Comparative analysis of the water diffusion in the corn grains, with and without pericarp during the thermo-alkaline treatment

Food and Bioproducts Processing 1 1 9 ( 2 0 2 0 ) 38–47

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Comparative analysis of the water diffusion in the corn grains, with and without pericarp during the thermo-alkaline treatment Posidia Pineda-Gomez a,b,∗ , Andres Rosales-Rivera b , Elsa Gutierrez-Cortez c , Mario Enrique Rodriguez-Garcia d a

Facultad de Ciencias Exactas y Naturales, Universidad de Caldas, Calle 65 No 26-10, Apartado aéreo 275, Manizales, Caldas, Colombia b Laboratorio de Magnetismo y Materiales Avanzados, Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Colombia, Carrera 27 # 64-60, Apartado aéreo 127, 916956 Manizales, Caldas, Colombia c Departamento de Ingeniería y Tecnología, FES-Cuautitlán, Universidad Nacional Autónoma de México, Laboratorio de Procesos de Transformación y Tecnologías Emergentes de Alimentos, Km 2.5 Carretera Cuautitlán–Teoloyucan, San Sebastián Xhala, Cuautitlán Izcalli, Edo de México, C.P. 54714, Mexico d Departamento de Nanotecnología, Centro de Física Aplicada y Tecnología Avanzada, Universidad Nacional Autónoma de México, Campus UNAM-Juriquilla, Boulevard Juriquilla No. 3001, Santiago de Querétaro, Qro. C.P. 76230, Mexico

a r t i c l e

i n f o

a b s t r a c t

Article history:

In this research, the water diffusion in whole corn grain (with pericarp) and threshed corn

Received 11 October 2018

grain (without pericarp) during thermo-alkaline treatment at different calcium hydroxide

Received in revised form 30

concentrations was studied, via measuring the moisture content as a function of time. The

September 2019

process was considered to be simultaneous unsteady-state water diffusion and first-order

Accepted 10 October 2019

irreversible water-starch reaction (gelatinization) phenomenon. According to microscopy

Available online 17 October 2019

analysis, the alkaline solution solubilized the pericarp in the first stage of the process, generating micro-holes to allow the subsequent entry of water to the endosperm. For this reason,

Keywords:

the whole grain showed a significant difference in the effective diffusivity in comparison to

Whole corn grain

the threshed grain according to the diffusion coefficient (Deff ) and the reaction rate constant

Threshed corn grain

(k) found in each of the concentrations used. The magnitude of the effective diffusion coeffi-

Thermo-alkaline treatment

cient for threshed grain decreased from 1.46 × 10−10 to 1.29 × 10−10 m2 /s, as the concentration

Water-diffusion

of calcium hydroxide was increased; this effective diffusion coefficient represents the water

Gelatinization

diffusivity in the corn endosperm. When the same model was applied in whole corn grain, an opposite trend was observed in this coefficient whose magnitude and increased from 7.24 × 10−11 to 7.92 × 10−11 m2 /s in the same concentration values; in this case, the coefficient represents not only the diffusivity in the endosperm but also the solubilization effect of the pericarp due to the alkaline solution. It has been concluded that the water diffusion mechanism was governed by the presence or absence of the pericarp during the cooking process. The analysis in-situ by DSC of starch gelatinization with alkaline solution showed that higher concentration delays the gelatinization beginning, and this concurs with a decrease in the effective diffusion coefficient in the endosperm of the grain without pericarp. The alkaline process increased the moisture, representing savings in cooking time. © 2019 Published by Elsevier B.V. on behalf of Institution of Chemical Engineers.

∗

Corresponding author at: Cra 23 # 75A-140, Torre B, Apto 807, Manizales, Caldas 170003, Colombia. E-mail address: [email protected] (P. Pineda-Gomez). https://doi.org/10.1016/j.fbp.2019.10.006 0960-3085/© 2019 Published by Elsevier B.V. on behalf of Institution of Chemical Engineers.

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Food and Bioproducts Processing 1 1 9 ( 2 0 2 0 ) 38–47

1.

Introduction

The corn grain consists on average of 83% by weight of endosperm (rich in starch), 11% of germ (rich in fat) and 6% of pericarp (rich in fiber). When raw corn grains are processed by cooking, above gelatinization temperature, the grain is converted into digestible and workable form as result of the starch granules gelatinization (Calzetta Resio et al., 2005). Thus, penetration of water into corn grain is theoretically and practically interesting to processing industries, because this helps to determine suitable processing conditions for cooking. The pericarp represents an important structure in the grain since it governs the diffusion of solvents into the inner grain structures (Gutiérrez-Cortez et al., 2010). Usually, the corn grain used in traditional foods in Central and South America countries consists only of endosperm. So, the pericarp and the major part of the germ are intentionally removed. This corn grain is hulled and, commercially, this product is called threshed corn (in Spanish, maíz trillado). It means that the final products have lower fiber and fat content. This kind of grain has been traditionally used in food processing because it permits to obtain a soft and white dough. However, from a nutritional point of view, these grains have poor quality (Pineda-Gómez et al., 2012a). On the other hand, whole corn grains have better nutritional quality but its dough may have non-soft appearance due to pericarp fiber. Additionally, the pericarp prolongs the cooking time of the whole corn grains in comparison with threshed corn. For this reason, traditionally threshed corn products are preferred. The thermo-alkaline treatment with calcium hydroxide (Ca(OH)2 ) has been widely used in Mexico and Central America, and this process

ever, they did not determine the effective diffusion coefficient for water. Tolaba et al. (1990) used a Fick’s diffusional model to fit drying curves of corn kernel in which the endosperm and germ were modeled as a homogeneous sphere with the pericarp being part of the external mass transfer resistance at 50 and 60 ◦ C, however, its process did not exceed the gelatinization temperature of starch, nor did the pericarp solubilization occur. From an industrial point of view, understanding the dynamics of the diffusion of moisture into the corn grains during cooking helps to determine suitable processing conditions. It is necessary to find methods for better uses of whole maize grain to increase its use in nutritive foods. Nevertheless, there is the lacking of a comparative study of water diffusion between whole and threshed grains of corn. In this context, the purpose of this study was to apply a model including simultaneous solvent-diffusion and starch-gelatinization in both kinds of grain by applying the same experimental conditions in thermo-alkaline treatment. It was analyzed the impact of the amount of Ca(OH)2 used in the process and the influence of pericarp during the solvent diffusion.

2. Theoretically approach of the diffusion phenomenon Diffusion is the physical process through which mass is transferred under the influence of concentration gradients. If the concentration gradient (c) is time-dependent, the diffusion may be better represented by Fick’s second law, for unsteady state diffusion, (Eq. (1)).

is known as nixtamalization. This treatment promotes the removal of the thin waxy layer (Santiago-Ramos et al., 2018) it opens diffusion paths, which allows the simultaneous entry of calcium and water into the pericarp at the beginning of the process (Valderrama-Bravo et al.,

∂c ∂2 c =D 2 ∂t ∂x

2010); this allows the entry of solvents into the inner structures of corn grain promoting the partial or total gelatinization of starch. Below the

Here, the Fick’s second law refers to unidirectional diffusion across some geometrical barriers. The unidirectional diffusion across in spherical coordinates (radial direction) may be written in Eq. (2) (Crank, 1975),

gelatinization temperature of starch, the diffusion process can be considered to be a water transfer phenomenon and described in terms of Fick’s law of diffusion (Calzetta Resio et al., 2005; Contreras-Jiménez et al., 2014; Yildirim et al., 2011). Above the gelatinization temperature, could be assessed as simultaneous water absorption and starch gelatinization (Bakshi, Singh, 1980; Lin, 1993; Pineda-Gómez et al., 2012b).

∂c =D ∂t



(1)

2 ∂c ∂2 c + r ∂r ∂r2

 =D

1 ∂2 (rc) r ∂r2

(2)

It must be considered that water diffusion in corn grain is a complex phenomenon and dependent of several factors such as the temperature, physical conditions of the grain as well as the concentration of calcium hydroxide when the thermo-alkaline process is applied. Water penetration into corn grain during soaking, cooking or steeping was the subject of various investigations (Ramos et al., 2004; Laria

If the diffusing substance is immobilized by an irreversible first-order reaction so that the rate of removal of diffusing substance is kc, where k is a constant, then the equation for diffusion in one dimension becomes:

et al., 2007; Gutierrez-Cortez et al., 2007; Gutiérrez-Cortez et al., 2010; ˜ Fernández-Munoz et al., 2011; Pineda-Gómez et al., 2012b; ContrerasJiménez et al., 2014). For instance, Ramos et al. (2004) reported diffusion coefficients for water in hydration at 40 ◦ C in three varieties of Mexican maize; Cabrera et al. (1984) reported diffusion coefficients for in whole corn grains during nixtamalization at a temperature range of 70–100 ◦ C; Contreras-Jiménez et al. (2014) calculated an effective diffusion coefficient of corn grits with and without calcium hydroxide during steeping at room temperature, solving Fick’s equation for a sphere. They found that this coefficient increases according to the concentra˜ tion of Ca(OH)2 . Fernández-Munoz et al. (2011) showed that moisture

D

1 ∂2 (rc) ∂c − kc = r ∂r2 ∂t

(3)

Eq. (3) may be rewritten as Eq. (4) making u = rc

D

∂2 u ∂u − ku = ∂t ∂r2

(4)

content in whole grain increases when the concentration of Ca(OH)2

This equation represents the simultaneous diffusion and chemical reaction (first order and irreversible) in a sphere with radius a. The initial and boundary conditions are:

and the temperature increases in the nixtamalization process, but they did not find the diffusion coefficient for water. Pineda-Gómez et al.

u=0

r=0

t≥0

u = aCs

r = a;

t>0

u = rC(r)

0 < r < a;

t=0

(2012b) applied a model including simultaneous solvent-diffusion and starch-gelatinization to explain the water diffusion and the calcium diffusion in threshed corn grains during cooking in isothermal stage at 92.5 ◦ C, but this was not done for the grain with pericarp. GutierrezCortez et al., 2016 developed a mathematical model to explain the Ca ion diffusion through the pericarp during a thermo alkaline treatment to correlate the apparent diffusion coefficients with the morphological changes that take place in pericarp for three different temperatures. They found that the Ca diffusion is a function of the temperature; how-

The analytical solution may be obtained with the following assumptions: (a) the mass diffusivity and reaction rate constant are independent of concentration. (b) Fick’s law holds for the diffusion of unreacted solvent. (c) Volume change during the process is negligible. (d) The geometrical shape is considered to be spherical. (e) The process is considered to be

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Food and Bioproducts Processing 1 1 9 ( 2 0 2 0 ) 38–47

isothermal, i.e., the heat transfer equations are neglected. (f) During the process, there is a first-order irreversible reaction. The solution of Eq. (4) and boundary conditions was derived by Crank (1975) in terms of the instantaneous rate of absorption by a sphere, q(t):

q(t) = 8aDCs

  2 2 ∞ ka2 + Dn2  2 exp −t(k − Dn  )  2 a n=1

3.2.



ka2 + Dn2 2

t

Q=

q(t)dt 0

Q value can be established by: Eq. (6).

3

Q = 8a DCs

∞ 







ka2 + Dn2 2 kt − Dn2 2 exp −t(k −

n=1

(ka2 + Dn2 2 )

Dn2 2 a2



3.3.

2

Where a is the radius of the sphere, D is the diffusion coefficient, Cs is the constant concentration at the surface of the sphere, and k is the reaction rate constant which quantifies the speed of a chemical reaction (Cussler, 2009).

Materials and methods

3.1.

Samples preparation

The chemical composition of the whole corn Valle Colombia was determined using AOAC (2000) and AACC (2000) methods: fiber content, 992.16 (AOAC, 2000), ash content, 08-01 (AACC, 2000), protein content, 46-13 (AACC, 2000), and fat, 30-25 (AACC, 2000). All analyses were performed in triplicate. Quantitative elemental analysis of the samples was obtained by inductively coupled plasma mass spectrometry, ICP-MS in a Thermo Elemental Mass system X-series, Standard Sample Introduction System, USA.

) + Dn2 2

(6)

3.

Chemical composition

(5)

The total quantity of solute (Q) absorbed in time t is given by:

was 9,80 ± 0,04 mm for threshed grain, and 9,72 ± 0,03 mm for whole grains. We took the measurements of the grain samples during the isothermal stage; this permitted us to adjust the conditions for the model. So, the volume changes in the isothermal stage were considered unimportant.

Corn grains Valle Colombia variety were used in these experiments. Part of the sample was whole corn grains (average diameter 8.13 ± 0.02 mm), and the other part was threshed corn grains without pericarp and germ, which were subjected to the threshing process (average diameter 8.12 ± 0.01 mm). Fig. 1 shows images of these raw grains. The thermo-alkaline treatment was carried out using a cooking system controlled by computer. The alkaline solution was prepared by mixing Ca(OH)2 with cool water (4.0 ◦ C) to obtain mass ratios of 0.0, 0.10, 0.20, 0.30, and 0.40% (w/w, Ca(OH)2 /corn). These mass ratios values were selected taking into account not to incorporate drastic changes in the taste or color of dough affecting the acceptability of corn products (Pineda-Gómez et al., 2012b). Initially, 4.0 L of the alkaline solution and 1.0 kg of corn were placed in the cooking container. The cooking system (reported by Pineda-Gómez et al. (2011)) was turned on, and the mixture was heated from room temperature to boiling temperature (92.5 ± 0.3 ◦ C) which took 13 min, and remained in this isotherm stage for 250 min. Additional hot water was added in the cooking system to recover lost liquid during evaporation. For the moisture content determination, a sample of approximately 10 g was removed from the container each 20 min. To determine the volume, some grains were removed from the container during the isothermal stage of the cooking process. After removing the surface moisture, the volume of grain sample was measured using the displaced volume of vegetal oil when it was fully immersed. The total volume of 30 grains was measured and the average grain volume was calculated. The equivalent spherical radius was computed from the expression of the volume of the sphere, taking into account, that the swelling grain approximates it to a spherical shape. The average diameter corresponding to the sphere during isothermal stage

Moisture content determination

The moisture content of the corn grains was measured using a halogen-heating thermobalance (Mettler-Toledo, USA). Before moisture content determination, the samples were gently wiped with a paper-towel to remove outer excess water. Then the wet grains were ground in an electric cutter mill and converted into a coarse dough. Approximately 3.50 g of sample was put in the aluminum dish into the oven. For moisture loss determination, the system automatically measured the sample mass while it was heated. The heating stops when the weight of the sample is stable for 30 s. The moisture content was calculated on a wet basis percentage (% w.b.). The samples were analyzed in duplicate.

3.4.

Differential scanning calorimetric (DSC) analysis

The starch gelatinization of the whole and threshed grains was determined in a DSC-Q100 TA Instruments calorimeter (TA Instruments, USA) in modulated mode. The calorimeter was calibrated at 5 ◦ C/min with indium (melting point = 156.6 ◦ C, H = 28.5 J/g). The DSC runs were operated under a nitrogen gas atmosphere (50 mL/min). For this analysis, whole and threshed corn grains were converted into flour by dry-milling and then these were passed through a 120 US mesh sieve (125 ␮m). An empty capsule was used as a reference. Samples of 6.0 ± 0.1 mg were prepared in an aluminum hermetic DSC capsule at 80% of moisture content, mixing corn flour and water. Once sealed, the preparation was allowed to equilibrate for 60 min to permit stabilization. Ramps from 25 to 100 ◦ C, at a heating rate of 5 ◦ C/min with 0.796 ◦ C and 60 s of amplitude and period, respectively were applied. The samples were analyzed in duplicate. Onset temperature (T0 ), peak temperature (Tp ), completion temperature (Tf ), and the enthalpy changes (H) were calculated from the thermograms. On the other hand, an analysis in-situ by DSC of the endosperm’s starch gelatinization was carried out with alkaline solution at different concentrations Ca(OH)2 , preparing the sample of the same form as was said before.

3.5. SEM morphology of the pericarp and endosperm during thermo alkaline process SEM images of the bare pericarp and endosperm as well as nixtamalized samples at the end of the cooking and 3 h of steeping time for a sample with 0.40% of Ca were analyzed

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Food and Bioproducts Processing 1 1 9 ( 2 0 2 0 ) 38–47

Fig. 1 – Photographs of (a) whole corn and (b) threshed corn grains (Valle Colombia variety). Table 1 – Chemical composition of whole and threshed corn grains. Sample

Moisture

Ash

Protein

Fat

Fiber

Carbohyd.

Whole corn grain Threshed corn grain

(%) 11.8 ± 0.6 11.6 ± 0.5

1.30 ± 0.07 0.30 ± 0.01

9.5 ± 0.5 7.6 ± 0.3

5.5 ± 0.3 1.3 ± 0.1

2.4 ± 0.1 1.3 ± 0.1

69.7 ± 3.5 78.1 ± 3.1

using a SEM Model JSM-6060LV at high vacuum (JEOL, TokyoJapan). In order to avoid damage of the sample due to power beams, the analysis was done by using a 20 kV acceleration voltage. The micrographs were taken at different magnification to study microscopy details of the changes in pericarp and endosperm due to the thermo alkaline process.

3.6. Diffusion coefficient and reaction rate constant determination The mathematical model describing simultaneous water diffusion and starch gelatinization reported by Pineda-Gómez et al. (2012b). Eq. (7) was used in this study, a nonlinear optimization procedure based on stepwise Gauss–Newton iteration method was used to determine the effective diffusion coefficient (Deff ) and reaction rate constant (k). The equation was programmed on a computer using the Origin software and it was obtained from the minimum value of the sum of squares of deviation between observed and estimated values.

4.

Results and discussion

4.1.

Chemical composition

Before the thermo-alkaline treatment, the chemical composition of whole and threshed corn grains was determined. The compositional analysis results (Table 1) showed that the values measured by whole corn grains are in the range of the values reported by a general chemical composition of different of corn (Eckhoff, Watson, 2009). However, the threshed corn grain presented lower amounts of fiber, fat, minerals, and protein content than whole corn grain. The lower values of the fiber and fat of the threshed corn are attributed to the removal of the pericarp and germ. It means that threshed grains have lower nutrimental value and the thermo-alkaline treatment could also help to increase its calcium content.

Table 2 – The thermal transitions of gelatinization of flour samples from whole and threshed corn grains. o

o

o

Sample

T0 ( C)

Tp ( C)

Tf ( C)

H(J/g)

Whole corn Threshed corn

58.94 ± 0.5 60.03 ± 0.4

66.32 ± 0.2 66.04 ± 0.2

76.80 ± 0.4 74.96 ± 0.5

3.07 ± 0.6 2.34 ± 0.8

4.2.

Differential scanning calorimetric analysis

The main change caused by the hydro-thermal or thermoalkaline treatment in corn grains is the gelatinization of the starch (Chen et al., 2011; Tan et al., 2004). Gelatinization is the thermal disordering of crystalline structures in native starch granules and it plays an important role in determining the structural and textural properties of many foods (Chen et al., 2011). By using DSC technique in modulated mode, the endothermic peak associated with starch gelatinization, using water as a solvent, was determined. Fig. 2(a) shows the DSC-curves of non-reversible heat flow of flour samples for the whole and threshed corn grains. The non-reversible heat flow represents the contribution to the heat flow that, at the time and temperature the measurement is made, is either irreversible (Jones et al., 1997). The endothermic peak in non-reversible heat flow signal between 58 and 75 ◦ C indicates a first-order irreversible reaction corresponding to starch gelatinization (Wajira et al., 2009; Jones et al., 1997). Table 2 shows the values of initial T0 , peak Tp , final Tf temperatures, as well as, the enthalpy change H. According with these results, gelatinization occurred in the same temperature range as well as the peak temperatures were equal in the threshed and whole grains. This result corroborates that starch granules in threshed and whole corn were provided from the same botanical source. However, a slight broadening of the peak, which originated major enthalpy, was observed of whole corn flour sample. As a consequence of whole grain has pericarp and germ, it is possible

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Food and Bioproducts Processing 1 1 9 ( 2 0 2 0 ) 38–47

Fig. 2 – (a) DSC thermograms of non-reversible heat flow of the flour samples from whole and threshed corn grains. (b) Temperature initial (T0 ) and peak (Tp) as function of Ca(OH)2 concentration during in-situ gelatinization of the endosperm’s starch.

Fig. 3 – SEM images: (a and b) native pericarp; (c and d) the changes of the structure at the end of the cooking; (e and f) the pericarp after 3 h of steeping time. to consider the influence of these components in this sample. In this case, starch was mixed with other minor components during gelatinization and DSC analysis cannot separate the individual endothermic events (Eliasson and Gudmundsson, 2006). Thus, the overall effect is a broadening of the peak

and, consequently, a higher enthalpy value. To avoid this is indicated that the starch gelatinization be studied from grain isolated starch. The effect of the concentration of calcium hydroxide on the gelatinization of corn endosperm starch was also evaluated

Food and Bioproducts Processing 1 1 9 ( 2 0 2 0 ) 38–47

43

Fig. 4 – SEM Images: (a) transversal cut of the raw corn grain with pericarp, (b) the bare endosperm for a threshed grain without thermo alkaline treatment, (c) the most external layers of the endosperm after alkaline cooking with 0.40% Ca. (d) Pericarp showing some micro holes after cooking, and (f) the threshed endosperm grains at the end of the stepping time (3 h). using DSC. The values of the initial and peak gelatinization temperatures are shown in Fig. 2(b). As seen in this graph, the gelatinization temperature remains approximately constant between 0 and 0.20% of concentration but from 0.20%, these values increase as the concentration increases. This can be interpreted as a shielding effect due to the calcium ions that have entered first inside starch granule and a delay in gelatinization beginning is produced

4.3. Morphology of the pericarp and endosperm during thermo alkaline process by SEM To analyze the changes in the pericarp and the endosperm occurred during the term-alkaline treatment, SEM images were taken. Fig. 3(a, b) shows the SEM images of the native pericarp, the average pericarp thickens for this corn grains was 92 ± 3 ␮m: it is formed by elongated cellulose and hemicellulose fibers covered by a waxy layer. Fig. 3(c and d) shows the

pericarp at the end of the cooking and after 3 h of steeping time for samples with of 0.40% of Ca (OH)2 . After the end of the cooking, this layer is removed as well as the epidermis and mesocarp (Gutierrez-Cortez et al., 2016) and the cross layer appears, the endosperm does not suffer any change; here is important to see, that some clusters of calcium carbonated are formed on the pericarp surface (see circle in Fig. 3(c), and some micro holes appear in the pericarp (Fig. 3(d)). It means that after the cooking the pericarp can allows the water entrance to the endosperm by these micro holes, but for the model the pericarp is almost integer. After 3 h of steeping the cross cells are more evident and some micro holes appear in the pericarp structure that connect these layers with the tubular cells and the Ca(CO)3 are still present. Fig. 3(e) shows the removing of the most external layers of the pericarp and some fraction of calcium carbonate formed in the surface (Gutierrez-Cortez et al., 2007). Fig. 3(f) evidences the pericarp removal in some part of the corn and the formation of some micro holes in the

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Food and Bioproducts Processing 1 1 9 ( 2 0 2 0 ) 38–47

Table 3 – The saturation value of moisture Ms , correlation coefficient R2 , and the parameters Deff and k found for water diffusion in threshed and whole corn grains. Concentration

(%) Ca (OH)2 0.00 0.10 0.20 0.30 0.40

Threshed corn grain Ms

Deff (×10−10 )

k (−10−5 )

R2

Ms

Deff (×10−10 )

k (×10−5 )

R2

%(d.b.) 190 215 225 230 255

m2 /s 1.46 1.45 1.34 1.31 1.29

(s−1 ) 7.97 9.00 8.67 9.14 10.11

0.9790 0.9893 0.9799 0.9824 0.9840

%(d.b.) 140 145 150 165 175

m2 /s 0.72 0.72 0.76 0.77 0,79

(s−1 ) 12.46 12.03 10.77 7.45 7.45

0.9988 0.9993 0.9982 0.9963 0.9945

Fig. 5 – Moisture values measured during the thermo-alkaline treatment of the threshed corn and whole corn at different concentrations (w/w) of Ca(OH)2 . endosperm. All these images suggest that the changes in the pericarp morphology govern the alkaline solution diffusion. Fig. 4(a) corresponds to a transversal cut of the corn grain in which the pericarp, aleurone layer, and the endosperm are visible. Fig. 4(b) shows the bare endosperm for a threshed grain without thermo alkaline treatment, while Fig. 4(c) and (d) show the changes in the most external layers of the endosperm after alkaline cooking with 0.40% Ca(OH)2 . In this process the aleurone layer was solubilized. It is observed that the protein matrix is removed and the alkaline treatment produce a granules separation promoting the water entrance into the most internal layers of the endosperm. Fig. 4(e, f) show the threshed endosperm grains at the end of the stepping time (3 h), some granules exhibits the presence of Ca(CO)3 and due to the alkaline environment the protein has been denaturalized.

4.4.

Whole corn grain

Water diffusion in threshed and whole corn grains

Fig. 5 shows the moisture content as time function at different mass ratios of Ca(OH)2 “w/w” (0, 0.10, 0.20, 0.30, and 0.40%). It can be seen that the incorporation of water in threshed grains was characterized by an initial stage of rapid water uptake during heating and the first stage of cooking (time <50 min), followed by slower water absorption in which the

in whole grain because the alkaline solution first is responsible for acting on the pericarp weakening the structure to later facilitate the entry of water to the endosperm, as can be seen in the SEM images (Fig. 3(c)). There was a notable difference in moisture gain between the two types of grain during cooking time. When Ca(OH)2 was not added (0.0%), threshed grains reached a moisture content of 64% while the whole grains reached only 53%. With the highest mass ratio used (0.40%), the moisture content reached 70% in threshed grains and only 57% in whole grains. These results indicate that the presence of the pericarp slowing down the whole corn grains because it limits the entry of water to the grains. The moisture content was dependent on the mass ratios of Ca(OH)2 in both cases. Similar results were reported from studies in the thermo-alkaline treatment applied in integral corn ˜ et al. (2011) and Pineda-Gómez et al. by Fernández-Munoz (2012b), in threshed corn. A very important point is that the thermo-alkaline treatment modify the pericarp morphology and solubilizes the aleurone layer, to allow the water entry. It is important to take into account that the grain is cover by a waxy layer that can be considered as a barrier for the water but the alkaline solution destroys it. Considering that moisture gained by corn grains determines the cooking time, these results indicate that the addition of Ca(OH)2 decreases the cooking time. Additionally, the inclusion of the Ca ions into the pericarp and endosperm improve the nutritional value of corn. The moisture data were used for modeling the diffusion stage in corn grains. As DSC analysis showed, corn starch of threshed and whole grain undergoes gelatinization between 60 and 75 ◦ C. Because gelatinization can only to occur if a plasticizer as water is present, this indicates that during the cooking process, a fraction of water is immobilized by gelatinization while water diffusion occurs, and it is necessary to apply a model combining diffusion and an irreversible firstorder reaction for diffusivity analysis. Diffusion in whole and threshed corn grains was analyzed taking into account the instantaneous rate of absorption by a sphere (Crank, 1975). The diffusion coefficient should be referred to as an effective diffusion coefficient (Deff ) and describes a net diffusional mass transfer through chemically and structurally complex heterogeneous systems, in isothermal conditions (Cussler, 2009). Eq. (6) corresponds to the model combining diffusion and gelatinization adjusted for water diffusion in the corn grains as Eq. (7).



  2 D n2 2 14 ka + Deff n2 2 kt − Deff n2 2 exp − t k − effa2 + Deff n2 2  Q = 8a3 Deff Ms  2 n=1

grains approach their full capacity of water absorption. On the other hand, in this initial stage, the water uptake was slower

ka2 + Deff n2 2

(7)

where Q (in m3 ) represents the total water uptake by the corn grain in time t, Ms is the saturation value of moisture (% d.b),

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Fig. 6 – Experimental data, the continue lines corresponding to the best fit, in the moisture analysis. a is the radius of the sphere (in m), Deff is the effective diffusion coefficient (in m2 /s), and k (in s−1 ) is the first-order rate constant, which quantifies the speed of a chemical reaction (Cussler, 2009). In this model, the corn grains were assumed to be a sphere. The Radius was quantified assuming the radius of the sphere of equal volume that the particle (corn grain). These values were calculated using the average of the volume during cooking as a = 4.90 mm in threshed corn and a = 4.86 mm in whole grain. The moisture saturation Ms values were determined for each curve in Fig. 5, using the first derivative at the point where dM/dt≈0. The parameters Deff and k were found by fitting each dataset considering fourteen terms in the series in Eq. (7). The terms number in the series was determined by using the first-derivate criterion in the variation of Deff , k and R2 , when n = 14, d(Deff )/dn, dk/dn, and d(R2 )/dn approached to zero. The fit curves are shown in Fig. 6 and Deff and k values obtained are given in Table 3. The Deff values are higher in threshed grains than in whole grain. The determination coefficients R2 > 0.9790 suggest that Eq. (7) was suitable in modeling the diffusion process in threshed grains during thermo-alkaline treatment. On the other hand, although a better fit (R2 > 0.99) for whole corn was achieved, the effective diffusion coefficient values are far from the expected values for starch in the endosperm, and rather represent the combined effect of solubilization of the pericarp at the early stage of the process and the subsequent entry of solvents into the endosperm. For a better analysis, Fig. 7 shows the values of Deff . For both kinds of grain, the mechanism of water diffusion is dependent on Ca(OH)2 mass ratio. Clearly, the result showed an opposite trend between both grains in relation to the Deff variation: in the whole grain, the Deff increases as mass ratio increases from 0.10 to 0.40%, while in the threshed grain it decreases. Deff remains constant while mass ratio is lower than 0.10% Ca(OH)2 in both cases. The pericarp plays an important role in the dynamic of diffusion: without pericarp in threshed corn grain, the solvents enter quickly to the endosperm, however, when mass ratio increases, a reduction in the speed of the diffusion was observed. This can be interpreted as an electrostatic shielding effect due to the calcium ions that have entered inside starch granule. This fact concurs with DSC analysis (Fig. 2(b)) of starch gelatinization using the alkaline solution as plasticizer. In contrast, with pericarp in the whole grain, Deff increases as the mass ratio does, indicating that the alkaline solution first solubilized the pericarp

Fig. 7 – Dependence of Deff and k in relation to the concentration of Ca(OH)2 during thermo-alkaline treatment of the corn grains. and so the entry of the solvent becomes faster. The values of the reaction rate constant (k) showed in Table 3 also kept an opposite trend. According to these results, the water diffusion process in thermo-alkaline treatment looks slower in the whole corn grain due to the pericarp. In relation to water diffusion coefficients, the results obtained in this research can be compared with those reported in the literature. In the case of whole corn grain, Ramos et al. (2004) reported diffusion coefficients between 1.64 × 10−11 and 3.39 × 10−11 m2 /s for diffusion of water in hydration at 40 ◦ C in three varieties of Mexican maize, this values are lower than results presented in this study for corn whole grain because temperature cooking was higher (92.5 ◦ C). Cabrera et al. (1984) found Deff values between 10−11 and 10-10 m2 /s for water diffusion in whole corn grains during nixtamalization at the temperature range of 70–100 ◦ C. Contreras-Jiménez et al. (2014) found that the effective diffusion coefficient of corn grits with and without calcium hydroxide mass ratio (1% or 2%) using broken corn at 30 ± 2 ◦ C. Their values calculated for the Deff increased from 2.24 × 10-10 to 2.56 × 10−10 m2 /s as the mass ratio of calcium hydroxide increased from 0 to 20%. Although broken grain should be similar to threshed corn because the pericarp in both cases is not present, this trend is opposite with our results in threshed corn. However, a comparison is not applicable due to the factors that affect the diffusion, as differences in the botanical source of corn, the temperature of process or the mass ratio of Ca(OH)2 . Applying the same experimental conditions during thermo-alkaline treatment in both kinds of grains was possible to establish a comparison in the diffusive process. The alkaline solution solubilized the pericarp allowing the water entry through the micro-holes, so the pericarp no act as an effective diffusion barrier for the applied model.

5.

Conclusions

The pericarp solubilization is an important factor for the diffusivity in whole corn grains during thermo alkaline process. DSC analysis of samples indicated that the gelatinization of starch in threshed and whole corn grains starts around 60 ◦ C and that alkaline solution at higher concentration delays

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the gelatinization beginning. The moisture curves showed notable differences on the dynamic of diffusion between grains with and without pericarp. The Deff and k values were found by considering simultaneous water-diffusion and starch-gelatinization phenomenon, the alkaline solution produced micro-holes in the pericarp permitting the water entry. It was found an opposite behavior in relation to the Deff variation between threshed and whole grains when the mass ratio was increased from 0.0 to 0.40%. Deff decreases in the threshed corn grains indicating a quick entry of solvent directly toward the endosperm, but for higher mass ratios the grain offered an opposition to solvent intake due to the electrostatic shielding effect caused by calcium ions that first reached the starch granules. In contrast, Deff increased in the whole grains as the mass ratio of Ca(OH)2 increased, but they were lower than those of threshed corn; in this case, the effective diffusion coefficient represents the combined effect of pericarp solubilization in the early stage of the process and the subsequent entry of solvents into the endosperm. The results of this study indicate that the alkaline solvent first acts in the pericarp for promoting its solubilization and subsequently opening paths to the diffusion inside the starch granules. From an industrial point of view, in both cases, the alkaline process increased the moisture gain, representing savings in cooking time besides enriching the corn with calcium.

Conflict of interest statement For this investigation the authors have no any actual or potential conflict of interest that could inappropriately influence their work.

Acknowledgments The authors are grateful to DIMA Universidad Nacional de Colombia, Sede Manizales and Universidad de Caldas for supporting the participation in scientific congresses.

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