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Contreras-Lozano et al / Revista DYNA, 85(204), pp. 302-310, March, 2018.

306

Table 2.
Fit parameters of the Arrhenius model

Treatment

Constants

R²
Ea
(kJ/mol)

K0

n0
K

parameter n parameter

1 5.90E-04

0.5190

0.9410

0.8876

11.4009

2 3.84E-07

1.6027

0.9905

0.7457

24.7166

3 4.12E-03

0.3853

0.9824

0.7793

7.1368

4 6.63E-03

0.3497

0.8412

0.5488

6.9723

5 2.69E-07

1.1592

0.9995

0.7740

28.4626

6 7.02E-04

0.5548

0.9907

0.4109

10.9654

7 1.52E-05

0.8846

0.9496

0.1959

21.5055

8 1.23E-07

0.0373

0.9627

0.6021

32.5717

9 1.87E-07

1.2782

0.9977

0.8955

27.7705

10 3.57E-06

0.9888

0.9896

0.4227

22.8265

11 2.18E-03

0.1828

0.8831

0.8058

10.6369

12 4.80E-06

0.8843

0.9985

0.2594

23.1282

13 1.49E-05

0.8415

0.9823

0.2649

20.6616

14 6.02E-06

0.8097

0.9984

0.1950

22.6898

15 1.34E-07

1.5518

0.9822

0.6503

30.6409

16 3.19E-04

0.8728

0.8764

0.1542

14.2953

17 7.17E-07

1.4094

0.9862

0.3791

25.3889

18 2.61E-03

0.4459

0.7793

0.4671

9.3439

Control

2.80E-16 52.7168

0.9015

0.8804

70.0709

Source: Elaborated by the authors

Figure 2. Response Surfaces.
A: Consistency coefficient (K) and B: frequency factor (K0) of sweet corn
beverages.
Source: Elaborated by the authors

Table 3.
Coefficients of fit to the quadratic model for rheological parameters of sweet
corn beverages

Coefficient

K (Pa.sn) (10 °C)

K0 (Pa.sn)

β0

-0.0624

-0.0003

β1

0.0092*

-0.0013

β2

1.6791

0.0335

β3

2.2558*

0.0033*

β11

-0.0122*

0.0027

β12

0.0820*

-0.0891

β13

0.1760*

-0.0372*

β22

-0.0122*

0.5104*

β23

-12.6800*

0.8649*

β33

-16.1316*

0.0616*

R2

0.9617

0.9373

Lack of fit (p value)

0.7427*

0.7199*

Model (p value)

0.0001

0.0007

Source: Elaborated by the authors. *Not significant (p>0.05)


The flow behavior index (n) of the drinks was not
properly adjusted to the Arrhenius model in most of the
treatments (tab. 2). Similar results have been reported in other
studies [20,30]. The behavior of the flow index of corn
beverages at 10 °C was not significantly affected by the
factors studied (p value >0.05). Therefore, at the storage
temperature, it can be assumed that the flow index (n) is
constant across all concentrations of gum and AV.
In the control sample, the Ea value was higher than that
in the beverages formulated with XG, CMC and AV,
indicating a significant effect of temperature on viscosity
[14,33,42,43]. Of the three components, only the XG
concentration had a significant effect on Ea (p value<0.05),
which may be caused by conformational changes that occur
during heating gum affecting the viscosity of solutions
[3,44].

3.2. Oscillatory test

From the amplitude sweep a value of 0.3 % was selected for
frequency sweeps. The behavior of the storage modulus (G') and
loss modulus (G") as a function of oscillatory frequency (ω) of
0.0628 to 628 rad/s (0.01-100Hz) at different temperatures was
plotted (Fig. 3). It is noted that G' and G" tend to increase with
the oscillatory frequency. The storage modulus (G') was always
higher than the loss modulus (G") over a wide frequency range,
approximately from 2.5 to 628 rad/s (0.4 to 100 Hz). For high
frequencies of oscillation the elastic properties are predominantly
viscous, indicating weak character or viscoelastic gel in corn
beverages [20,24]. This behavior is confirmed by the values of
loss tangent (tan (δ)), which was lower than unity (tan (δ) <1) in
a large high-frequency range (Fig. 4). At low frequencies, the
behaviors of some drinks have cross-over points in which G"
prevails over G'. This phenomenon is typical of concentrated
solutions and has been observed in beverages stabilized with
similar concentrations of gums [4,17,45].
The fit to second-order models indicates that the
viscoelastic behavior of drinks (G' and G") is dependent on
oscillatory

frequency,

with R2>0.94

and R2>0.97,
respectively. In general, the values of consistency coefficient

A

B

Contreras-Lozano et al / Revista DYNA, 85(204), pp. 302-310, March, 2018.

307

Figure 3. Storage (G') and loss (G") modules of sweet corn beverages. A: Control, B: Central point, C: Upper axial point and D: Lower axial point.
Source: Elaborated by the authors


K' were higher than the values of K", confirming that the
elastic component overrides the viscous component (G'> G").
This phenomenon has been observed in fruit juices and other
products derived from plants [5,16,37,46]. The values for n’
were higher than the values of n". This implies that G' is more
dependent than G" on oscillating frequency [37]. At low
frequencies (<2.5 rad/s), G' and G" modules were almost
independent of oscillatory frequency and reached similar
values. The effect of the concentration of XG, CMC and AV
on the parameters of fit to second-order models, K’, K”, n’ y
n”, was not statistically significant.
The adjustment of K’, K", n’ and n” (eq. 6 and 7) to the
Arrhenius equation showed that the viscoelastic behavior is
not satisfactorily described by this model (R2<0.5), then there
is no linear dependence between the viscoelastic parameters
studied and the temperature.
The loss tangent tan (δ) has been considered as a relevant
measure of physical stability, with tan(δ)<1 behavior
indicating some form of stable dispersion [24]. It has also
been shown that when tan (δ) <0.5, dispersions stabilized
with gums are less susceptible to phase separation [25].
Consequently, this parameter was evaluated at a frequency of
0.1 Hz to study the effect of the concentration of
hydrocolloids and aloe vera gel, as well as the effect of the
temperature, on the viscoelastic properties of corn beverages.
The frequency value (0.1 Hz) was selected because that point

produces low deformation conditions of the product or rest,
such as during storage and sedimentation of suspended
particles [37].
Tan (δ) at 0.1 Hz is not statistically significant affected by
temperature (p value >0.05), as shows treatments studied
(Fig. 4), even this behavior is more evident at higher
frequencies. Additionally, the loss tangent is not affected by
the concentration of gums and AV (p value >0.05) at storage
conditions of 0.1 Hz and temperature of 10°C. It is possible
to establish that the average value of tan (δ) in beverages
formulated with hydrocolloids was 0.94, slightly higher than
the control beverage with a value of 0.85; however, in both
cases, some stability was observed (tab. 4).
Values of tan (δ) under the established frequency and
temperature conditions were in the range of 0.5-0.7 and were
achieved with treatments 3, 4, 6, 8, 13 and 14. Treatments 6,
8, 13 and 15 correspond to the central point of the
experimental design, that is, XG and CMC concentrations of
0.05 %w/w and 1 %w/w AV. Treatments 3 and 4 correspond
to equal concentrations of gum (0.05 %w/w and 0.075% w/w,
respectively), and lower AV concentrations (<0.5 %w/w).
Therefore, it is evident that the desirable viscoelastic
properties (tan (δ) <1) are achieved at gum concentrations ≥
0.05% w/w in the same proportion and a maximum
concentration of 1% w/w AV.

0,01

0,1

1101001000
0,01

0,1

1

10

100

1000

10000

100000

0,01

0,1

1101001000
0,01

0,1

1

10

100

1000

10000

100000

0,01

0,1

1101001000
0,01

0,1

1

10

100

1000

10000

100000

0,01

0,1

1101001000
0,01

0,1

1

10

100

1000

10000

100000

10°C
20°C
30°C
40°C
50°C

10°C
20°C
30°C
40°C
50°C

10°C
20°C
30°C
40°C
50°C

10°C
20°C
30°C
40°C
50°C

G' G'' (Pa)

ω (rad/s)

A

G' G'' (Pa)

ω (rad/s)

B

G' G'' (Pa)

ω (rad/s)

C

G' G'' (Pa)

ω(rad/s)

D