Scientia Agropecuaria 7 (4): 409 – 417 (2016)

a. Facultad de Ciencias

Scientia Agropecuaria Agropecuarias

Universidad Nacional de
Website: http://revistas.unitru.edu.pe/index.php/scientiaagrop Trujillo

Isotherms and isosteric heat of sorption of two varieties of

Peruvian quinoa
Augusto Pumacahua-Ramos1,2,*; José Antonio Gomez Vieira2; Javier Telis-
Romero2; Harvey Alexander Villa-Vélez3; Jose Francisco Lopes Filho2
1
Professional School of Engineering in Food Industry, Universidad Peruana Unión - UPeU, Carretera Arequipa, Km 06,
Juliaca, Puno, Peru.
2
Department of Food Engineering, Instituto de Biociências, Letras e Ciências Exatas – IBILCE, Universidade Estadual
Paulista – UNESP, Rua, Cristóvão Colombo, 2265. ZIP 15054-000 São José do Rio Preto, SP- Brazil.
3
Coordination of Chemical Engineering, Center of Exact Sciences and Technologies, Universidade Federal do Maranhão,
Av. dos Portugueses 1966, Zip: 65085-580, São Luís – MA, Brazil.

Received May 31, 2016. Accepted November 07, 2016.

Abstract
The isosteric heats of sorption of two varieties of quinoa (Chenopodium quinoa Willd.) grain were determined
by the static gravimetric method at four temperatures (40, 50, 60 and 70 °C) and in relative humidity
environments provided by six saturated salt solutions. Six mathematical equations were used to model the
experimental data: GAB, Oswin, Henderson, Peleg, Smith and Halsey. The isosteric heat of sorption was
determined using the parameters of the GAB model. All the equations were shown to be appropriate by the
coefficients of determination (R2) and the mean absolute error (MA%E). The influence of temperature was
observed because the adsorption of water by the grains was lower at higher temperatures. The equilibrium
moisture contents for security of storage, for long periods of time at water activity lower than 0.65, were 12 -
13%. The effect of temperature on the parameters of the GAB model was analysed using the exponential
Arrhenius equation. The isosteric heats of sorption were determined by applying the Clausius-Clapeyron
equation as a function of humidity. The isosteric heat at 5% moisture for grains of the Blanca de Juli variety
was 3663 kJ/kg and for the Pasankalla variety it was 3393 kJ/kg. The experimental data for isosteric heat as a
function of humidity were satisfactorily modelled using three mathematical equations.
Keywords: Quinoa grains; moisture security; sorption isotherms; isosteric heat of sorption; mathematical
models.

1. Introduction million US dollars at an average value of

Quinoa (Chenopodium quinoa Willdenow) U.S. $ 3.46/kg of quinoa. The USA is the
is considered to be one of the most main destination for these exports follo-
complete foods in the world; it is rich in wed by the Unites Kingdom, Netherlands
nutrients, with a unique pattern of amino and Canada (AGRODATA, 2016).
acids and a high content of polyunsaturated In Peru, 80% of quinoa is grown in the
fatty acids and minerals (Bojanic, 2011). highland region located at an altitude of
For this reason, the United Nations, 2500-4000 m. The air at these altitudes
through the auspices of the FAO, declared contains saturation pressures, densities,
2013 as the "International Year of moisture and temperatures that are lower
Quinoa". Peru is one of the leading than in the Amazonian and coastal regions.
manufacturers and exporters of quinoa This causes the grains to naturally contain
worldwide. In 2015, exports reached 142.2 between 9 and 10% moisture at harvesting
---------

* Corresponding author © 2016 All rights reserved.

E-mail: augusto.pumacahua@upeu.pe (A. Pumacahua-Ramos). DOI: 10.17268/sci.agropecu.2016.04.06

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time. However, the regions where quinoa orange seeds, beans and soybeans (Aviara
is exported from are located at an altitude et al., 2004; Miranda et al., 2011; de
of less than 1500 m. Under these Oliveira et al., 2014; Resende et al., 2006;
conditions, if the quinoa grains are not Rosa et al., 2013; Villa-Vélez et al., 2015).
properly stored they can absorb water up to Taking into consideration the importance
levels that are not permitted by law, of greater knowledge of the isotherms and
causing microbial deterioration and other energies involved in the process of water
adverse reactions. sorption, the objectives of this study were
Knowledge about the gain or loss of water the following: to obtain the isothermic
in foods due to relative humidity is of vital curves of two varieties of quinoa; to
importance in various stages of the determine the models that best represented
consumption chain. This characteristic is the experimental data; and to verify the
specific to each type of food and can be sorption heat involved in the process.
checked experimentally. The water activity
(aw) of a food is a characteristic that is
2. Materials and methods
temperature dependent, because above
certain limits, chemical, enzymatic and The experimental tests were conducted in
microbiological reactions occur that are the process laboratory at the Institute of
capable of causing it to deteriorate. The Biosciences, Letters and Exact Sciences of
main cause of deterioration, apart from the State University of São Paulo, SP,
production, transportation, trade and Brazil and the materials microscopy
consumption, is deterioration due to excess laboratory at the State University of Ponta
water absorbed from the environment. Grossa, PR, Brazil. Quinoa grains of the
Sorption isotherms can be determined Blanca de Juli and Pasankalla varieties,
experimentally and can be adjusted to and of the seed type, from the 2009-10
facilitate mathematical models that crop, were obtained from the National
determine storage conditions and types of Institute of Agrarian Investigation (INIA),
packaging. Various studies have been Puno, Peru.
conducted to determine the sorption
isotherms of dried foods and to adjust data 2.1 Physical properties
to mathematical models (de Oliveira et al., The grains were selected, placed in plastic
2014; Polachini et al., 2016; Rosa et al., bags, identified and stored in a cold room
2015; Villa-Vélez et al., 2015). at 5 °C. The initial moisture was deter-
Every aspect of the sorption or desorption mined by the standard oven method (105
of water involves energy. According to °C/24 h) and the physical properties
Aguerre and Viollaz (1989), this pheno- (geometric mean diameter, real density,
menon occurs in the gas/solid interface of apparent density, unit mass, porosity and
foods but it is the thermodynamic sphericity) were determined according to
properties of water that regulate this the methodology of (Vilche et al., 2003).
phenomenon. The isosteric heat of sorption The surface of the grains was observed
is a measure of the energy required for the using a scanning electron microscope
evaporation or condensation of water from (SEM); the grains were previously coated
foods. This energy is variable in foods, due in gold.
to the chemical bonding that the water
molecules form with components such as 2.2 Water sorption isotherms
fats, proteins, carbohydrates, etc. One way The saturated solutions of six salts (MgCl2,
to understand more about this heat is K2CO3, NaBr, NaNO2, NaCl and KCl)
through the study of sorption isotherms. were used to determine the sorption
There are have been several studies about isotherms. The saturated solutions provi-
isotherms and isosteric heats of sorption in ded water activity (aw) values from 0.278
grains such as quinoa, rice, orange peels, to 0.823 for temperatures of 40, 50, 60 and

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70 °C. Approximately two grams of quinoa ∆H, Ho, Hm and HL (kJ/kg) are the heats of
were placed in each container and then sorption of water in Xe, in the monolayer,
placed in a BOD, model SP-500, incubator in the multilayer, and in pure water,
chamber. Constant mass was reached respectively (Martín-Santos et al., 2012;
between 20 and 25 days and was Moreira et al., 2008; Polachini et al., 2016;
quantified by the standard oven (105 °C/24 Rosa et al., 2013; Villa-Vélez et al., 2015).
h) method. The tests were performed in In the Peleg model, K1, K2, n1 and n2 are
triplicate for both varieties. constants and have the restrictions that
n1<1 and n2 >1. In the Oswin, Henderson,
2.3 Modeling of sorption isotherms Halsey and Smith models, A, B, C are
Six mathematical models used to fit constants and T is the absolute tempe-
experimental data are collected in Table 1 rature. The adjustments to the models were
(Eqs. 1, 5 and 9). These were used to made using SOLVER from the Excel©
adjust the experimental data and to programme of Windows© 2010.
determine the model that gave the best fit
for the experimental data. 2.4 Determination of the isosteric heat of
sorption
Table 1 The isosteric heat of sorption, QS, (Eq. 10),
Mathematical models applied to the or heat of sorption, is the energy required
experimental sorption data for quinoa grains of
to remove water from a solid matrix. This
two varieties
corresponds to the enthalpy of the
Models Equations vaporisation of water from a food, which is
GAB (Van den always greater than pure water. In seeds,
Berg and Bruin, (1)
1981) such as quinoa grains, water molecules are
Moisture (2) distributed in the intercellular and extra-
monolayer
Constant (3)
cellular spaces in such a way that they are
monolayer linked to molecules of starch, fat, protein
Constant (4) and other components. QS represents the
multilayer
Peleg (Peleg, (5)
sum of the net isosteric heat, qS, and the
1993) enthalpy of vaporisation of pure water, HL.
Oswin (Oswin, (6) (10)
1946)
(7)
The enthalpy of vaporisation or conden-
Henderson
(Henderson, sation of pure water can be calculated
1952) using Eq. (11):
Halsey (Halsey, (8)
(11)
1948)
Smith (Smith, (9)
The qS can be calculated by using the
1947) Clausius-Clapeyron graphical Eq. (12) on a
given Xe (Martín-Santos et al., 2012;
In the equations shown in Table 1, Xe is the Miranda et al., 2011; Thys et al., 2010)
equilibrium moisture content in % dry and by the integrated method of Eq. (13)
basis. In the GAB model the constants Xm, (Chen, 2006; Thys et al., 2010):
C and K are dependent on the temperature; (12)
Xm represents the moisture of the mole-
(13)
cular monolayer on the inner surface
(Blahovec, 2004), C is the constant related Where R is the general gas constant (0.462
to the heat of sorption of the monolayer kJ/kg K) and T is the absolute temperature
and K is the heat of sorption of the in degrees Kelvin. Plotting ln aw vs 1/T
multilayer compared to pure water (Eq. 12) for different equilibrium moisture
(Moreira et al., 2008). In Table 1 (Eqs. 2, 3 contents and adjusting to a straight, the
and 4) the constants Xo, Co and Ko are the slope (qs/R) is obtained. In Eq. (13), the
parameters of the entropic character and water activities correspond to temperatures

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of 40 (T1) and 70 °C (T2). Both methods magnified by 270x. The grain is a seed
showed no significant differences in the type, untreated for the removal of saponin,
calculated values (Mulet et al., 1999), which is a characteristic of commercial
which were obtained using Eq. (13). grains. It can be seen that the surface
The (aw) for each Xe were determined by roughness is well organised, which
the constants of the GAB model, Xm, C and contributes to the increase in the surface
K, according to the methodology used by area for adsorption or desorption.
(Villa-Vélez et al., 2012). In order to According to Sukhorukov and Zhang
obtain the expressions for predicting the (2013) this is a typical characteristic of
QS of the quinoa grain, the following Eqs. seeds from the Chenopodioideae family.
(14 to 16) were used (Chen, 2006; Mulet et
al., 1999; Tsami, 1991):
(14)
(15)
(16)
Where qo is the heat of sorption of the
monolayer, Xo is the initial moisture of the
product; K1, K2 and K3 are constants.
The moisture equilibriums and heats of
sorption calculated by the models in
relation to the experimental values were
evaluated by the coefficient of
2 Figure 1. Scanning electron microphotographs
determination, R and the mean absolute of grain quinoa at 30x magnification.
error (MA%E) (Chen, 2006; Miranda et
al., 2011; Silva et al., 2010; Tolaba et al.,
2004), defined as:
(17)

3. Results and discussion

3.1 Physical properties
The moisture content (% dry basis),
geometric mean diameter (mm), unit mass
(mg), real density (kg/m3), apparent
density (kg/m3), porosity (%) and
sphericity (%) of the grains at the Figure 2. Scanning electron microphotographs
beginning of the tests were 11.81 ±0.07 of grain quinoa surface at 270x magnification.
and 11.16% ±0.06; 1.66 ±0.04 and 1.73
±0.15 mm; 2.92 ±0.05 and 3.55 ±0.15;
1213.1 ±36.8 and 1277.6 ±22.9; 661.7 ±2.9 3.2 Water sorption isotherms
and 681.6 ±2.6; 45.45 and 46.64%; 85 ±7 The data for water activity and moisture
and 86 ±6 for the Blanca de Juli quinoa equilibrium for the four temperatures are
and the Pasankalla quinoa, respectively. shown in Table 2. Figure 3 shows the
Similar diameters and densities were deter- effect of temperature on the isotherms of
mined for Ecuadorian and Argentinian both varieties of quinoa. An inverse
quinoa (Alvarado, 2012; Vilche et al., relationship between Xe and temperature
2003). was observed. Foods with water activity
Figure 1 shows a quinoa grain magnified less than 0.65 can be stored for long
by 30x and Figure 2 shows a grain periods without risk of mould growth.

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Table 2
Equilibrium moisture content (Xe, % d.b.) obtained by adsorption at different water activity and
temperatures for quinoa grains of two varieties
Blanca de Juli
Salts 40 oC 50 oC 60 oC 70 oC
aw Xeq aw Xeq aw Xeq aw Xeq
MgCl2 0.316 8.95 0.3054 7.27 0.2926 5.49 0.278 4.73
K2CO3 0.4 10.10 0.381 9.14 0.362 6.87 0.343 6.41
NaBr 0.5317 12.19 0.5093 10.20 0.4966 8.55 0.497 8.26
NaNO2 0.615 12.85 0.599 10.79 0.59 9.73 0.587 8.95
NaCl 0.7468 14.66 0.7443 14.08 0.745 12.66 0.751 11.85
KCl 0.8232 17.03 0.812 15.74 0.8025 13.70 0.795 12.36
Pasankalla
MgCl2 0.316 7.13 0.3054 6.35 0.2926 5.44 0.278 5.06
K2CO3 0.4 8.38 0.381 7.33 0.362 6.68 0.343 6.19
NaBr 0.5317 9.88 0.5093 9.25 0.4966 8.32 0.497 8.04
NaNO2 0.615 11.46 0.599 10.13 0.59 9.19 0.587 9.07
NaCl 0.7468 15.69 0.7443 14.46 0.745 12.88 0.751 12.62
KCl 0.8232 18.51 0.812 17.24 0.8025 14.42 0.795 13.73

In the present study, in terms of water The maximum experimental equilibrium

activity, the quinoa grains that showed moisture contents, with water activities
values of 0.615 reached moisture contents from 0.80 to 0.82 at the four experimental
of 12.85 and 11.46% at 40 °C for the temperatures, were 17.03 - 12.36% and
Blanca de Juli and Pasankalla varieties, 18.51 - 13.73% for the Blanca de Juli and
respectively. Similar behaviour has been Pasankalla varieties, respectively. The
determined in grains of different varieties Pasankalla variety absorbed more water
of quinoa (Alvarado, 2012; Miranda et al., than the Blanca de Juli variety, with water
2011; Tolaba et al., 2004). activities greater than 0.8 at the four
temperatures.
Table 3 shows the values of the regression
parameters for the adjustments of data for
Xe versus aw in terms of the mathematical
models for the two varieties of quinoa.
All the models had good fits, with R2
greater than 0.977 and MA%E less than
8.48%. The mean MA%E for the four
temperatures was less than 5.7%. The
constants of the GAB model (Xm, C and
K) varied with temperature, confirming
behaviour found by other authors
(Blahovec, 2004; Moreira et al., 2008).
According to Blahovec (2004), the cons-
tant C decreases and K increases with
increasing temperature. This observation
was confirmed in the present study. On the
other hand, the constant C was greater than
2.0, and the constant K was less than 1.0,
so the isotherms were classified as Type II
(Brunauer et al., 1940). This behaviour has
Figure 3. Experimental data of equilibrium also been observed for several varieties of
moisture contents for quinoa grains of varieties yellow corn and quinoa (Alvarado, 2012;
Blanca de Juli (A) and Pasankalla (B). Lines Miranda et al., 2011; Samapundo et al.,
correspond to the GAB model (Eq. 1). 2007; Tolaba et al., 2004).
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Table 3
Estimated values of coefficients models; determination coefficient (R2) and mean relative error
(MR%E) for quinoa grains of two varieties
Blanca de Juli Pasankalla
Model Constant 40 °C 50 °C 60 °C 70 °C 40 °C 50 °C 60 °C 70 °C
Xm 8.77 7.30 6.09 5.62 6.43 5.73 5.08 4.71
C 15.39 14.45 13.60 12.50 13.68 12.83 11.55 10.65
GAB K 0.63 0.69 0.74 0.75 0.80 0.83 0.84 0.84
R² 0.99 0.98 0.99 0.98 0.996 0.996 0.995 0.995
MA%E 2.83 2.93 3.31 5.79 2.3 2.7 3.8 6.8
A 11.26 10.09 8.50 8.03 9.81 9.07 8.34 8.01
B 0.27 0.30 0.37 0.35 0.41 0.44 0.39 0.40
OSWIN
R² 0.98 0.98 0.99 0.98 0.995 0.996 0.996 0.998
MA%E 1.66 3.24 2.91 5.19 2.0 1.3 2.5 2.0
K 0.002 0.007 0.007 0.010 0.018 0.019 0.012 0.011
N 2.35 1.97 2.16 2.02 1.58 1.60 1.86 1.90
HENDERSON
R² 0.988 0.977 0.998 0.988 0.984 0.982 0.990 0.994
MA%E 1.71 2.82 5.18 4.38 3.7 3.8 6.5 7.5
K1 14.48 13.52 9.81 10.97 10.17 13.11 11.41 10.31
n1 3.84 4.33 1.90 2.68 3.87 5.64 3.68 3.55
K2 7.81 8.83 7.71 4.96 19.08 18.44 10.42 10.33
PELEG
n2 0.42 0.51 0.59 0.54 0.34 0.61 0.49 0.52
R² 0.980 0.982 0.996 0.988 0.998 0.997 0.995 0.998
MA%E 1.66 2.89 1.46 4.24 1.2 1.1 2.4 1.8
A 7.20 5.48 4.04 4.12 3.87 3.23 2.35 3.45
B 5.67 6.14 6.31 5.46 8.45 8.23 7.70 6.49
SMITH
R² 0.982 0.981 0.986 0.968 0.995 0.994 0.995 0.997
MA%E 2.37 3.65 3.41 5.65 2.12 2.20 5.37 2.37
A 874.08 359.36 235.63 323.15 64.41 61.74 46.67 43.80
B 2.97 2.70 2.68 2.65 2.00 2.00 2.00 2.00
HALSEY
R² 0.981 0.981 0.983 0.965 0.996 0.997 0.992 0.993
MA%E 2.41 3.77 8.12 8.48 2.43 5.75 3.68 3.85

The GAB model is often used to determine break or bind water molecules to the solid
energies related to adsorption sites in the water system in this position (Martín-
monolayer and multilayer and the thermos- Santos et al., 2012). The values for this
dynamic properties of water in foods energy were 943.25 and 523.38 kJ/kg for
(Martín-Santos et al., 2012; Miranda et al., the Blanca de Juli and Pasankalla varieties,
2011; Moreira et al., 2008; Thys et al., respectively (Table 4). This shows that the
2010; Tolaba et al., 2004; Villa-Vélez et Pasankalla grains absorbed water faster
al., 2015). Figure 2 shows the adjustments than the Blanca de Juli grains. The heats of
to the GAB model for the experimental sorption of the monolayer and multilayer
points of moisture equilibrium and the aw of Blanca de Juli quinoa (2413 and 2074
of the two varieties of quinoa at the four kJ/kg, respectively) were lower than the
tested temperatures. heats of sorption for the Pasankalla quinoa
The activation energy (Table 4), ∆H, (2705 and 2282 kJ/kg, respectively) (Table
obtained for the moisture of the mono- 4).
layer, Xm, represents the energy required to

Table 4
Estimated values of coefficients models GAB; determination coefficient (R2) and mean relative
error (MR%E) for quinoa grains of two varieties
∆H R2 Ho- Hm R2 HL- Hm R2 Ho Hm HL
Variety
kJ/kg - kJ/kg - kJ/kg - kJ/kg
Blanca de Juli 943.25 0.981 338.78 0.989 297.17 0.932 2413 2074 2371
Pasankalla 523.38 0.995 423.84 0.989 89.66 0.905 2705 2282 2371

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When these figures are compared to the At 5% moisture levels, the Blanca de Juli
heats of sorption of the monolayer of two variety had a sorption heat of 3663 kJ/kg
varieties of Ecuadorian quinoa (between and the value for the Pasankalla variety
2667 and 2946 kJ/kg) and the heats of was 3393 kJ/kg, confirming that the
sorption of the multilayer (2483 to 2544 Pasankalla grains absorbed more water
kJ/kg) at temperatures of 20, 25 and 30 °C than the Blanca de Juli grains. Quinoa
(Alvarado, 2012), it can be seen that the grains of the Real variety from Bolivia
energy value of the monolayer in the needed between 4000 - 5000 kJ/kg of
Ecuadorian quinoa was higher, due to the energy for moisture between 2 - 5% at
water being more strongly bound to the temperatures of 20, 30 and 40 °C (Tolaba
substrate at lower temperatures. et al., 2004). Quinoa grains from Chile
showed values of 3400 - 3880 kJ/kg for
3.3 Isosteric heat of sorption moisture levels below 4% at temperatures
The dependency of QS with Xe for the two of 20, 40 and 60 °C (Miranda et al., 2011).
varieties of quinoa is shown in Figure 4. Two Ecuadorian varieties of quinoa had
The graph in Figure 4 shows that the grains values of between 3600-3900 kJ/kg at 6%
of Pasankalla quinoa showed lower heats moisture and temperatures of 20, 25 and 30
of sorption than the Blanca de Juli grains; °C (Alvarado, 2012).
they were in the range of 5 - 17% moisture. Table 5 shows the constants of the adjus-
This demonstrates that the grains of ment models for the experimental data for
Pasankalla quinoa absorbed and/or lost sorption heat. The three equations repre-
more water than the Blanca de Juli grains. sented the experimental data very well.
When moisture levels were over 20%, the However, Eq. (17), with three parameters,
sorption heats were similar for both showed a better R2 and a MA%E of 0.997
varieties of quinoa; there was a tendency and 0.991; and 0.338 and 1.115% for the
for similar values for the enthalpy of Blanca de Juli and Pasankalla varities,
vaporisation of pure water (HL); 2371 respectively.
kJ/kg at an average temperature of 55 °C.
Thus, it was confirmed that the QS Table 5
increased with decreasing moisture in the Estimated values of coefficients models Eqs.
grains. Similar results were observed in the (14 to 16) for determination isosteric heats of
sorption
desorption isotherms obtained by using Eq.
(14) (Miranda et al., 2011; Tolaba et al., Model Constant
Blanca de
Pasankalla
2004). Juli
qo (kJ/kg) 4192.200 2000.647
Tsami Xo (%bs) 5.555 6.558
(Eq. 14) R² 0.959 0.977
MA%E 1.396 1.054
K1 (kJ/kg) 4167.860 2001.887
Tsami K2 0.180 0.153
(Eq. 15) R² 0.959 0.977
MA%E 1.399 1.055
K1 (kJ/kg) 761.066 1310.405
K2 0.309 0.220
Mulet
K3 1.326 0.495
(Eq. 16)
R² 0.997 0.991
MA%E 0.338 1.115

Figure 4. Effect of moisture content on the

isosteric heat of sorption for quinoa grains of 4. Conclusions
varieties Blanca de Juli and Pasankalla. Lines Sorption curves were determined for two
correspond to the models and heat of vapo- quinoa grain varieties at temperatures of 40
rization of water, HL. - 70 °C and water activity from 0.28 - 0.82.

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The moisture safety values for long storage Bojanic, A. 2011. La quinua: Cultivo milenario para
contribuir a la seguridad alimentaria mundial.
periods were approximately 12 - 13% for Available in:
both varieties. At high relative humidities http://www.fao.org/fileadmin/templates/aiq2013/res/es
(aw > 0.74), the Pasankalla variety had a /cultivo_quinua_es.pdf
Brunauer, S.; Deming, L. S.; Deming, W. E.; Teller, E.
higher equilibrium moisture content than 1940. On a theory of the van der Waals adsorption of
the Blanca de Juli variety. Of the six gases. Journal of the American Chemical Society 62:
1723–1732.
mathematical models that were tested, five Chen, C. 2006. Obtaining the isosteric sorption heat
models showed a MA%E of less than directly by sorption isotherm equations. Journal of
3.9%; the most successful model was Food Engineering 74(2): 178–185.
de Oliveira, D.E.C; Resende, O.; Campos, R.C.; Donadon,
Peleg. The sigmoid type isotherms were J. R. 2014. Obtenção e modelagem das isotermas de
classified as type II. The moisture contents dessorção e do calor isostérico para sementes de arroz
for safe storage using the Xm constant in em casca. Científica 42(3): 203–210.
Halsey, G. 1948. Physical adsorptionon non-
the GAB model were 8.77 - 5.62%, and uniformsurfaces. Jornal Chemical Physical 16: 931–
6.43 - 4.71% for the Blanca de Juli and 937.
Henderson, S. M. 1952. A basic concept of equilibrium
Pasankalla varieties, respectively at the moisture. Agricultural Engineering 33: 29–32.
studied temperature range. The energy Martín-Santos, J.; Vioque, M.; Gómez, R. 2012.
required for water absorption (activation Thermodynamic properties of moisture adsorption of
whole wheat flour. Calculation of net isosteric heat.
energy), the heats of sorption of the International Journal of Food Science & Technology
monolayer and multilayer, and the isosteric 47(7): 1487–1495.
heat, were higher for the Blanca de Juli Miranda, M.; Vega-Gálvez, A.; Sanders, M.; López, J.;
Lemus-Mondaca, R.; Martínez, E.; Scala, K. 2011.
variety compared to the Pasankalla variety. Modelling the Water Sorption Isotherms of Quinoa
The Pasankalla variety tended to gain Seeds (Chenopodium quinoa Willd.) and
Determination of Sorption Heats. Food and Bioprocess
water faster than the grains of the Blanca Technology 5(5): 1686–1693.
de Juli variety. The three presented models Moreira, R.; Chenlo, F.; Torres, M.D.; Vallejo, N. 2008.
can be used to determine the isosteric heat Thermodynamic analysis of experimental sorption
isotherms of loquat and quince fruits. Journal of Food
as a function of grain moisture. Engineering 88(4): 514–521.
Mulet, A.; Sanjuán, R.; Bon, J. 1999. Sorption Isosteric
Heat Determination by Thermal Analysis and Sorption
Acknowledgements Isotherms. Journal of Food Science 64(1): 64–68.
The authors acknowledge the University Oswin, C.R. 1946. The kinetics of package life III. The
isotherm. Journal of Chemical Industry 65: 419–421.
Peruana Unión - Juliaca (UPeU-J), the Institute
Peleg, M. 1993. Assessment of a semi-empirical four
of Biosciences, Letters and Exact Sciences of parameter general model for sigmoid moisture sorption
the State University of São Paulo, SP, Brazil isotherms. Journal of Food Process Engineering 16:
and the State University of Ponta Grossa, PR 21–37.
Polachini, T.C.; Betiol, L.F.L.; Lopes-Filho, J.F.; Telis-
for financial support.
Romero, J. 2016. Water adsorption isotherms and
thermodynamic properties of cassava bagasse.
Thermochimica Acta 632: 79–85.
References Resende, O.; Corrêa, P. C.; Goneli, L.A.D.; Ribeiro, D.M.
2006. Isotermas e Calor Isostérico de Sorção do
AGRODATA. 2016. Exportaciones de quinua peruana. Feijão. Ciência Tecnologia Alimentaria 26(3): 626–
Available in: 631.
http://www.agrodataperu.com/category/quinua- Rosa, D.P.; Luna-solano, G.; Polachini, T.C.; Telis-
exportacion Romero, J. 2015. Modelagem matemática da cinética
Aguerre, R.J.; Viollaz, P.E. 1989. Swelling and Pore de secagem de semente de laranja. Ciência
Structure in Starchy Materials. Journal of Food Agrotecnologia Lavras 39(3): 291–300.
Engineering 9: 71–80. Rosa, D.P.; Villa-vélez, H.A.; Telis-Romero, J. 2013.
Alvarado, J. de D. 2012. Propiedades termodinámicas Study of the enthalpy-entropy mechanism from water
relacionadas con el agua constitutiva de alimentos. sorption of orange seeds (C. sinensis cv. Brazilian) for
(Grafitext, Ed.) (1st ed.). Ambato, Ecuador. Retrieved the use of agro-industrial residues as a possible source
from of vegetable oil production. Ciência E Tecnologia de
http://fcial.uta.edu.ec/images/stories/docs/libros/jdda_p Alimentos 33: 95–101.
trceacda.pdf Samapundo, S.; Devlieghere, F.; Meulenaer, B. De;
Aviara, N.A.; Ajibola, O.O.; Oni, S.A. 2004. Sorption Atukwase, A.; Lamboni, Y.; Debevere, J. M. 2007.
Equilibrium and Thermodynamic Characteristics of Sorption isotherms and isosteric heats of sorption of
Soya Bean. Biosystems Engineering 87: 179–190. whole yellow dent corn. Journal of Food Engineering
Blahovec, J. 2004. Sorption isotherms in materials of 79: 168–175.
biological origin mathematical and physical approach. Silva, S.A.; de Almeida, C.F.; Alves, N.M.C.; Melo,
Journal of Food Engineering 65(4): 489–495. D.S.C.; Gomes, J.P. 2010. Hygroscopic and thermos-

-416-
 A. Pumacahua-Ramos et al. / Scientia Agropecuaria 7 (4) 409 – 417 (2016)

dynamic features of dehydrated coriander. Ciência Tsami, E. 1991. Heat of sorption of water in dried fruits.
Agronômica 41(2): 237–244. International Journal of Food Science and Technology
Smith, S.E. 1947. The sorption of water vapour by high 25(3): 350–359.
polymers. Journal of the American Chemical Society Van den Berg, C.; Bruin, S. 1981. Water activity and its
69: 646. estimation in food systems: theoretical aspects. In
Sukhorukov, A.P.; Zhang, M. 2013. Fruit and seed Water Activity: Influences on Food Quality (pp. 1–
anatomy of Chenopodium and related genera 61). New York: Academic Press.
(Chenopodioideae, Chenopodiaceae/ Amaranthaceae): Vilche, C.; Gely, M.; Santalla, E. 2003. Physical properties
Implications for evolution and taxonomy. Plos One of quinoa seeds. Biosystems Engineering 86(1): 59–
8(4): 1–18. 65.
Thys, R.C.S.; Noreña, C.P.Z.; Marczak, L.D.F.; Aires, Villa-Vélez, H.A.; de Souza, S.J.F.; Pumacahua-Ramos,
A.G.; Cladera-Olivera, F. 2010. Adsorption isotherms A.; Polachini, T.; Telis-Romero, J. 2015. Thermo-
of pinhão (Araucaria angustifolia seeds) starch and dynamic properties of water adsorption from orange
thermodynamic analysis. Journal of Food Engineering peels. Journal of Bioenergy and Food Science 2(2):
100(3): 468–473. 72–81.
Tolaba, M.P.; Peltzer, M.; Enriquez, N.; Lucı́a-Pollio, M. Villa-Vélez, H.; Váquiro, H.; Bon, J.; Telis-Romero, J.
2004. Grain sorption equilibria of quinoa grains. 2012. Modelling Thermodynamic Properties of
Journal of Food Engineering 61(3): 365–371. Banana Waste by Analytical Derivation of Desorption
Isotherms. International Journal of Food Engineering
8(1): 1–19.

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