Rheological Characterization of Blackberry
Pulp
Caracterização Reológica da Polpa de
Amora-Preta
AUTORES
AUTHORS
Charles Windson Isidoro HAMINIUK
Programa de Pós-graduação em Tecnologia de Alimento
– UFPR
CP 19011, Curitiba-PR, Brasil
Laboratório de Biopolímeros – UFPR,
CP 19081, Curitiba-PR, Brasil
e-mail: [email protected]
Maria-Rita SIERAKOWSKI
Laboratório de Biopolímeros – UFPR
SUMMARY
The effect of temperature on the rheological behaviour of whole blackberry pulp
(Rubus spp) was determined, with temperatures ranging from 10 °C to 60 °C. The whole
pulp was adequately described by the Herschel-Bulkley model and exhibited shear thinning
behaviour, whereas decreases in the apparent viscosity and consistency coefficient occurred
as the temperature increased, as expected for a fruit pulp. No defined tendency was observed
with respect to the yield stress and flow behaviour index. The Arrhenius model gave a good
description of the effect of temperature on the apparent viscosity of the pulp and the Ea
(activation energy) determined at a shear rate of 50s–1 was 18.27 kJmol–1.
Dayane Rosalyn IZIDORO
Maria Lucia MASSON
Programa de Pós-graduação em Tecnologia de Alimento
– UFPR
RESUMO
Foi determinado o efeito na temperatura no comportamento reológico da polpa
integral de amora-preta (Rubus spp) na faixa de temperatura de 10 °C a 60 °C. A polpa
integral foi adequadamente descrita pelo modelo de Herschel-Bulkley e exibiu comportamento
pseudoplástico, sendo que com o aumento da temperatura ocorreu uma diminuição na
viscosidade aparente e coeficiente de consistência, conforme esperado para polpa de fruta.
Não foi observado uma tendência definida para a tensão inicial e índice de comportamento.
A equação de Arrhenius descreveu bem o efeito da temperatura na viscosidade aparente da
polpa, onde a Ea(energia de ativação) determinada a uma taxa de deformação de 50s–1 foi
de 18.27 kJmol–1.
PALAVRAS-CHAVE
KEY WORDS
Pulp; Blackberry; Rheology; Arrhenius.
Polpa; Amora-Preta; Reologia; Arrhenius
Braz. J. Food Technol., v. 9, n. 4, p. 291-296, out./dez. 2006
291
Recebido/Received: 30/09/2005. Aprovado/Approved: 20/11/2006.
haminiuk, C. W. I. et al.
1. INTRODUCTION
Originally from Asia, blackberry fruits were probably
introduced into Europe around the XVII century. In Brazil,
blackberries were introduced into the State of Rio Grande do Sul
via EMBRAPA (Agricultural Research Centre) in the city of Pelotas
in 1972 when the first plants arrived, coming from Arkansas
University, United States. The blackberry has also been cultivated
in other States, such as Santa Catarina, São Paulo, Paraná and
Minas Gerais, with prominence in the State of Rio Grande do
Sul, which is the largest national producer with approximately
700 ton/year (SANTOS et al., 1996).
The fruit is dark-red in colour, almost black in the
mature stage, with the pulp presenting the same colour as
the fruit. Regarding cultivation, it grows well in all Brazilian
states, presenting fast growth and good adaptation to different
kinds of soil, with a harvest from September to November. The
blackberry tree, like the raspberry tree, belongs to the Rubus
genus, of the Rosacea family, which includes other important
gendera (Malus, Prunus, Pyrus, Prunus, Pyrus, amongst others)
for fruit production in Brazil (BIBVIRT, 2005).
Due to the low cost of plantation, orchard maintenance
and principally the reduced use of agricultural pesticides, this
crop has a fast economic return and is considered as an option
for family agriculture (ANTUNES, 2002).
Besides the raw fruits, manufactured products, such
as juices, nectars, ice creams and jellies, contain the pulp as
a basic raw material, which is used in the unit operations,
such as pumping, mixing and separation processes. For such
industrial processes to be technically and economically feasible,
it is important to have knowledge of the physical chemical
properties. Of these properties, the rheological behaviour is
one of the most important (IBARZ et al., 1996).
The rheological properties of fluid foods should be taken
carefully into account for designing and modelling purposes.
Furthermore, rheology is critically important for products like
fruit pulps, in which the rheological property is considered as
an indicator of product quality. In processes involving fluid
flow, such as pumping, extraction or filtration, the calculations
require knowledge of the rheological data and the rheology of
the product, in order to analyse the flow conditions of various
food processes (MARCOTTE et al., 2001).
According to BRANCO (1995), knowledge of the
rheological parameters is important in industrial applications
not only to determine the energy consumption required to
pump a highly viscous fruit pulp, but also to solve problems
with air incorporation, which causes difficulties in the pumping
operation and with undesirable reactions such as oxidation and
contamination.
Fruit pulps are generally non-Newtonian fluids in which
the apparent viscosity decreases with increasing shear rate,
and therefore they exhibit a shear-thinning behaviour. Several
models have been used to characterize the flow behaviour of
fruit pulps, amongst which the most used are the Power Law,
Casson, Bingham, Herschel-Bulkley and Mizrahi-Berk models.
Braz. J. Food Technol., v. 9, n. 4, p. 291-296, out./dez. 2006
Rheological Characterization of
Blackberry Pulp
Therefore, the objective of this work was to study the
rheological behaviour of whole blackberry pulp in a temperature
range from 10 °C to 60 °C. Three rheological models were used
as a tool for the calculation of the relation between shear rate
and shear stress in order to obtain the rheological parameters
of the pulp. The Arrhenius equation was used to evaluate the
influence of temperature on the viscosity.
2. MATERIAL AND METHODS
2.1Sample preparation
The blackberry fruits (Rubus spp) used in this work
were obtained from a single batch from Vacaria, Rio Grande
do Sul State. The fruits were chosen based on their skin colour,
appearance and ripeness (determined from the ratio of oBrix/
titratable acidity), according to HAMINIUK et al., (2006b). The
average ratio obtained for the ripe fruits was 6.32. The fruits
(5kg) were processed in a depulper (Recifer) with a 0.5mm
screen. This mesh was chosen in order to achieve maximum
yield in the pulp extraction, according to industrial practice,
producing an homogeneous pulp. The pulp was packed in
polyethylene bags (100g) to reduce contact with the air, and
then quickly plate-frozen and stored at –20 °C, to avoid the
formation of large ice crystals on the surface and damage to the
cell structures, and also to inhibit enzyme action (HAMINIUK et
al, 2006b). The packed and frozen material was preserved for a
period of 2 months. Before analysis, the samples were thawed
at room temperature (25 °C).
2.2Chemical and physical analyses
Soluble solids (oBrix), pH, moisture (%) and titratable
acidity (g/100ml) were determined according to the standard
A.O.A.C. method (2000).
2.3Rheological measurements
The rheological measurements were carried out using
a concentric cylinder Brookfield (DV-III) with a small sample
adapter (13R/RP, 19.05mm in diameter and a depth of 64.77mm)
and the SC4-34 spindle (9.39mm in diameter and 24.23mm in
length) connected to a microcomputer for control purposes and
data acquisition. A Thermo Haake B3 (Haake, Model FK-2) was
used to adjust the temperature of the sample to the 10–60 °C
range. The measurements were made in this temperature range
considering that 10 °C is the usual thawed pulp temperature and
60 °C corresponds to the industrial pasteurisation temperature.
The choice of this system was due to the possibility of obtaining
a better control of the temperature during the assays and the
use of a small sample size (10mL). Each experimental run lasted
4 min in the upward curve, with a shear rate range from 2.8
to 70 s–1, and 4 min in the downward curve, with a shear rate
range from 70 to 2.8s–1 (this shear rate range was chosen since
292
haminiuk, C. W. I. et al.
it represented a typical process condition used in flow pipes).
With both decreasing and increasing shear rate, 25 points of
shear stress were obtained, resulting in a total of 50 points,
the average value for shear stress being measured for each
shear rate. Three experimental runs were carried out for each
material and the resulting shear stress was the average of the
three experimental values.
2.4Rheological models
Numerous factors influence the selection of a rheological
model to describe the flow behaviour of a particular fluid. Many
models have been used to represent the flow behaviour of nonNewtonian fluids (STEFFE, 1996). Some of the most widely used
rheological models are the Power Law, with two parameters
(consistency coefficient and flow behaviour index), Casson,
with two parameters (Casson’s viscosity and yield stress), and
the Herschel-Bulkley (H-B) and Mizrahi–Berk (M–B) models,
with three parameters (consistency coefficient, flow behaviour
index and yield stress). In this work, the experimental data were
statistically evaluated and fitted according to the rheological
models of Mizrahi-Berk (equation 1), Herschel-Bulkley (equation
2) and Power Law (equation 3). The rheological model of
Ostwald-De-Waele, or power law, is used to characterize the
behaviour of juices and fruit pulps because it fits the experimental
data well, being a simple model and having wide technological
application. The Mizrahi-Berk and Herschel-Bulkley models were
also chosen due to their reliability in fitting data and because
they include the yield stress term.
Rheological Characterization of
Blackberry Pulp
where:
σ = Shear stress (Pa)
γ = Shear Rate (s–1)
K = Consistency coefficient (Pa.sn)
n = Flow behaviour index (dimensionless)
In order to obtain the rheological (σo, n and K) and
statistical parameters (R2 and χ2) the Software Origin 7.0
(OriginLab Corporation, MA, USA) was used. The choice of the
most appropriate model was based on the statistical parameters
of the determination coefficient (R2), chi-square (χ2) and the sum
of the squared residuals (SSR). The model that best fits the data
is that with the highest values for the determination coefficient
(R2) and lowest values for chi-square (χ2) and the sum of the
squared residuals (SSR).
2.4.1 Influence of temperature on apparent viscosity
The influence of temperature on the apparent viscosity
of non-Newtonian fluids may be expressed in terms of an
Arrhenius-type equation (equation 4), involving the absolute
temperature (T), the universal gas constant R, the preexponential factor (ηo) and the energy of activation for viscosity
(Ea) (STEFFE, 1996). A shear rate of 50s–1 was chosen since this
is the speed used in the pumping (start pump) and agitation
processes, according to BRANCO (1995).
 Ea 
 
ηap = η0e  RT 
(4)
Mizrahi-Berk model:
σ = K oM + K M γ nM
(1)
3. RESULTS AND DISCUSSION
where:
σ = Shear stress (Pa)
3.1Chemical and physical characteristics
KoM = Square-root of the yield stress (Pa)
γ = Shear rate (s–1)
KM = Consistency coefficient
(Pa.sn)
nM = Flow behaviour index (dimensionless)
Herschel-Bulkley model
σ = σ oH + K H γ nH
(2)
where:
The chemical and physical characteristics of the
blackberry pulp are shown in Table 1. The pulp showed a soluble
solid content of 5.37 oBrix. This result is in agreement with that
of ANTUNES et al., 2003 during their study on the post-harvest
conservation of blackberry fruits. The value for titratable acidity
was lower than those found by GRANADA et al. (2001), which
may be explained by the physiological condition of the plant
(season and place of cultivation). Regarding moisture and pH,
the values found in the analyses were typical of tropical fruits.
σ = Shear stress (Pa)
TABLE 1. Physical-chemical composition of the blackberry
pulp.
σ0H = Yield stress (Pa)
γ = Shear Rate
(s–1)
Parameters
KH = Consistency coefficient (Pa.sn)
Experimental values
nH = Flow behaviour index (dimensionless)
pH
Power Law model
Titratable acidity (g/100g)
0.85
Moisture (%)
89.00
σ = Kγ n
Soluble solids
(3)
Braz. J. Food Technol., v. 9, n. 4, p. 291-296, out./dez. 2006
#
3.20
(oBrix)
Expressed in citric acid.
293
5.37
haminiuk, C. W. I. et al.
3.2Rheological behavior of the pulp
Rheological Characterization of
Blackberry Pulp
behaviour was found in previous studies carried out with
mango pulp (VIDAL, 2000; SUGAI, 2002), guava pulp (FERREIRA
et al., 2002) and Araçá pulp (HAMINIUK et al., 2006b). However,
a defined tendency for the yield stress and flow behaviour index
with increase in temperature was not verified. According to
KROKIDA et al., (2001) the heat treatment has a major effect
on the consistency coefficient (K) of non-Newtonian fluid foods,
analogous to the effect on Newtonian viscosity (η). The flow
behaviour index (n) was slightly affected by temperature (with
a small increase at high temperatures).
Tables 2, 3 and 4 present the rheological parameters of
the whole blackberry pulp. From the industrial point of view,
the three models were considered suitable to represent the
rheological data of the blackberry pulp due to the high values
of the determination coefficient. However the Herschel-Bulkley
model was chosen to fit the experimental data in this work due
to its characteristics of being a full model that could describe all
the rheological parameters (yield stress, consistency coefficient
and flow behaviour index) well, when compared to the Power
Law model (two parameters model) that does not present the
yield stress term. Yield stress is an important quality control
parameter in industrial processes, particularly for comparing the
overall characteristics of products made on different production
lines (HAMINIUK et al., 2006a).
For the Herschel-Bulkley model, the determination
coefficient (R2) values were higher than 0.99 and the chi-square
(χ2) values lower than 0.01 at all temperatures (Table 3). These
results show a good fit for the Herschel-Bulkley model.
The experimental data were in better agreement with
the Herschel-Bulkley model than with the Mizrahi-Berk and
Power Law models, since the H-B model showed values of R2
closer to one and values of χ2 and SSR closer to zero. All the
estimates and fits were significant at 95% of probability.
Figure 1 represents the relation between shear stress
and shear rate at all the temperatures studied with whole
blackberry pulp. The marked points represent the average values
for the experimental data of the rheograms and the continuous
lines are the fitted results calculated using the Herschel-Bulkley
model. It can be observed that for a constant shear rate value,
the shear stress value decreased with increase in temperature.
As shown in Table 3, blackberry pulp showed shear
thinning behaviour, the values for the flow behaviour index
(nH) being less than 1 (nH<1) at all temperatures. The same
TABLE 2. Mizrahi-Berk model parameters for whole blackberry pulp.
Yield stress (σoM)
(Pa)
0.34
0.45
0.87
0.62
0.51
0.66
Temperature ( °C)
10
20
30
40
50
60
Consistency coefficient
KM (Pa sn)
1.61
1.36
0.21
0.38
0.43
0.12
Flow behaviour index
nM (dimensionless)
0.18
0.19
0.47
0.34
0.30
0.52
χ2
SSR
R2
0.02
0.00
0.03
0.01
0.00
0.02
0.07
0.20
0.11
0.37
0.13
0.14
0.99
0.97
0.99
0.98
0.97
0.98
χ2
SSR
R2
0.00
0.00
0.00
0.01
0.00
0.00
0.07
0.21
0.11
0.38
0.13
0.14
0.99
0.99
0.99
0.99
0.99
0.99
TABLE 3. Herschel-Bulkley model parameters for whole blackberry pulp.
Yield stress (σoH)
(Pa)
0.35
0.29
1.00
0.57
0.45
0.54
Temperature ( °C)
10
20
30
40
50
60
Consistency coefficient
KH (Pa sn)
1.95
1.12
0.24
0.44
0.45
0.09
Flow behaviour index
nH (dimensionless)
0.38
0.44
0.70
0.55
0.50
0.77
TABLE 4. Power Law model parameters for whole blackberry pulp.
Temperature ( °C)
10
20
30
40
50
60
Consistency coefficient K
(Pa sn)
1.72
0.95
0.69
0.75
0.72
0.31
Braz. J. Food Technol., v. 9, n. 4, p. 291-296, out./dez. 2006
Flow behaviour index
n (dimensionless)
0.41
0.48
0.50
0.44
0.42
0.53
294
χ2
SSR
R2
0.00
0.00
0.01
0.01
0.00
0.01
0.08
0.22
0.38
0.42
0.15
0.24
0.99
0.99
0.99
0.97
0.99
0.98
haminiuk, C. W. I. et al.
Rheological Characterization of
Blackberry Pulp
FIGURE 1. Relation between shear stress and shear rate for
the blackberry pulp fitted according to the Herschel-Bulkley
model.
The apparent viscosity of the blackberry pulp decreased
with increases in temperature and shear rate until the
Newtonian platform was reached. When shear force, associated
with temperature, was applied, the particles could rearrange
themselves in a direction parallel to the shear force, and big
particles could break into small particles. The particles flowed
easily as a result of the resistance arising from particle–particle
interactions, which resulted in a decrease in viscosity (CHARM,
1962). After a sharp reduction, the apparent viscosity changed
slightly and became steady at higher shear rates. This could be
related to the reduction in size of the colloidal aggregates as
the shear rate increased (IBANOGLU, 2002). Several researchers
have reported that the decrease in viscosity of fruit pulps is a
result of the heat treatment (HAMINIUK et al., 2006b, STEFFE,
1996, SILVA et al., 2005, KAYA et al., 2005). From an industrial
point of view, the decrease in viscosity facilitates pulp flow and
heat exchange during processing. It is known that fluids with
lower viscosity have lower head loss during flow, resulting in a
decreased energy demand for the process.
The effect of temperature on the apparent viscosity of
fluid foods at a constant shear rate can be described by the
Arrhenius equation (RAO & TATTIYAKUL, 1999), in which the
apparent viscosity decreases in an exponential function with
temperature. The Arrhenius model gave a good description
of the temperature effect on apparent viscosity in the whole
blackberry pulp at a constant shear rate of 50s–1, as can be
seen in Figure 2.
The activation energy calculated for the whole blackberry
pulp was 18.27 kJmol–1, with a determination coefficient (R2)
of 0.97 and a standard error of 0.06. It is not always easy
to compare the values for the activation energy of different
fluid food, mostly because they are obtained at different
concentrations and shear rates. In addition, the activation
energy value indicates the sensitivity of the apparent viscosity
to temperature changes. Higher activation energy means that
the apparent viscosity is relatively more sensitive to temperature
change (KAYA et al., 2005).
Braz. J. Food Technol., v. 9, n. 4, p. 291-296, out./dez. 2006
FIGURE 2. Effect of temperature on the apparent viscosity of
whole blackberry pulp.
4. CONCLUSIONS
In the light of the results, it can be stated that the
rheological behaviour of whole blackberry pulp in a temperature
range from 10 °C to 60 °C was adequately described by the
Herschel-Bulkley model, showing a non-Newtonian shear
thinning behaviour (nH<1). The yield stress (σo­) flow behaviour
index (nH) and consistency coefficient (KH) were significantly
affected by temperature. The apparent viscosity decreased with
increase in shear rate and temperature. The Arrhenius equation
represented the effect of temperature on the apparent viscosity
of the pulp well, and the activation energy value obtained at a
constant shear rate of 50s–1 was 18.27 kJmol–1.
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