 B = 78.74	0.932	0.000
	Caurie	r = 1.06 Xws = − 4.42	0.983	0.000
	Henderson	f = − 134.17 n = 65.67	0.999	0.000
	Smith	A = − 0.04 B = 1.06	0.872	0.000
	Oswin	A = 1.08 B = 0.0098	0.964	0.638
70 °C	Halsey	A = 0.0249 B = − 0.0124	0.737	0.026
	Caurie	r = 0.69 Xws = − 0.52	0.846	0.015
	Henderson	f = 17.98 n = − 8.83	0.920	0.007
	Smith	A = 0.28 B = 1.42	0.608	0.039
	Oswin	A = 1.28 B = − 0.06	0.831	0.441

Figure 1 shows the drying curve behavior of S. fruticosa at 50, 60 and 70 °C. At higher temperatures was observed a decrease of the moisture content and an increase of the drying time. The time required to achieve equilibrium moisture content in all experiments was between 175 and 390 min. Similar results were obtained by Doymaz et al. (2006) using dill and parsley leaves. At 50 °C, the equilibrium drying temperature was reached at about 333 min, whereas at 70 °C, the equilibrium drying temperature was reached at about 180 min. This represents a 45.95% reduction in the overall drying time, indicating that there was as increase in mass transfer rate when a higher temperature was used. Also, the results show that the whole drying process occurred in the decreasing drying period, due to absence of a constant drying period. Therefore, in this food matrix the phenomenon that limited the drying rate was the transfer of water (or water vapor) from the inside to the product surface. This suggests that is more difficult to remove water bound to the food components, consequently its movement through the dried layer becomes increasingly slower (Toujani et al. 2013).

Fig. 1.

Drying curves of S. fruticosa at different drying temperatures: 50 (●), 60 (♦) and 70(■) °C. Solid line corresponds to the Midilli-Kucuk model

Kinetic parameters of drying models

Table 3 shows the kinetic parameters obtained for each mathematical model applied to the drying curves of S. fruticosa at different temperatures. All models were evaluated statistically to determine which fitted best the drying curve. The Midilli–Kucuk model showed a good adjustment to the experimental data at 70 °C. In general, it presented a high R² value and low χ² values that were considered as an optimum criterion for evaluating fitting quality of the proposed model (Table 4). The better performance of the Midilli–Kucuk model is likely because it is an Arrhenius-type equation, thus it provided a better mathematical estimation of the experimental drying curves. The statistical treatment (ANOVA) indicated that the parameters a and n in Midilli–Kucuk model (best fit model) were dependent on the drying temperature (p < 0.05). Instead, parameters k and b did not significantly changed (p < 0.05) in relation to the drying temperature. This means that they probably depend on the product geometry or its porosity. Furthermore, the predicted moisture ratio decreased with the increasing air drying temperature and consequently, the drying time decreased. It can be concluded that the Midilli–Kucuk equation is the appropriate model to describe the drying curves of S. fruticosa.

Table 4.

Fitting criteria for empirical models of drying temperature of S. fruticosa dried at 50, 60 and 70 °C

Empirical model	Drying temperature
	Statistics	50 °C	60 °C	70 °C
Logarithmic	χ2	0.000	0.009	0.014
	R2	0.999	0.899	0.905
Two-Terms	χ2	0.003	0.001	0.002
	R2	0.916	0.990	0.999
Midilli–Kucuk	χ2	0.000	0.008	0.004
	R2	0.999	0.999	0.981
Exponential two-terms	χ2	0.004	0.008	0.002
	R2	0.997	0.999	0.913

Mathematical model validation

The temperature profiles obtained experimentally and by means of numerical solutions are shown below (Fig. 1 of Electronic Supplementary Material). In all cases the air temperature showed sudden variations at the beginning, stabilizing as time passes. These changes in air temperature lead to variations in the temperature of the samples. This effect is clearly seen after drying at 50 °C in which variations in the sample temperature were captured with the mathematical model considering the experimental temperature ${\text{T}}_{\infty }$ as a function of time.

For all profiles, a good fit was observed between the numerical model and the experimental data at the beginning of the process, where the temperature increases exponentially. Once the air and sample temperature reached a balance, a temperature difference remains constant in time. This difference may be since upon reaching the equilibrium temperature, the mass transfer begins to intensify causing a loss of moisture in the sample and therefore loss of energy, preventing the sample from reaching the equilibrium temperature. The mathematical model does not consider the loss of energy by mass transfer, because in this case the equilibrium temperature is reached, which corresponds to the air temperature.

Quality parameters

Mineral analysis

The mineral content focused on levels of Cu, Fe, K, Ca, Na and Mg were not found to be statistically significant (p < 0.05) for S. fruticosa samples dried at different temperatures. Due to the increment in dry matter during drying, dried samples had similar mineral contents per kg to the fresh samples.

Na and K were found in a greater proportion, followed by Ca and Mg (Table 5). The macroelements present in the fresh sample: Na (63.929 mg/g f.m.) and K (25.410 mg/g f.m.) are characteristic of plants from a saline environment, were minerals are found in great abundance. These values were found at levels as those reported for other halophytes such as by Barreira et al. (2017) (Na = 109-64.1 mg/g f.w.; K = 8.92-15.8 mg/g f.m.) and by Lu et al. (2010) for Salicornia bigelovii Torr (Na = 84.45 mg/g f.m.; K = 15.19 mg/g f.m.) and by Bertin et al. (2014) for Sarcocornia ambigua (Na = 10.19 mg/g f.m. and K = 2.90 mg/g f.m.). The other major elements present in S. fruticosa samples were Ca and Mg with a similar concentration for the halophyte Sarcocornia ambigua in Brazil (Mg = 0.92 mg/g f.m.; and Ca = 0.54 mg/g f.m.) (Bertin et al. 2014). The Fe and Cu trace elements were found in a lower proportion with concentrations of 0.022 and 0.015 mg/g f.m., respectively, but Riquelme et al. (2016) have reported similar values in halophyte Sarcocornia neei (collected at the Salina de Pullally in Valparaíso, Chile) for Fe 0.334 mg/g f.m. and for Cu 0.017 mg/g f.m. In general, the levels of Fe, K and Cu minerals found were similar to those reported for other edible wild plants (Yildirim et al. 2001), while Na levels were higher than those reported by Cook et al. (2000). S. fruticosa can be considered a good source of minerals important for health, and it can be used as natural condiment in traditional kitchen.

Table 5.

Quality parameters for fresh and dried S. fruticosa samples

Parameter	Fresh	50 °C	60 °C	70 °C
Minerals (mg/g)
Cu	0.015 ± 0.006a	0.008 ± 0.002a	0.008 ± 0.004a	0.012 ± 0.001a
Fe	0.022 ± 0.001a	0.025 ± 0.011a	0.009 ± 0.004b	0.005 ± 0.001b
K	25.410 ± 0.813a	25.668 ± 0.745a	30.905 ± 0.315ab	31.306 ± 0.582ab
Ca	8.655 ± 0.019ab	8.739 ± 0.006a	7.518 ± 0.001bc	7.552 ± 0.026c
Na	63.929 ± 6.787a	63.748 ± 6.914a	64.854 ± 1.780a	56.826 ± 0.515a
Mg	5.643 ± 0.247a	7.250 ± 0.300b	7.546 ± 1.124b	7.533 ± 0.235b
Color
L*	28.54 ± 0.05a	53.52 ± 0.50b	50.89 ± 0.16c	47.93 ± 0.20d
a*	2.96 ± 0.24a	2.05 ± 0.06b	2.97 ± 0.03a	1.16 ± 0.05 c
b*	29.51 ± 0.27a	20.39 ± 0.16b	21.82 ± 0.04c	20.77 ± 0.17b
ΔΕ		26.61 ± 0.84	23.64 ± 0.03	21.38 ± 0.75
Antio×idant capacity
DPPH (μmol TE/g)	18.306 ± 1.402a	9.475 ± 0.082b	9.438 ± 0.531b	8.177 ± 0.316b

Values represent the mean ± SD of three replicates (n = 3). Different lowercase letters in same row indicate that values are significantly different (p < 0.05)

Total antioxidant activity

During the drying process S. fruticosa plants were exposed to a high temperature for a long time which can contribute to the loss of antioxidants (Kalt et al. 2000). The effect of each drying temperature over antioxidant capacity (DPPH) is shown in Table 5. Fresh S. fruticosa had the highest antioxidant capacity (18.31 ± 1.40 µmol TE/g d.m.). The scavenging effect of S. fruticosa fresh samples on the DPPH radical significantly decreased with increasing the drying temperature in about 45%, but there were no statistical differences (p > 0.05) between dried samples at 50, 60 and 70 °C.

The antioxidant capacity from samples dried at 50, 60 and 70 °C had similar values to that reported for the halophyte Sarcocornia neei cultivated in Chile (Riquelme et al. 2016). The antioxidant capacity content for S. fruticosa as a green leafy vegetable was lower compared with fresh spinach cultivated in Chile (136.6 µmol TE/g d.m.) (Lutz et al. 2015). Considering the short drying time and the low level of nutrients loss compared to the other tested temperatures used, 70 °C was established as the optimum drying temperature for S. fruticosa.

Color

Food color is the first parameter of quality evaluated by consumers and rules the acceptance of the product even before being consumed (Markovic et al. 2013). Color is also one the most crucial sensory qualities of food products. L*, a* and b* of fresh S. fruticosa were 28.54 ± 0.05; 2.96 ± 0.24 and 29.51 ± 0.27, respectively (Table 5). Drying caused a significant increase in lightness in comparison with fresh S. fruticosa. The a* and b* values slightly decreased with increasing the drying temperature. Delta E (ΔE) reflected the total color difference between dried and fresh samples. In general, the color of the dried samples was brighter than that of fresh S. fruticosa samples and there was no significant difference (p > 0.05) between ΔE values at 50, 60 and 70 °C (Table 5). In dried wild asparagus (Asparagus maritimus L.) (Jokič et al. 2009), convective drying resulted in the smallest color change of the fresh material, whereby drying at 60 °C presented the optimum.

Conclusion

The Henderson equation was found to be the most suitable for predicting the equilibrium moisture content of S. fruticosa samples in the temperature and relative humidity ranges investigated. Convective drying of S. fruticosa showed that the drying kinetics of S. fruticosa can be accurately predicted using the empirical models of Logarithmic, Two-terms, Midilli–Kucuk and Exponential Two terms.

According to these results and based on the statistical test, the Midilli–Kucuk model was the most adequate for describing the convective drying of S. fruticosa. The mathematical modeling of the drying process included temperature predictions over time using the energy equation, with the transient term and the heat entering the sample by convection. To all drying temperatures studied, a good fit was observed between the numerical model and the experimental data at the beginning of the process, where the temperature increases exponentially. The drying process did not significantly affect S. fruticosa mineral composition, albeit the antioxidant capacity showed a decrease of approximately 45% and lightness (> L*) had a significant increase at higher drying temperature in comparison with the fresh sample.

The findings of this study highlight the potential of this halophyte as a valuable source of natural antioxidants, minerals and nutrients for use in the food and even in the pharmaceutical industries. Considering the scarcity of water worldwide, the use of halophytes in the future as a source of vegetables is promising and the vision of their commercial production must be evaluated and considered.

Electronic supplementary material

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