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Effect of temperature on dynamic and steady-state shear rheological properties of siriguela (Spondias purpurea L.) pulp
Journal of Food Engineering 108 (2012) 283–289
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Effect of temperature on dynamic and steady-state shear rheological properties of siriguela (Spondias purpurea L.) pulp Pedro E.D. Augusto a,b,⇑, Marcelo Cristianini a, Albert Ibarz c a
Department of Food Technology (DTA), School of Food Engineering (FEA), University of Campinas (UNICAMP), Brazil Technical School of Campinas (COTUCA), University of Campinas (UNICAMP), Brazil c Department of Food Technology (DTA), School of Agricultural and Forestry Engineering (ETSEA), University of Lleida (UdL), Lleida, Spain b
a r t i c l e
i n f o
Article history: Received 21 February 2011 Received in revised form 3 August 2011 Accepted 21 August 2011 Available online 30 August 2011 Keywords: Food properties Rheology Viscoelasticity Viscosity
a b s t r a c t The present work has evaluated the dynamic and steady-state shear rheological properties of siriguela (Spondias purpurea) pulp as function of temperature (0–80 °C), as well as the applicability of the CoxMerz rule. The product flow behavior could be well described by the Herschel–Bulkley’s model (R2 > 0.98), whose parameters were modeled as function of temperature (R2 > 0.91). The product has shown a weak gel behavior, with storage modulus higher than loss modulus in the evaluated frequency range. The storage and loss modules could be well described by a power function of the oscillatory frequency (R2 > 0.93), whose parameters were modeled as function of temperature (R2 > 0.97). Moreover, a power modified Cox-Merz rule could describe the rheological properties of S. purpurea pulp (R2 > 0.96). The obtained data are potentially useful for future studies on food properties and process design. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Spondias purpurea L. is a native fruit of Central America, dispersed in Mexico, Guatemala and the Caribbean, and in some countries of South America, mainly in the northeast region of Brazil (Sampaio et al., 2008; Augusto et al., 2000). The species belongs to the family Anacardiaceae, the same as mango (Mangifera índica), cashew apple (Anacardium occidentale) (Sampaio et al., 2008), cajá (Spondias mombin L.) and umbu (Spondias tuberosa Arruda Camara) (Bicas et al., 2011). It is a small red fruit, with a pleasant aroma and taste which is consumed in natura or as juice and other products such as jams and different candies. The S. purpurea L. is called by different names, which are function of the geographic region, such as red mombin, siriguela, seriguela, ceriguela, ciriguela, jocote, jocote de corona, ciruela, ciruela Mexicana, jobillo, spanish plum and hog plum (Bicas et al., 2011; Furtado et al., 2010; Ceva-Antunes et al., 2006; Parada et al., 2006; Martins et al., 2003; Augusto et al., 2000). The consumer demand for native and exotic products is growing, in special for food products, creating the need for better understanding of its processing and properties. Moreover, Furtado et al. (2010) and Ceva-Antunes et al. (2006) observed that the native fruit commercialization plays an important role in social and employment perspectives in development countries like in Brazil. ⇑ Corresponding author at: Technical School of Campinas (COTUCA), University of Campinas (UNICAMP), R. Culto à Ciência, 177 Botafogo, CEP: 13020-060 Campinas, SP, Brazil. E-mail address: [email protected] (P.E.D. Augusto). 0260-8774/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2011.08.015
The rheological characterization of food is important for unit operations design, process optimization and high quality products assurance (Ibarz and Barbosa-Cánovas, 2003; Rao, 1999). Although the rheological characterization of exotic fruits is being studied for various authors, there is no work in literature related to the rheological characterization of S. purpurea L. pulp, even though it is essential for processing design. The present work has evaluated and modeled the rheological properties of siriguela (S. purpurea L.) pulp as function of temperature.
2. Material and methods A pasteurized frozen commercial siriguela (S. purpurea L.) pulp was used in order to guarantee the standardization and repeatability. After washing, the fruits are pulped, pasteurized, packaged in small plastic bags and then frozen. Further information related to siriguela fruits and pulp can be obtained in the works of Sampaio et al. (2008) and Martins et al. (2003). Samples were thawed and carefully homogenized before the rheological measurements were taken. Its soluble solids content was determined by using a refractometer (digital refractometer r2 mini, Reichert Analytical Inst., Japan), after filtering the samples in cotton, being 10.9 ± 0.1°Brix (mean of three replicates ± standard deviation). The sample total solid content was measured using the pulp moisture, determined by an infra-red moisture analyzer (IV2002, Gehaka, Brazil). The sample total solid content was 15.8 ± 0.4% (mean of three replicates ± standard deviation).
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Nomenclature
a b
c_ ga g⁄ r r0 x A0 Ea
behavior index in power modified Cox-Merz rule (Eq. (11)) [-] magnitude index in power modified Cox-Merz rule (Eq. (11)) [-] shear rate [s1] apparent viscosity (= r/c_ ) [Pa s] complex viscosity [Pa s] shear stress [Pa] yield stress, Herschel–Bulkley’s model [Pa] oscillatory frequency [Hz] Arrhenius’s pre-exponential parameter model activation energy in Arrhenius’s model [J mol1]
storage modulus [Pa] loss modulus [Pa] consistency coefficient, Herschel–Bulkley’s model [Pa sn] consistency coefficient in power law model of viscoelas0 00 ticity properties (Eqs. (2) and (3)) [Pa sn , Pa sn ] flow behavior index, Herschel–Bulkley’s model [-] behavior index in power law model of viscoelasticity properties (Eqs. (2) and (3)) [-] absolute temperature [K] temperature [°C]
k0 , k00 n n0 , n00 TK TC
monly used for describing the viscoelastic behavior of food and dispersions (Rao, 1999):
2.1. Rheology procedures Rheological measurements were carried out with a controlled stress (r) rheometer (AR2000ex, TA Instruments, USA), using a grooved plate–plate geometry (40 mm of diameter). The gap dimension (1.0 mm) was determined by using a gap-independency procedure, as described by Tonon et al. (2009). The rheological properties were evaluated from 0 to 80 °C, and temperature was controlled by a Peltier system in each procedure. Geometry material thermal expansion was considered in order to guarantee the appropriated gap dimension. Moreover, at the temperatures of 60 and 80 °C, a solvent trap was used in order to minimize water vaporization from the product (it was observed that it was not necessary in temperatures below 60 °C). The rheological evaluation was carried out with new samples, i.e., with non-mechanical history. Thus, samples were placed in the rheometer and kept at rest for 5 min before shearing. The experiments were carried out in three replicates, and the regressions were done for each replicate. The parameters of each model were obtained by non-linear regression using the software CurveExpert Professional v.1.0.1 using a significant probability level of 95%. 2.1.1. Steady-state shear properties The steady-state shear experiments were carried out in the shear rate (c_ ) range of 0.01–100 s1. After rest, samples were submitted to shearing at 300 s1 for 5 min to avoid any thixotropy (data not shown). Then, a logarithmic decreasing stepped protocol (100–0.01 s1) was used in order to guarantee the stead-state condition. The products flow behavior was modeled using the Herschel–Bulkley’s model (Eq. (1)). Herschel–Bulkley’s model comprises Newton, Bingham and Ostwald-de-Waele (power law) models. It is commonly used to describe the rheological properties of food products.
r ¼ r0 þ k c_ n
G0 G00 k
ð1Þ
2.1.2. Viscoelastic properties Oscillatory stress sweeps between 0.01 and 100 Pa were performed at a frequency of 1 Hz to determine the products’ linear viscoelastic range. Then, frequency sweep measurements were carried out at 1.0 Pa, a shear stress value within the linear viscoelastic range. The oscillatory frequency (x) was then varied from 0.01 to 100 Hz. The storage modulus (G0 ), loss modulus (G00 ) and complex viscosity (g⁄) were thus obtained, as function of frequency (x). The storage (G0 ) and loss (G00 ) modules were modeled as a power function of oscillatory frequency (x) (Eqs. (2) and (3)), as com-
0
G0 ¼ k xn 00
0
ð2Þ 00
G00 ¼ k xn
ð3Þ
2.2. Applicability of the Cox-Merz rule The Cox-Merz rule states that the apparent viscosity (ga = r/c_ ) at a specific shear rate (c_ ) is equal to the complex viscosity (g⁄) at a specific oscillatory frequency (x), when c_ = x (Eq. (4); Rao, 2005). When this rule is valid, the rheological food properties can be determined by either oscillatory or steady-state shear experiments, which are useful due to limitations in each kind of experiment (Gunasekaran and Ak, 2000). Thus, the obtained results from the steady-state shear and viscoelastic analysis were used for the evaluation of the Cox-Merz rule applicability:
ga ðcÞ ¼ g ðxÞjc_ ¼x
ð4Þ
3. Results and discussions 3.1. Steady-state shear properties Fig. 1 shows the flow curves (r versus c_ ) of siriguela (S. purpurea L.) pulp at 0, 20, 40, 60, and 80 °C. As expected, the S. purpurea pulp showed a shear-thinning behavior (n < 1) with a representative yield stress (r0). The yield stress is the minimum shear stress required to initiate product flow, being related to the material’s internal structure which must be broken (Genovese and Rao, 2005; Tabilo-Munizaga and Barbosa-Cánovas, 2005). At stress below the yield stress, the material deforms elastically, behaving like an elastic solid; above the yield stress, it starts flowing, behaving like a viscous liquid (Bayod et al., 2007). The presence of a yield stress is a typical characteristic of multiphase materials (Sun and Gunasekaran, 2009), as fruit pulps and juices, which are formed by a dispersion of insoluble components (materials of cellular walls) in a water solution (serum, containing sugars, minerals, proteins, and soluble polysaccharides). Table 1 shows the values of the Herschel–Bulkley model parameters for S. purpurea pulp in the evaluated temperature range. The R2 values were always higher than 0.98. The obtained values of yield stress (r0), flow behavior index (n), and consistency coefficient (k) are close to those described in the literature for fruit products (Table 2; 20–30 °C).
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100
o
0C
o
20 C
o
40 C
o
60 C
each parameter A is modeled by a pre-exponential factor – A0, and the activation energy – Ea; R is the constant of the ideal gases, and TK is the absolute temperature):
o
80 C
75 σ (Pa)
A ¼ A0 exp 50
25
0 0
25
.
50
75
100
γ (s-1)
Fig. 1. Flow curves of S. purpurea L. pulp at 0, 20, 40, 60, and 80 °C. Mean of three replicates; vertical bars represent the standard deviation in each value.
Table 1 Values for the parameters of Herschel–Bulkley model the S. purpurea L. pulp (mean of three replicates ± standard deviation; R2 higher than 0.98 in each regression). T (°C)
r0 (Pa)
k (Pa sn)
n
0 20 40 60 80
11.24 ± 0.53 13.26 ± 0.15 12.56 ± 0.25 1.50 ± 0.04 1.37 ± 0.12
21.54 ± 0.95 15.22 ± 0.20 11.22 ± 0.13 3.01 ± 0.07 1.71 ± 0.19
0.25 ± 0.01 0.30 ± 0.00 0.34 ± 0.01 0.44 ± 0.00 0.48 ± 0.01
Ea R TK
ð5Þ
The consistency coefficient (k, Fig. 2) could be well modeled by the Arrhenius Equation (Eq. (6); R2 = 0.91). Although being in the same order of magnitude, the siriguela (S. purpurea) pulp activation energy value (Ea = 17509.2 J mol1) was higher than those described for other fruit products as tomato derivates (Table 3). Thus, the S. purpurea pulp internal structure is less affected by temperature than those products. Even though, its activation energy (Ea) value is closed to those described in the literature for fruit products (Table 3), such as tomato paste, jabuticaba pulp and Juniperus drupacea fruit juice. Massa et al. (2010) observed that the Brownian motion increased with the temperature, resulting in a less developed structure at higher temperatures, which explains the lower consistency coefficient values:
k ¼ 20:92 exp
17509:2 R TK
ð6Þ
The flow behavior index (n) is generally assumed to be relatively constant with temperature (Rao, 1999). However, as can be seen in Fig. 2, the flow behavior index showed a rising trend in relation to temperature, which could be well modeled by a linear function (Eq. (7); R2 = 0.97):
n ¼ 0:241 þ 0:03 T C The S. purpurea pulp is characterized by a high consistency, which can be observed by the magnitudes of r0 (13.3 Pa) and k (15.2 Pa sn) at 20 °C. As can be seen in Table 2, it is closed to the values reported for other fruit pulps as peach (r0 = 25.3 Pa; k = 11.3 Pa sn), umbu (r0 = 8.1 Pa; k = 37.7 Pa sn) and mango (r0 = 6.2 Pa; k = 11.3 Pa sn). As expected, the increase in temperature reduces the yield stress (r0) and consistency coefficient (k), increasing the flow behavior index (n). Although the temperature reduces the shearthinning behavior (i.e., increasing in n), the pulp shear-thinning behavior is still representative even at 80 °C (n80 °C = 0.48). The most used approach to modeling the temperature influence on the rheological properties of food is to consider its effect on the viscosity or apparent viscosity. However, the most important approach for the evaluation of non-Newtonian fluids is modeling each Herschel–Bulkley model’s parameter separately. Thus, the Herschel–Bulkley parameters were modeled as function of temperature. The effect of temperature on the consistency coefficient (k) are generally modeled using the Arrhenius Equation (Eq. (5), where
ð7Þ
The yield stress (r0) modeling is not often carried out in literature works, as it behavior is the less pronounced. In some products it tends to remain constant (as, for example, in 21°Brix peach puree between 5 and 55 °C; Massa et al., 2010), while in others it shows a monotonous falling behavior (as, for example, in butia pulp between 10 and 60 °C; Haminiuk et al., 2006). In some products, however, it shows a non-identifiable behavior (as, for example, in potato puree between 25 and 65 °C; Canet et al., 2005). In fact, it is important to observe that the property behavior in relation to temperature is function not only of the product itself, but also of the studied temperature range. Although having a falling behavior with temperature increasing, the yield stress (r0) could not be modeled by the Arrhenius Equation. This behavior is different than those observed in tomato juice (Augusto et al., in press-a), where the yield stress was modeled using the Arrhenius Equation (the other works listed in Table 2 have not modeled each Herschel–Bulkley model’s parameter separately). As can be observed in Fig. 2, the yield stress has shown a falling sigmoidal trend in relation to temperature, in contrast with the continuous decrease of the exponential function (Arrhenius Equa-
Table 2 Values for the parameters of Herschel–Bulkley model for fruit products. Product
T (°C)
r0 (Pa)
k (Pa sn)
n
References
S. purpurea L. pulp Peach puree (12–21°Brix) Butia pulp Apple, apricot and banana based babyfood Umbu pulp (10–25°Brix) Peach juice (10% fiber) Mango pulp Concentrated tamarind juice (71°Brix) Açai pulp Jabuticaba pulp Tomato juice
20 25 20 20 20 20 20 30 25 25 20
13.26 1.11–25.3 32.54 3.38–7.41 3.18–8.06 3.26 3.81–6.24 1.46 4.35 1.55 0.94
15.22 2.46–11.3 0.15 4.76–13.7 14.00–37.74 13.1 8.82–11.33 4.32 0.17 0.48 0.19
0.30 0.32–0.34 0.86 0.18–0.38 0.29–0.31 0.46 0.31–0.34 0.59 0.78 0.60 0.56
Present work Massa et al. (2010) Haminiuk et al. (2006) Ahmed et al. (2007) Pereira et al. (2007) and Pereira et al. (2008) Augusto et al. (2011) Ahmed et al. (2005) Ahmed et al. (2007) Tonon et al. (2009) Sato and Cunha (2009) Augusto et al. (in press-a)
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273.15 25
293.15
T (K) 313.15
333.15
353.15
Experimental (stress) Power sigmoidal
σ (Pa); k (Pa.sn)
20
Experimental (k) Arrhenius
15 o
10
5
0 0.6 0
20
40 T(ºC)
60
80
0.4 n
o
0.2 Experimental Fig. 3. Mechanical spectra of S. purpurea L. pulp at 0 and 80 °C. Mean of three replicates; vertical bars represent the standard deviation in each value.
Linear 0.0 0
20
40
60
80 3.2. Viscoelastic properties
o
T( C) Fig. 2. Parameters of the Herschel–Bulkley model as function of temperature. Mean of three replicates; vertical bars represent the standard deviation in each value.
Table 3 Activation energy (Ea) of the Arrhenius model (A = A0 exp(Ea/RT)) for the consistency index (k) in fruit products. Product
Ea (k) (J mol1)
References
S. purpurea L. pulp Tomato juice Tomato paste Reconstituted tomato concentrates Jabuticaba pulp Juniperus drupacea fruit juice
17509.2 7353.3 8600–13000 7360–3630
Present work Augusto et al. (in press-a) Dak et al. (2008) Barbana and El-Omri (in press)
13000 60380–78230
Sato and Cunha (2007) Akbulut et al. (2008)
tion). Until 40 °C, the yield stress shows quasi-constant values (11– 13 Pa) followed by a great decrease in temperatures between 40 and 60 °C. Then, it tends to stay back in a constant value (1– 2 Pa). This trend could be well modeled by a power sigmoidal function (Eq. (8); R2 = 0.98), and shows that an important transformation is carried out in siriguela (S. purpurea) pulp between 40 and 60 °C, as the yield stress value changes are more important in this temperature range when compared to temperatures below 40 °C and above 60 °C. The viscoelastic analysis corroborates this observation (Fig. 3). Bhattacharya (1999) had studied the mango pulp yield stress in temperatures of 5, 30, 55 and 80 °C, observing a great fall in yield stress value between 55 and 80 °C:
r0 ¼
12:36 1 þ ð0:018 T C Þ20:77
ð8Þ
Fig. 3 shows the mechanical spectra of S. purpurea L. pulp at 0 and 80 °C. The siriguela (S. purpurea L.) pulp storage modulus values (G0 ) were always higher than those of the loss modulus (G00 ), which indicates that the pulp has dominant elastic properties over the viscous ones. Thus, the product can be classified as a weak gel (Rao, 1999). Similar behavior has been reported for other food products such as peach puree (Massa et al., 2010), açai pulp (Tonon et al., 2009), jabuticaba pulp (Sato and Cunha, 2009), umbu pulp (Pereira et al., 2008), baby foods (Ahmed and Ramaswamy, 2006), potato puree (Alvarez et al., 2004), tomato juice (Augusto et al., in press-b) and concentrates (Bayod et al., 2008; Valencia et al., 2002; Yoo and Rao, 1996). As expected, the values of G0 and G00 had shown a rising tendency with the oscillatory frequency, the opposite behavior of the complex viscosity (g⁄). Thus, it was possible to model the storage and loss modules as a power function of the oscillatory frequency (Eqs. (2) and (3)). Table 4 shows the values for the power law model (Eqs. (2) and (3)) as a function of temperature. The R2 values were always higher than 0.93 in each replicate. The ob-
Table 4 Values for the power law model for storage (G0 ) and loss (G00 ) modules of S. purpurea L. pulp as a function of oscillatory frequency (x) (1 Pa, mean of three replicates ± standard deviation; R2 higher than 0.93 in each regression). 0
00
T (°C)
k0 (Pa sn )
n0
k00 (Pa sn )
n00
0 20 40 60 80
303.0 ± 6.2 286.3 ± 4.3 294.7 ± 15.2 92.7 ± 6.4 37.1 ± 2.8
0.16 ± 0.01 0.14 ± 0.01 0.15 ± 0.01 0.16 ± 0.02 0.14 ± 0.01
74.4 ± 1.5 66.4 ± 0.8 71.3 ± 4.4 23.3 ± 1.6 11.7 ± 0.6
0.28 ± 0.01 0.27 ± 0.00 0.23 ± 0.01 0.28 ± 0.01 0.30 ± 0.02
P.E.D. Augusto et al. / Journal of Food Engineering 108 (2012) 283–289
tained values are in accordance with those reported in the literature by other food products. Ahmed and Ramaswamy (2006) have evaluated the viscoelastic behavior of vegetable based baby food. The values of k0 and k00 ran0 00 ged from 131.0–13500 Pa sn to 19.7–1750 Pa sn , respectively (20– 0 00 25 °C). The values of n and n were in the range from 0.06–0.14 to 0.16–0.22, respectively. The viscoelastic behavior of tomato products (concentrates and ketchups; 24–27% of total solids, 22–27°Brix) have been evaluated by Bayod et al. (2008) and Yoo and Rao (1996). The values of k0 and 0 00 k00 ranged from 1660–16982 Pa sn to 106.6–3802 Pa sn , respec0 00 tively (20–25 °C). The values of n and n were in the range from 0.12–0.25 to 0.10–0.33, respectively. Augusto et al. (2011) studied the effect of fiber addition on the rheological properties of peach juice (10–12.5% fiber; 0–40 °C). The 0 values of k0 and k00 ranged from 263.9–1567.1 Pa sn to 59.8– n00 0 00 616.6 Pa s , respectively. The values of n and n were in the range from 0.14–0.28 to 0.24–0.54, respectively. The values of n00 were always higher than n0 (Table 4), which demonstrate that the viscous behavior of S. purpurea pulp becomes more important in high frequencies. Moreover, the viscous behavior becomes more important in high temperatures, as can be seen by the convergence of k0 and k00 (Table 4, Fig. 4). When the parameters of the power law model for storage (G0 ) and loss (G00 ) moduli (Eqs. (2) and (3)) were evaluated in relation to the temperature, a different behavior was observed. The values of n0 and n00 have shown to be relatively constant with temperature,
287
as expected for the flow behavior index (n; Rao, 1999). It can be clearly seen in Fig. 4, where the mean values for the n0 and n00 are, respectively, 0.15 and 0.27. The k0 and k00 values, though, have shown a sigmoidal decay behavior with temperature, as observed for the yield stress (r0). As can be seen in Fig. 4, both k0 and k00 showed almost constant values in the temperature range between 0 and 40 °C. It indicates that the S. purpurea pulp viscoelastic properties are low dependent of temperature at this range, reflecting low internal structure changes. In fact it is the same behavior observed for the yield stress (r0, Fig. 2). Once more, it is observed that the most important changes in the k0 and k00 values are carried out between 40 and 60 °C, corroborating the yield stress (r0) discussion. This behavior could be well modeled by a power sigmoidal function (Eqs. (9) and (10); R2 > 0.97). It is interesting to observe that, even for k0 and k00 , the parameters related to the sigmoidal shape are quite the same (the proportional and power parameters in temperature). It demonstrates that the decrease in the magnitudes of G0 and G00 in relation to temperature follows the same trend: 0
k ¼
00
k ¼
299:8 1 þ ð0:018 T C Þ8:52 72:17 1 þ ð0:018 T C Þ7:63
ð9Þ
ð10Þ
The observed behavior is different than those observed in other products, although there are just few studies which have modeled the values of k0 , k00 , n0 and n00 as function of temperature. Ahmed et al. (2007) and Ahmed and Ramaswamy (2006) described that the temperature effect was not systematic in the evaluation of k0 , k00 , n0 and n00 of baby food (20–80 °C). Augusto et al. (2011) have modeled the values of n0 and n00 as a quadratic function (2nd order polynomial function) in relation to temperature in peach juices with fibers (0–40 °C). The values of k0 and k00 were modeled using the Arrhenius Equation. It is important to highlight that the property behavior in relation to temperature is function not only of the product itself, but also of the studied temperature range. 3.3. Applicability of the Cox-Merz rule
Fig. 4. Temperature dependency of the parameters of the power law model for storage (G0 ) and loss (G00 ) modules as a function of oscillatory frequency (x). Mean of three replicates; vertical bars represent the standard deviation in each value; dashed lines are the models.
When the applicability of the Cox-Merz rule was evaluated, it was not possible to use it straight. As commonly observed in food products, the complex viscosity (g⁄) magnitudes were always higher than the apparent viscosity (ga) magnitudes (Fig. 5). Although the Cox-Merz rule has been confirmed experimentally for several polymers dispersions and solutions, in complex systems as food products it is generally necessary to modify the original rule (Rao, 2005; Gunasekaran and Ak, 2000). The non-fitting of the Cox-Merz rule for complex dispersions is attributed to structural decay due to the extensive strain applied (Ahmed and Ramaswamy, 2006), presence of high-density entanglements or to the development of structure and intermolecular aggregation in solution (Da Silva and Rao, 1992). Thus, the rheological properties of the S. purpurea pulp differ from those of the polymer solutions and are more similar to structured systems (Ahmed and Ramaswamy, 2006). The rheological oscillatory and steady-state shear rheological properties of foods are generally correlated by modifications to the Cox-Merz rule (Rao, 2005; Gunasekaran and Ak, 2000). Bistany and Kokini (1983) have proposed a power modification of the original rule (Eq. (11), which has been used for the evaluation of different food products. Table 5 shows the values for the parameters of this modified Cox-Merz rule for S. purpurea pulp, with R2 always higher than 0.96:
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3.4. General discussion
Fig. 5. Oscillatory and steady-state shear rheological properties of S. purpurea L. pulp at 0 and 80 °C. Complex viscosity (g⁄) as function of oscillatory frequency (x) (white symbols); and apparent viscosity (ga) as function of shear rate (c_ ) (black symbols).
Table 5 Values for the parameters of the modified Cox-Merz rule (Eq. (11)) for S. purpurea L. pulp. T (°C)
a
b
R2
0 20 40 60 80
1.417 1.317 1.216 2.101 2.166
0.109 0.220 0.492 0.072 0.037
0.99 0.99 0.99 0.96 0.96
b ½ga ðcÞa ¼ g ðxÞjc_ ¼x
ð11Þ
It can be seen that the obtained values are in accordance to those described by other fruit products as potato puree, fruit based baby foods, ketchup and tamarind juice (Table 6), although S. purpurea pulp b values are proportionally small. In the evaluated modified Cox-Merz rule, the b value is related to the magnitude difference between the apparent (ga) and the complex (g⁄) viscosities, while the a value is related to the behavior difference. Thus, the small b values indicate that both S. purpurea pulp apparent (ga) and the complex (g⁄) viscosities magnitudes are closed, which in fact can be seen in Fig. 5. Moreover, as observed by Ahmed et al. (2007) and Alvarez et al. (2004), the values of a and b have not shown a particular trend in relation to temperature. The obtained results indicate that the rheological properties of S. purpurea pulp can be determined by either oscillatory or steady-state shear experiments.
Table 6 Values for the parameters of the modified Cox-Merz rule (Eq. (11)) for fruit products. Product
T (°C)
a
b
References
S. purpurea L. pulp Potato puree Apple baby food Apricot baby food Banana baby food Ketchup Tamarind juice
0–80
1.22–2.17
0.04–0.49
Present work
25–65 5–80
0.90–1.35 1.15–1.20
2.15–39.83 4.64–6.99
Alvarez et al. (2004) Ahmed et al. (2007)
5–80
1.16–1.44
0.41–1.26
Ahmed et al. (2007)
5–80
1.15–1.33
1.91–11.80
Ahmed et al. (2007)
25 10–90
0.94 0.67–1.06
13.97 0.86–30.82
Bistany, Kokini (1983) Ahmed et al. (2007)
As consumer demand for native and exotic products is growing, it is necessary to conduct scientific studies in order to better understand their processing and properties. The rheological characterization of fruit pulps and juices is essential for their processing and product design and optimization. We highlighted the need for carry other works related with physical properties of those fruit products. The present work has evaluated the rheological properties of a commercial siriguela (S. purpurea L.) pulp as function of temperature. The product flow behavior was described by the Herschel– Bulkley’s model. The siriguela pulp viscoelastic behavior was described as a weak gel, and its storage and loss modules were described using a power function of the oscillatory frequency. A power modified Cox-Merz rule was used for describe the pulp rheology, i.e., it was shown that the pulp rheological properties can be determined by either oscillatory or steady-state shear experiments. The obtained data are potentially useful for future studies on food properties and process design. However, other studies are needed for understanding the influence of each unit operation (as pulping or thermal processing) on the siriguela (S. purpurea L.) pulp rheological pulp.
4. Conclusions The present work has evaluated the steady and dynamic shear rheological properties of siriguela (S. purpurea L.) pulp as function of temperature. The product flow behavior could be well described by the Herschel–Bulkley’s model, whose parameters were modeled as function of temperature. The storage and loss modules could be well described by a power function of the oscillatory frequency, whose parameters were modeled as function of temperature. Moreover, a power modified Cox-Merz rule could describe the rheological properties of S. purpurea pulp. The obtained data is potentially useful for future studies on food properties and process design. Acknowledgments The authors thank the São Paulo Research Foundation (FAPESP) for funding Project No. 2010/05241-8. References Ahmed, J., Ramaswamy, H.S., 2006. Viscoelastic and thermal characteristics of vegetable puree-based baby foods. Journal of Food Process Engineering 29, 219– 233. Ahmed, J., Ramaswamy, H.S., Hiremath, N., 2005. The effect of high pressure treatment on rheological characteristics and color of mango pulp. International Journal of Food Science & Technology 40 (8), 885–895. Ahmed, J., Ramaswamy, H.S., Sashidhar, K.C., 2007. Rheological characteristics of tamarind (Tamarindus indica L.) juice concentrates. LWT-Food Science and Technology 40, 225–231. Akbulut, M., Çoklar, H., Özen, G., 2008. Rheological characteristics of Juniperus drupacea fruit juice (pekmez) concentrated by boiling. Food Science and Technology International 14 (4), 321–328. Alvarez, M.D., Fernández, C., Canet, W., 2004. Rheological behavior of fresh and frozen potato puree in steady and dynamic shear at different temperatures. European Food Research Technology 218, 544–553. Augusto, F., Valente, A.L.P., Tada, E.S., Rivellino, S.R., 2000. Screening of Brazilian fruit aromas using solid-phase microextraction–gas chromatography–mass spectrometry. Journal of Chromatography A 873, 117–127. Augusto, P.E.D., Falguera, V., Cristianini, M., Ibarz, A., in press-a. Rheological behavior of tomato juice: steady-state shear and time-dependent modeling. Food and Bioprocess Technology. doi:10.1007/s11947.010.0472.8. Augusto, P.E.D., Falguera, V., Cristianini, M., Ibarz, A., 2011. Influence of fiber addition on the rheological properties of peach juice. International Journal of Food Science and Technology 46, 1086–1092.
P.E.D. Augusto et al. / Journal of Food Engineering 108 (2012) 283–289 Augusto, P.E.D., Falguera, V., Cristianini, M., Ibarz, A., in press-b. Viscoelastic properties of tomato juice: applicability of the Cox–Merz Rule. Food and Bioprocess Technology, (doi:10.1007/s11947-011-0655-y). Barbana, C., El-Omri, A., in press. Viscometric behavior of reconstituted tomato concentrate. Food and Bioprocess Technology. doi: 10.1007/s11947-009-0270-3. Bayod, E., Månsson, P., Innings, F., Bergenståhl, B., Tornberg, E., 2007. Low shear rheology of concentrated tomato products. Effect of particle size and time. Food Biophysics 2, 146–157. Bayod, E., Willers, E.P., Tornberg, E., 2008. Rheological and structural characterization of tomato paste and its influence on the quality of ketchup. LWT-Food Science and Technology 41, 1289–1300. Bhattacharya, S., 1999. Yield stress and time-dependent rheological properties of mango pulp. Journal of Food Science 64 (6), 1029–1033. Bicas, J.L., Molina, G., Dionisio, A.P., Barros, F.F.C., Wagner, R., Marostica Jr., M.R., Pastore, G.M., 2011. Volatile constituents of exotic fruits from Brazil. Food Research International 44, 1843–1855. Bistany, K.L., Kokini, J.L., 1983. Dynamic viscoelastic properties of foods in texture control. Journal of Rheology 27 (6), 605–620. Canet, W., Alvarez, M.D., Fernández, C., Luna, P., 2005. Comparisons of methods for measuring yield stresses in potato puree: effect of temperature and freezing. Journal of Food Engineering 68, 143–153. Ceva-Antunes, P.M.N., Bizzo, H.R., Silva, A.S., Carvalho, C.P.S., Antunes, O.A.C., 2006. Analysis of volatile composition of siriguela (Spondias purpurea L.) by solid phase microextraction (SPME). LWT-Food Science and Technology 39, 436–442. Da Silva, J.A.L., Rao, M.A., 1992. Viscoelastic Properties of Food Hydrocolloid Dispersions. In: Rao, M.A., Steffe, J.F. (Eds.), Viscoelastic Properties of Foods. Elsevier Science Publishers Ltd., London. Dak, M., Verma, R.C., Jaaffrey, S.N.A., 2008. Rheological properties of tomato concentrate. International Journal of Food Engineering 4 (7) (article11). Furtado, G., Silva, F., Porto, F.S., Santos, A.G., 2010. Secagem de polpa de ceriguela pelo método de camada de espuma. Revista Brasileira de Produtos Agroindustriais 12 (1), 9–14. Genovese, D.B., Rao, M.A., 2005. Components of vane yield stress of structured food dispersions. Journal of Food Science 70, E498–E504. Gunasekaran, S., Ak, M.M., 2000. Dynamic oscillatory shear testing of foods – Selected applications. Trends in Food Science and Technology 11, 115–127. Haminiuk, C.W.I., Sierakowski, M.R., Maciel, G.M., Vidal, R.M.B., Branco, I.G., Masson, M.L., 2006. Rheological properties of butia pulp. International Journal of Food Engineering 2 (1). Article 4. Ibarz, A., Barbosa-Cánovas, G.V., 2003. Unit Operations in Food Engineering. CRC Press, Boca Raton.
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Martins, L.P., Silva, S.M., Alves, R.E., Filgueiras, H.A.C., 2003. Fisiologia do dano pelo frio em ciriguela (Spondias purpurea L.). Revista Brasileira de Fruticultura 25 (1), 23–26. Massa, A., González, C., Maestro, A., Labanda, J., Ibarz, A., 2010. Rheological characterization of peach purees. Journal of Texture Studies 41, 532–548. Parada, R.Y., Castro, S., Serrano, R.D., Castillo, B.E., Ayala, J., Vides, E., Romero, J., 2006. First report of a phytoplasma associated with Spondias purpurea (Jocote de Corona) in El Salvador. Journal of General Plant Pathology 72 (1), 40–42. Pereira, E.A., Brandão, E.M., Borges, S.V., Maia, M.C.A., 2007. Effect of xanthan gum addition on the rheological properties of umbu fruit pulp. Boletim do CEPPA 25 (2), 285–294. Pereira, E.A., Brandão, E.M., Borges, S.V., Maia, M.C.A., 2008. Influence of concentration on the steady and oscillatory shear behavior of umbu pulp. Revista Brasileira de Engenharia Agrícola e Ambienta 12 (1), 87–90. Rao, M.A., 1999. Flow and Functional Models for Rheological Properties of Fluid Foods. In: Rao, M.A. (Ed.), Rheology of Fluid and Semisolid Foods: Principles and Applications. Aspen Publishers, Gaithersburg. Rao, M.A., 2005. Rheological Properties of Fluid Foods, 3rd ed.. In: Rao, M.A., Rizvi, S.S.H., Datta, A.K. (Eds.), Engineering Properties of Foods. CRC Press, Boca Raton. Sampaio, S.A., Bora, P.S., Holschuh, H.J., 2008. Postharvest respiration and maturation of some lesser-known exotic fruits from Brazil–ciriguela (Spondias purpurea L.). Revista Ceres 55 (2), 141–145. Sato, A.C.K., Cunha, R.L., 2007. Influência da temperatura no comportamento reológico da polpa de jabuticaba. Ciência e Tecnologia de Alimententos 27 (4), 890–896. Sato, A.C.K., Cunha, R.L., 2009. Effect of particle size on rheological properties of jaboticaba pulp. Journal of Food Engineering 91, 566–570. Sun, A., Gunasekaran, S., 2009. Yield stress in foods: measurements and applications. International Journal of Food Properties 12, 70–101. Tabilo-Munizaga, G., Barbosa-Cánovas, G.V., 2005. Rheology for the food industry. Journal of Food Engineering 67, 147–156. Tonon, R.V., Alexandre, D., Hubinger, M.D., Cunha, R.L., 2009. Steady and dynamic shear rheological properties of açai pulp (Euterpe oleraceae Mart.). Journal of Food Engineering 92, 425–431. Valencia, C., Sánchez, M.C., Ciruelos, A., Latorre, A., Franco, J.M., Gallegos, C., 2002. Linear viscoelasticity of tomato sauce products: influence of previous tomato paste processing. European Food Research Technology 214, 394–399. Yoo, B., Rao, M.A., 1996. Creep and dynamic rheological behavior of tomato concentrates: effect of concentration and finisher screen size. Journal of Texture Studies 27, 451–459.
Contents lists available at SciVerse ScienceDirect
Journal of Food Engineering journal homepage: www.elsevier.com/locate/jfoodeng
Effect of temperature on dynamic and steady-state shear rheological properties of siriguela (Spondias purpurea L.) pulp Pedro E.D. Augusto a,b,⇑, Marcelo Cristianini a, Albert Ibarz c a
Department of Food Technology (DTA), School of Food Engineering (FEA), University of Campinas (UNICAMP), Brazil Technical School of Campinas (COTUCA), University of Campinas (UNICAMP), Brazil c Department of Food Technology (DTA), School of Agricultural and Forestry Engineering (ETSEA), University of Lleida (UdL), Lleida, Spain b
a r t i c l e
i n f o
Article history: Received 21 February 2011 Received in revised form 3 August 2011 Accepted 21 August 2011 Available online 30 August 2011 Keywords: Food properties Rheology Viscoelasticity Viscosity
a b s t r a c t The present work has evaluated the dynamic and steady-state shear rheological properties of siriguela (Spondias purpurea) pulp as function of temperature (0–80 °C), as well as the applicability of the CoxMerz rule. The product flow behavior could be well described by the Herschel–Bulkley’s model (R2 > 0.98), whose parameters were modeled as function of temperature (R2 > 0.91). The product has shown a weak gel behavior, with storage modulus higher than loss modulus in the evaluated frequency range. The storage and loss modules could be well described by a power function of the oscillatory frequency (R2 > 0.93), whose parameters were modeled as function of temperature (R2 > 0.97). Moreover, a power modified Cox-Merz rule could describe the rheological properties of S. purpurea pulp (R2 > 0.96). The obtained data are potentially useful for future studies on food properties and process design. Ó 2011 Elsevier Ltd. All rights reserved.
1. Introduction Spondias purpurea L. is a native fruit of Central America, dispersed in Mexico, Guatemala and the Caribbean, and in some countries of South America, mainly in the northeast region of Brazil (Sampaio et al., 2008; Augusto et al., 2000). The species belongs to the family Anacardiaceae, the same as mango (Mangifera índica), cashew apple (Anacardium occidentale) (Sampaio et al., 2008), cajá (Spondias mombin L.) and umbu (Spondias tuberosa Arruda Camara) (Bicas et al., 2011). It is a small red fruit, with a pleasant aroma and taste which is consumed in natura or as juice and other products such as jams and different candies. The S. purpurea L. is called by different names, which are function of the geographic region, such as red mombin, siriguela, seriguela, ceriguela, ciriguela, jocote, jocote de corona, ciruela, ciruela Mexicana, jobillo, spanish plum and hog plum (Bicas et al., 2011; Furtado et al., 2010; Ceva-Antunes et al., 2006; Parada et al., 2006; Martins et al., 2003; Augusto et al., 2000). The consumer demand for native and exotic products is growing, in special for food products, creating the need for better understanding of its processing and properties. Moreover, Furtado et al. (2010) and Ceva-Antunes et al. (2006) observed that the native fruit commercialization plays an important role in social and employment perspectives in development countries like in Brazil. ⇑ Corresponding author at: Technical School of Campinas (COTUCA), University of Campinas (UNICAMP), R. Culto à Ciência, 177 Botafogo, CEP: 13020-060 Campinas, SP, Brazil. E-mail address: [email protected] (P.E.D. Augusto). 0260-8774/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2011.08.015
The rheological characterization of food is important for unit operations design, process optimization and high quality products assurance (Ibarz and Barbosa-Cánovas, 2003; Rao, 1999). Although the rheological characterization of exotic fruits is being studied for various authors, there is no work in literature related to the rheological characterization of S. purpurea L. pulp, even though it is essential for processing design. The present work has evaluated and modeled the rheological properties of siriguela (S. purpurea L.) pulp as function of temperature.
2. Material and methods A pasteurized frozen commercial siriguela (S. purpurea L.) pulp was used in order to guarantee the standardization and repeatability. After washing, the fruits are pulped, pasteurized, packaged in small plastic bags and then frozen. Further information related to siriguela fruits and pulp can be obtained in the works of Sampaio et al. (2008) and Martins et al. (2003). Samples were thawed and carefully homogenized before the rheological measurements were taken. Its soluble solids content was determined by using a refractometer (digital refractometer r2 mini, Reichert Analytical Inst., Japan), after filtering the samples in cotton, being 10.9 ± 0.1°Brix (mean of three replicates ± standard deviation). The sample total solid content was measured using the pulp moisture, determined by an infra-red moisture analyzer (IV2002, Gehaka, Brazil). The sample total solid content was 15.8 ± 0.4% (mean of three replicates ± standard deviation).
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Nomenclature
a b
c_ ga g⁄ r r0 x A0 Ea
behavior index in power modified Cox-Merz rule (Eq. (11)) [-] magnitude index in power modified Cox-Merz rule (Eq. (11)) [-] shear rate [s1] apparent viscosity (= r/c_ ) [Pa s] complex viscosity [Pa s] shear stress [Pa] yield stress, Herschel–Bulkley’s model [Pa] oscillatory frequency [Hz] Arrhenius’s pre-exponential parameter model activation energy in Arrhenius’s model [J mol1]
storage modulus [Pa] loss modulus [Pa] consistency coefficient, Herschel–Bulkley’s model [Pa sn] consistency coefficient in power law model of viscoelas0 00 ticity properties (Eqs. (2) and (3)) [Pa sn , Pa sn ] flow behavior index, Herschel–Bulkley’s model [-] behavior index in power law model of viscoelasticity properties (Eqs. (2) and (3)) [-] absolute temperature [K] temperature [°C]
k0 , k00 n n0 , n00 TK TC
monly used for describing the viscoelastic behavior of food and dispersions (Rao, 1999):
2.1. Rheology procedures Rheological measurements were carried out with a controlled stress (r) rheometer (AR2000ex, TA Instruments, USA), using a grooved plate–plate geometry (40 mm of diameter). The gap dimension (1.0 mm) was determined by using a gap-independency procedure, as described by Tonon et al. (2009). The rheological properties were evaluated from 0 to 80 °C, and temperature was controlled by a Peltier system in each procedure. Geometry material thermal expansion was considered in order to guarantee the appropriated gap dimension. Moreover, at the temperatures of 60 and 80 °C, a solvent trap was used in order to minimize water vaporization from the product (it was observed that it was not necessary in temperatures below 60 °C). The rheological evaluation was carried out with new samples, i.e., with non-mechanical history. Thus, samples were placed in the rheometer and kept at rest for 5 min before shearing. The experiments were carried out in three replicates, and the regressions were done for each replicate. The parameters of each model were obtained by non-linear regression using the software CurveExpert Professional v.1.0.1 using a significant probability level of 95%. 2.1.1. Steady-state shear properties The steady-state shear experiments were carried out in the shear rate (c_ ) range of 0.01–100 s1. After rest, samples were submitted to shearing at 300 s1 for 5 min to avoid any thixotropy (data not shown). Then, a logarithmic decreasing stepped protocol (100–0.01 s1) was used in order to guarantee the stead-state condition. The products flow behavior was modeled using the Herschel–Bulkley’s model (Eq. (1)). Herschel–Bulkley’s model comprises Newton, Bingham and Ostwald-de-Waele (power law) models. It is commonly used to describe the rheological properties of food products.
r ¼ r0 þ k c_ n
G0 G00 k
ð1Þ
2.1.2. Viscoelastic properties Oscillatory stress sweeps between 0.01 and 100 Pa were performed at a frequency of 1 Hz to determine the products’ linear viscoelastic range. Then, frequency sweep measurements were carried out at 1.0 Pa, a shear stress value within the linear viscoelastic range. The oscillatory frequency (x) was then varied from 0.01 to 100 Hz. The storage modulus (G0 ), loss modulus (G00 ) and complex viscosity (g⁄) were thus obtained, as function of frequency (x). The storage (G0 ) and loss (G00 ) modules were modeled as a power function of oscillatory frequency (x) (Eqs. (2) and (3)), as com-
0
G0 ¼ k xn 00
0
ð2Þ 00
G00 ¼ k xn
ð3Þ
2.2. Applicability of the Cox-Merz rule The Cox-Merz rule states that the apparent viscosity (ga = r/c_ ) at a specific shear rate (c_ ) is equal to the complex viscosity (g⁄) at a specific oscillatory frequency (x), when c_ = x (Eq. (4); Rao, 2005). When this rule is valid, the rheological food properties can be determined by either oscillatory or steady-state shear experiments, which are useful due to limitations in each kind of experiment (Gunasekaran and Ak, 2000). Thus, the obtained results from the steady-state shear and viscoelastic analysis were used for the evaluation of the Cox-Merz rule applicability:
ga ðcÞ ¼ g ðxÞjc_ ¼x
ð4Þ
3. Results and discussions 3.1. Steady-state shear properties Fig. 1 shows the flow curves (r versus c_ ) of siriguela (S. purpurea L.) pulp at 0, 20, 40, 60, and 80 °C. As expected, the S. purpurea pulp showed a shear-thinning behavior (n < 1) with a representative yield stress (r0). The yield stress is the minimum shear stress required to initiate product flow, being related to the material’s internal structure which must be broken (Genovese and Rao, 2005; Tabilo-Munizaga and Barbosa-Cánovas, 2005). At stress below the yield stress, the material deforms elastically, behaving like an elastic solid; above the yield stress, it starts flowing, behaving like a viscous liquid (Bayod et al., 2007). The presence of a yield stress is a typical characteristic of multiphase materials (Sun and Gunasekaran, 2009), as fruit pulps and juices, which are formed by a dispersion of insoluble components (materials of cellular walls) in a water solution (serum, containing sugars, minerals, proteins, and soluble polysaccharides). Table 1 shows the values of the Herschel–Bulkley model parameters for S. purpurea pulp in the evaluated temperature range. The R2 values were always higher than 0.98. The obtained values of yield stress (r0), flow behavior index (n), and consistency coefficient (k) are close to those described in the literature for fruit products (Table 2; 20–30 °C).
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100
o
0C
o
20 C
o
40 C
o
60 C
each parameter A is modeled by a pre-exponential factor – A0, and the activation energy – Ea; R is the constant of the ideal gases, and TK is the absolute temperature):
o
80 C
75 σ (Pa)
A ¼ A0 exp 50
25
0 0
25
.
50
75
100
γ (s-1)
Fig. 1. Flow curves of S. purpurea L. pulp at 0, 20, 40, 60, and 80 °C. Mean of three replicates; vertical bars represent the standard deviation in each value.
Table 1 Values for the parameters of Herschel–Bulkley model the S. purpurea L. pulp (mean of three replicates ± standard deviation; R2 higher than 0.98 in each regression). T (°C)
r0 (Pa)
k (Pa sn)
n
0 20 40 60 80
11.24 ± 0.53 13.26 ± 0.15 12.56 ± 0.25 1.50 ± 0.04 1.37 ± 0.12
21.54 ± 0.95 15.22 ± 0.20 11.22 ± 0.13 3.01 ± 0.07 1.71 ± 0.19
0.25 ± 0.01 0.30 ± 0.00 0.34 ± 0.01 0.44 ± 0.00 0.48 ± 0.01
Ea R TK
ð5Þ
The consistency coefficient (k, Fig. 2) could be well modeled by the Arrhenius Equation (Eq. (6); R2 = 0.91). Although being in the same order of magnitude, the siriguela (S. purpurea) pulp activation energy value (Ea = 17509.2 J mol1) was higher than those described for other fruit products as tomato derivates (Table 3). Thus, the S. purpurea pulp internal structure is less affected by temperature than those products. Even though, its activation energy (Ea) value is closed to those described in the literature for fruit products (Table 3), such as tomato paste, jabuticaba pulp and Juniperus drupacea fruit juice. Massa et al. (2010) observed that the Brownian motion increased with the temperature, resulting in a less developed structure at higher temperatures, which explains the lower consistency coefficient values:
k ¼ 20:92 exp
17509:2 R TK
ð6Þ
The flow behavior index (n) is generally assumed to be relatively constant with temperature (Rao, 1999). However, as can be seen in Fig. 2, the flow behavior index showed a rising trend in relation to temperature, which could be well modeled by a linear function (Eq. (7); R2 = 0.97):
n ¼ 0:241 þ 0:03 T C The S. purpurea pulp is characterized by a high consistency, which can be observed by the magnitudes of r0 (13.3 Pa) and k (15.2 Pa sn) at 20 °C. As can be seen in Table 2, it is closed to the values reported for other fruit pulps as peach (r0 = 25.3 Pa; k = 11.3 Pa sn), umbu (r0 = 8.1 Pa; k = 37.7 Pa sn) and mango (r0 = 6.2 Pa; k = 11.3 Pa sn). As expected, the increase in temperature reduces the yield stress (r0) and consistency coefficient (k), increasing the flow behavior index (n). Although the temperature reduces the shearthinning behavior (i.e., increasing in n), the pulp shear-thinning behavior is still representative even at 80 °C (n80 °C = 0.48). The most used approach to modeling the temperature influence on the rheological properties of food is to consider its effect on the viscosity or apparent viscosity. However, the most important approach for the evaluation of non-Newtonian fluids is modeling each Herschel–Bulkley model’s parameter separately. Thus, the Herschel–Bulkley parameters were modeled as function of temperature. The effect of temperature on the consistency coefficient (k) are generally modeled using the Arrhenius Equation (Eq. (5), where
ð7Þ
The yield stress (r0) modeling is not often carried out in literature works, as it behavior is the less pronounced. In some products it tends to remain constant (as, for example, in 21°Brix peach puree between 5 and 55 °C; Massa et al., 2010), while in others it shows a monotonous falling behavior (as, for example, in butia pulp between 10 and 60 °C; Haminiuk et al., 2006). In some products, however, it shows a non-identifiable behavior (as, for example, in potato puree between 25 and 65 °C; Canet et al., 2005). In fact, it is important to observe that the property behavior in relation to temperature is function not only of the product itself, but also of the studied temperature range. Although having a falling behavior with temperature increasing, the yield stress (r0) could not be modeled by the Arrhenius Equation. This behavior is different than those observed in tomato juice (Augusto et al., in press-a), where the yield stress was modeled using the Arrhenius Equation (the other works listed in Table 2 have not modeled each Herschel–Bulkley model’s parameter separately). As can be observed in Fig. 2, the yield stress has shown a falling sigmoidal trend in relation to temperature, in contrast with the continuous decrease of the exponential function (Arrhenius Equa-
Table 2 Values for the parameters of Herschel–Bulkley model for fruit products. Product
T (°C)
r0 (Pa)
k (Pa sn)
n
References
S. purpurea L. pulp Peach puree (12–21°Brix) Butia pulp Apple, apricot and banana based babyfood Umbu pulp (10–25°Brix) Peach juice (10% fiber) Mango pulp Concentrated tamarind juice (71°Brix) Açai pulp Jabuticaba pulp Tomato juice
20 25 20 20 20 20 20 30 25 25 20
13.26 1.11–25.3 32.54 3.38–7.41 3.18–8.06 3.26 3.81–6.24 1.46 4.35 1.55 0.94
15.22 2.46–11.3 0.15 4.76–13.7 14.00–37.74 13.1 8.82–11.33 4.32 0.17 0.48 0.19
0.30 0.32–0.34 0.86 0.18–0.38 0.29–0.31 0.46 0.31–0.34 0.59 0.78 0.60 0.56
Present work Massa et al. (2010) Haminiuk et al. (2006) Ahmed et al. (2007) Pereira et al. (2007) and Pereira et al. (2008) Augusto et al. (2011) Ahmed et al. (2005) Ahmed et al. (2007) Tonon et al. (2009) Sato and Cunha (2009) Augusto et al. (in press-a)
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273.15 25
293.15
T (K) 313.15
333.15
353.15
Experimental (stress) Power sigmoidal
σ (Pa); k (Pa.sn)
20
Experimental (k) Arrhenius
15 o
10
5
0 0.6 0
20
40 T(ºC)
60
80
0.4 n
o
0.2 Experimental Fig. 3. Mechanical spectra of S. purpurea L. pulp at 0 and 80 °C. Mean of three replicates; vertical bars represent the standard deviation in each value.
Linear 0.0 0
20
40
60
80 3.2. Viscoelastic properties
o
T( C) Fig. 2. Parameters of the Herschel–Bulkley model as function of temperature. Mean of three replicates; vertical bars represent the standard deviation in each value.
Table 3 Activation energy (Ea) of the Arrhenius model (A = A0 exp(Ea/RT)) for the consistency index (k) in fruit products. Product
Ea (k) (J mol1)
References
S. purpurea L. pulp Tomato juice Tomato paste Reconstituted tomato concentrates Jabuticaba pulp Juniperus drupacea fruit juice
17509.2 7353.3 8600–13000 7360–3630
Present work Augusto et al. (in press-a) Dak et al. (2008) Barbana and El-Omri (in press)
13000 60380–78230
Sato and Cunha (2007) Akbulut et al. (2008)
tion). Until 40 °C, the yield stress shows quasi-constant values (11– 13 Pa) followed by a great decrease in temperatures between 40 and 60 °C. Then, it tends to stay back in a constant value (1– 2 Pa). This trend could be well modeled by a power sigmoidal function (Eq. (8); R2 = 0.98), and shows that an important transformation is carried out in siriguela (S. purpurea) pulp between 40 and 60 °C, as the yield stress value changes are more important in this temperature range when compared to temperatures below 40 °C and above 60 °C. The viscoelastic analysis corroborates this observation (Fig. 3). Bhattacharya (1999) had studied the mango pulp yield stress in temperatures of 5, 30, 55 and 80 °C, observing a great fall in yield stress value between 55 and 80 °C:
r0 ¼
12:36 1 þ ð0:018 T C Þ20:77
ð8Þ
Fig. 3 shows the mechanical spectra of S. purpurea L. pulp at 0 and 80 °C. The siriguela (S. purpurea L.) pulp storage modulus values (G0 ) were always higher than those of the loss modulus (G00 ), which indicates that the pulp has dominant elastic properties over the viscous ones. Thus, the product can be classified as a weak gel (Rao, 1999). Similar behavior has been reported for other food products such as peach puree (Massa et al., 2010), açai pulp (Tonon et al., 2009), jabuticaba pulp (Sato and Cunha, 2009), umbu pulp (Pereira et al., 2008), baby foods (Ahmed and Ramaswamy, 2006), potato puree (Alvarez et al., 2004), tomato juice (Augusto et al., in press-b) and concentrates (Bayod et al., 2008; Valencia et al., 2002; Yoo and Rao, 1996). As expected, the values of G0 and G00 had shown a rising tendency with the oscillatory frequency, the opposite behavior of the complex viscosity (g⁄). Thus, it was possible to model the storage and loss modules as a power function of the oscillatory frequency (Eqs. (2) and (3)). Table 4 shows the values for the power law model (Eqs. (2) and (3)) as a function of temperature. The R2 values were always higher than 0.93 in each replicate. The ob-
Table 4 Values for the power law model for storage (G0 ) and loss (G00 ) modules of S. purpurea L. pulp as a function of oscillatory frequency (x) (1 Pa, mean of three replicates ± standard deviation; R2 higher than 0.93 in each regression). 0
00
T (°C)
k0 (Pa sn )
n0
k00 (Pa sn )
n00
0 20 40 60 80
303.0 ± 6.2 286.3 ± 4.3 294.7 ± 15.2 92.7 ± 6.4 37.1 ± 2.8
0.16 ± 0.01 0.14 ± 0.01 0.15 ± 0.01 0.16 ± 0.02 0.14 ± 0.01
74.4 ± 1.5 66.4 ± 0.8 71.3 ± 4.4 23.3 ± 1.6 11.7 ± 0.6
0.28 ± 0.01 0.27 ± 0.00 0.23 ± 0.01 0.28 ± 0.01 0.30 ± 0.02
P.E.D. Augusto et al. / Journal of Food Engineering 108 (2012) 283–289
tained values are in accordance with those reported in the literature by other food products. Ahmed and Ramaswamy (2006) have evaluated the viscoelastic behavior of vegetable based baby food. The values of k0 and k00 ran0 00 ged from 131.0–13500 Pa sn to 19.7–1750 Pa sn , respectively (20– 0 00 25 °C). The values of n and n were in the range from 0.06–0.14 to 0.16–0.22, respectively. The viscoelastic behavior of tomato products (concentrates and ketchups; 24–27% of total solids, 22–27°Brix) have been evaluated by Bayod et al. (2008) and Yoo and Rao (1996). The values of k0 and 0 00 k00 ranged from 1660–16982 Pa sn to 106.6–3802 Pa sn , respec0 00 tively (20–25 °C). The values of n and n were in the range from 0.12–0.25 to 0.10–0.33, respectively. Augusto et al. (2011) studied the effect of fiber addition on the rheological properties of peach juice (10–12.5% fiber; 0–40 °C). The 0 values of k0 and k00 ranged from 263.9–1567.1 Pa sn to 59.8– n00 0 00 616.6 Pa s , respectively. The values of n and n were in the range from 0.14–0.28 to 0.24–0.54, respectively. The values of n00 were always higher than n0 (Table 4), which demonstrate that the viscous behavior of S. purpurea pulp becomes more important in high frequencies. Moreover, the viscous behavior becomes more important in high temperatures, as can be seen by the convergence of k0 and k00 (Table 4, Fig. 4). When the parameters of the power law model for storage (G0 ) and loss (G00 ) moduli (Eqs. (2) and (3)) were evaluated in relation to the temperature, a different behavior was observed. The values of n0 and n00 have shown to be relatively constant with temperature,
287
as expected for the flow behavior index (n; Rao, 1999). It can be clearly seen in Fig. 4, where the mean values for the n0 and n00 are, respectively, 0.15 and 0.27. The k0 and k00 values, though, have shown a sigmoidal decay behavior with temperature, as observed for the yield stress (r0). As can be seen in Fig. 4, both k0 and k00 showed almost constant values in the temperature range between 0 and 40 °C. It indicates that the S. purpurea pulp viscoelastic properties are low dependent of temperature at this range, reflecting low internal structure changes. In fact it is the same behavior observed for the yield stress (r0, Fig. 2). Once more, it is observed that the most important changes in the k0 and k00 values are carried out between 40 and 60 °C, corroborating the yield stress (r0) discussion. This behavior could be well modeled by a power sigmoidal function (Eqs. (9) and (10); R2 > 0.97). It is interesting to observe that, even for k0 and k00 , the parameters related to the sigmoidal shape are quite the same (the proportional and power parameters in temperature). It demonstrates that the decrease in the magnitudes of G0 and G00 in relation to temperature follows the same trend: 0
k ¼
00
k ¼
299:8 1 þ ð0:018 T C Þ8:52 72:17 1 þ ð0:018 T C Þ7:63
ð9Þ
ð10Þ
The observed behavior is different than those observed in other products, although there are just few studies which have modeled the values of k0 , k00 , n0 and n00 as function of temperature. Ahmed et al. (2007) and Ahmed and Ramaswamy (2006) described that the temperature effect was not systematic in the evaluation of k0 , k00 , n0 and n00 of baby food (20–80 °C). Augusto et al. (2011) have modeled the values of n0 and n00 as a quadratic function (2nd order polynomial function) in relation to temperature in peach juices with fibers (0–40 °C). The values of k0 and k00 were modeled using the Arrhenius Equation. It is important to highlight that the property behavior in relation to temperature is function not only of the product itself, but also of the studied temperature range. 3.3. Applicability of the Cox-Merz rule
Fig. 4. Temperature dependency of the parameters of the power law model for storage (G0 ) and loss (G00 ) modules as a function of oscillatory frequency (x). Mean of three replicates; vertical bars represent the standard deviation in each value; dashed lines are the models.
When the applicability of the Cox-Merz rule was evaluated, it was not possible to use it straight. As commonly observed in food products, the complex viscosity (g⁄) magnitudes were always higher than the apparent viscosity (ga) magnitudes (Fig. 5). Although the Cox-Merz rule has been confirmed experimentally for several polymers dispersions and solutions, in complex systems as food products it is generally necessary to modify the original rule (Rao, 2005; Gunasekaran and Ak, 2000). The non-fitting of the Cox-Merz rule for complex dispersions is attributed to structural decay due to the extensive strain applied (Ahmed and Ramaswamy, 2006), presence of high-density entanglements or to the development of structure and intermolecular aggregation in solution (Da Silva and Rao, 1992). Thus, the rheological properties of the S. purpurea pulp differ from those of the polymer solutions and are more similar to structured systems (Ahmed and Ramaswamy, 2006). The rheological oscillatory and steady-state shear rheological properties of foods are generally correlated by modifications to the Cox-Merz rule (Rao, 2005; Gunasekaran and Ak, 2000). Bistany and Kokini (1983) have proposed a power modification of the original rule (Eq. (11), which has been used for the evaluation of different food products. Table 5 shows the values for the parameters of this modified Cox-Merz rule for S. purpurea pulp, with R2 always higher than 0.96:
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3.4. General discussion
Fig. 5. Oscillatory and steady-state shear rheological properties of S. purpurea L. pulp at 0 and 80 °C. Complex viscosity (g⁄) as function of oscillatory frequency (x) (white symbols); and apparent viscosity (ga) as function of shear rate (c_ ) (black symbols).
Table 5 Values for the parameters of the modified Cox-Merz rule (Eq. (11)) for S. purpurea L. pulp. T (°C)
a
b
R2
0 20 40 60 80
1.417 1.317 1.216 2.101 2.166
0.109 0.220 0.492 0.072 0.037
0.99 0.99 0.99 0.96 0.96
b ½ga ðcÞa ¼ g ðxÞjc_ ¼x
ð11Þ
It can be seen that the obtained values are in accordance to those described by other fruit products as potato puree, fruit based baby foods, ketchup and tamarind juice (Table 6), although S. purpurea pulp b values are proportionally small. In the evaluated modified Cox-Merz rule, the b value is related to the magnitude difference between the apparent (ga) and the complex (g⁄) viscosities, while the a value is related to the behavior difference. Thus, the small b values indicate that both S. purpurea pulp apparent (ga) and the complex (g⁄) viscosities magnitudes are closed, which in fact can be seen in Fig. 5. Moreover, as observed by Ahmed et al. (2007) and Alvarez et al. (2004), the values of a and b have not shown a particular trend in relation to temperature. The obtained results indicate that the rheological properties of S. purpurea pulp can be determined by either oscillatory or steady-state shear experiments.
Table 6 Values for the parameters of the modified Cox-Merz rule (Eq. (11)) for fruit products. Product
T (°C)
a
b
References
S. purpurea L. pulp Potato puree Apple baby food Apricot baby food Banana baby food Ketchup Tamarind juice
0–80
1.22–2.17
0.04–0.49
Present work
25–65 5–80
0.90–1.35 1.15–1.20
2.15–39.83 4.64–6.99
Alvarez et al. (2004) Ahmed et al. (2007)
5–80
1.16–1.44
0.41–1.26
Ahmed et al. (2007)
5–80
1.15–1.33
1.91–11.80
Ahmed et al. (2007)
25 10–90
0.94 0.67–1.06
13.97 0.86–30.82
Bistany, Kokini (1983) Ahmed et al. (2007)
As consumer demand for native and exotic products is growing, it is necessary to conduct scientific studies in order to better understand their processing and properties. The rheological characterization of fruit pulps and juices is essential for their processing and product design and optimization. We highlighted the need for carry other works related with physical properties of those fruit products. The present work has evaluated the rheological properties of a commercial siriguela (S. purpurea L.) pulp as function of temperature. The product flow behavior was described by the Herschel– Bulkley’s model. The siriguela pulp viscoelastic behavior was described as a weak gel, and its storage and loss modules were described using a power function of the oscillatory frequency. A power modified Cox-Merz rule was used for describe the pulp rheology, i.e., it was shown that the pulp rheological properties can be determined by either oscillatory or steady-state shear experiments. The obtained data are potentially useful for future studies on food properties and process design. However, other studies are needed for understanding the influence of each unit operation (as pulping or thermal processing) on the siriguela (S. purpurea L.) pulp rheological pulp.
4. Conclusions The present work has evaluated the steady and dynamic shear rheological properties of siriguela (S. purpurea L.) pulp as function of temperature. The product flow behavior could be well described by the Herschel–Bulkley’s model, whose parameters were modeled as function of temperature. The storage and loss modules could be well described by a power function of the oscillatory frequency, whose parameters were modeled as function of temperature. Moreover, a power modified Cox-Merz rule could describe the rheological properties of S. purpurea pulp. The obtained data is potentially useful for future studies on food properties and process design. Acknowledgments The authors thank the São Paulo Research Foundation (FAPESP) for funding Project No. 2010/05241-8. References Ahmed, J., Ramaswamy, H.S., 2006. Viscoelastic and thermal characteristics of vegetable puree-based baby foods. Journal of Food Process Engineering 29, 219– 233. Ahmed, J., Ramaswamy, H.S., Hiremath, N., 2005. The effect of high pressure treatment on rheological characteristics and color of mango pulp. International Journal of Food Science & Technology 40 (8), 885–895. Ahmed, J., Ramaswamy, H.S., Sashidhar, K.C., 2007. Rheological characteristics of tamarind (Tamarindus indica L.) juice concentrates. LWT-Food Science and Technology 40, 225–231. Akbulut, M., Çoklar, H., Özen, G., 2008. Rheological characteristics of Juniperus drupacea fruit juice (pekmez) concentrated by boiling. Food Science and Technology International 14 (4), 321–328. Alvarez, M.D., Fernández, C., Canet, W., 2004. Rheological behavior of fresh and frozen potato puree in steady and dynamic shear at different temperatures. European Food Research Technology 218, 544–553. Augusto, F., Valente, A.L.P., Tada, E.S., Rivellino, S.R., 2000. Screening of Brazilian fruit aromas using solid-phase microextraction–gas chromatography–mass spectrometry. Journal of Chromatography A 873, 117–127. Augusto, P.E.D., Falguera, V., Cristianini, M., Ibarz, A., in press-a. Rheological behavior of tomato juice: steady-state shear and time-dependent modeling. Food and Bioprocess Technology. doi:10.1007/s11947.010.0472.8. Augusto, P.E.D., Falguera, V., Cristianini, M., Ibarz, A., 2011. Influence of fiber addition on the rheological properties of peach juice. International Journal of Food Science and Technology 46, 1086–1092.
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