Revista Brasileira de Produtos Agroindustriais, Campina Grande, v.11, n.1, p.35-42, 2009
ISSN 1517-8595
THERMOPHYSICAL PROPERTIES OF CASHEW JUICE AT DIFFERENT
CONCENTRATIONS AND TEMPERATURES
Renata Cristina Ferreira Bonomo1*, Rafael da Costa Ilhéu Fontan2, Tatiana Sant’Anna de
Souza3 , Cristiane Martins Veloso2, Maycon Fagundes Teixeira Reis4, Sérgio de Souza
Castro2
ABSTRACT
Density and viscosity of commercial cashew juice were studied at a temperature range from (5
to 80) °C and soluble solids contents between (0.8 to 11.2) ºBrix. Polynomial models fitted the
experimental data very well, showing a linear relationship between temperature, soluble solids
content and the thermophysical properties. The thermal expansion coefficient was computed
from its thermodynamic definition at constant pressure. The effect of temperature was very well
correlated with the Arrhenius-Guzman equation (R2 > 0.96). The values of activation energy
(Ea) increased with soluble solids contents from (12.512 to 18.673) kJ.mol-1.
Keywords: density, viscosity, thermal expansion coefficient, activation energy.
PROPRIEDADES TERMOFÍSICAS DO SUCO DE CAJÚ EM DIFERENTES
CONCENTRAÇÕES E TEMPERATURAS
RESUMO
Densidade e viscosidade de suco de caju comercial foram avaliadas na faixa de temperatura de
(5 a 80) ºC e teor de sólidos solúveis entre (0,8 e 11,2) ºBrix. Modelos polinomiais ajustaram-se
satisfatoriamente aos resultados experimentais, sendo verificada uma relação linear entre a
temperatura, sólidos solúveis e as propriedades termofísicas. O coeficiente de expansão térmica
foi determinado a partir de sua definição termodinâmica em pressão constante. O efeito da
temperatura na viscosidade foi bem descrito pela equação de Arrhenius-Guzman (R2 > 0,96). Os
valores da Energia de ativação (Ea) aumentou com o aumento da concentração de sólidos
solúveis a partir de (12,512 até 18,673) kJ.mol-1.
Palavras-chave: densidade, viscosidade, coeficiente de expansão térmica, energia de ativação.
Protocolo 1137 de 22/08/2008
1
Professora Doutora – Universidade Estadual do Sudoeste da Bahia - Itapetinga – BA, *Corresponding author:
[email protected]
2
Professor(a) Mestre – Universidade Estadual do Sudoeste da Bahia - Itapetinga – BA, [email protected],
[email protected], [email protected]
3
Mestre em Engenharia de Alimentos – Universidade Estadual do Sudoeste da Bahia - Itapetinga – BA,
tati [email protected]
4
Graduando em Engenharia de Alimentos – Universidade Estadual do Sudoeste da Bahia - Itapetinga – BA,
[email protected]
35
36
Thermophysical properties of cashew juice at different concentrations and temperatures
INTRODUCTION
Bonomo et al.
MATERIAL AND METHODS
Cashew juice is widely available in the
Brazilian market. This juice, which is a
complex mixture of vitamins, polyphenols,
sugar, mineral salts, organic acids and amino
acids is an excellent source of vitamin C and
contains around six times more vitamin C than
orange juice (da Silva et al., 2000; Azoubel et.
al., 2005).
Generally,
food
composition
and
temperature are the important factors which
affect thermal properties and the knowledge of
these properties is necessary for effective
design of food processing equipment such as
heat exchangers and other equipments which
require pumping of the products (Tansakul &
Chaisawang, 2006; Azoubel et. al., 2005;
Zainal et. al., 2000). According to Zuritz et al.
(2005) an adequate manufacturing process, a
correct design of the concentrate plants and an
appropriate evaluation of their performance will
facilitate optimization of the concentrated juice
quality parameters.
The thermophysical properties of several
juices have been reported, such as pink guava
(Zainal et al., 2000), orange (Telis-Romero et
al., 1998), grape (Zuritz et al., 2005),
pomegranate and pear (Magerramov et al.,
2007), cashew (Azoubel et al., 2005) and Malus
floribunda (Cepeda & Villarán, 1999).
Empirical models of thermal properties have
been developed for each specific food material,
in spite of the general models developed by
Choi & Okos (1983) so that they would give a
more accurate prediction. The thermal
expansion coefficient is a physical property that
represents density change in the material, due to
an increase in its temperature at constant
pressure.
In spite of thermophysical properties of
fruit juice as well as mathematical models for
their calculation have been published, the
majority of the available data for fruits are for
sub-tropical ones. In an attempt to fill this gap,
the objective of this work was to measure the
density, viscosity and thermal expansion
coefficient of cashew juice as a function of
temperature and soluble solute content and to
obtain simple
equations
to
correlate
experimental data.
Materials
Cashew juice with 11.2 °Brix of soluble
solids content was obtained at a local market in
Itapetinga, Brazil. Dilutions from this juice
were made with distilled water until obtain
samples with (0.8, 1.4 and 2.6) °Brix. All the
juices prepared were filtered to remove particles
in suspension using a 50 mesh sieve. The total
soluble solids were measured using a portable
refractometer (Atago, Brazil).
Density and thermal expansion coefficient
Cashew juice density was determined by
applying the picnometric method (Constenla et
al.,1989). The sample kept in a 25 mL standard
volumetric picnometer was weighed using an
analytical balance (precision of ±0.0001 g,
Gehaka). The picnometer was previously
calibrated with distilled water at each
temperature studied, (5, 20, 35, 50, 65 and 80)
°C, and kept constant through a thermostatic
water bath (Quimis, Brazil). All of these
determinations were carried out by three
repetions.
The thermal expansion coefficient was
calculated from the thermodynamic expression
(Equation 1), at constant pressure, using the
best fitting polynomial to represent density
(Zuritz et al., 2005).
  1  
  
    1     
    
    T 
P
 T 
  

P
(1)
Viscosity
Some authors have considered that the fruit
juices present Newtonian behavior when pulp
content is low, soluble solids content is lower
than 30 °Brix, or if the juices have been
depectinised (Cepeda & Villarán, 1999;
Saravacos, 1970; Zuritz et. al., 2005).
Revista Brasileira de Produtos Agroindustriais, Campina Grande, v.11, n.1, p.35-42, 2009
Thermophysical properties of cashew juice at different concentrations and temperatures
In order to determine the apparent viscosity,
at first the kinematic viscosity was obtained in
the studied temperatures. It was used a 75
cappilary
Cannon-Fenske
viscosimeter,
immersed in a cinematic bath for temperature
control. The kinematic viscosity value for each
temperature was calculated by Equation 2.
  nt
(2)
Once the density and cinematic viscosity
was known, the apparent viscosity could be
calculated by Equation 3 (Bird et al., 1960).
   
(3)
From viscosity values () as function of
temperature, flow Activation Energy values for
each studied concentration were calculated
using the Arrhenius-Guzman equation (Cepeda
& Villarán, 1999):
     exp Ea RT 


(4)
Experimental design
The experiments were carried out at 4
levels of soluble solute content, (0.8, 1.4, 2.6
and 11.2) °Brix, and 6 levels of temperature, (5,
20, 35, 50, 65 and 80) °C, in a factorial design.
All statistical analysis was performed using the
SAEG statistical package (Ribeiro Junior,
2001). The suitability of the fitted functions
Bonomo et al.
37
was evaluated by the determination coefficient
(R2), the level of significance and residual
analysis.
RESULTS AND DISCUSSION
Effect of temperature and concentration on
density and thermal expansion coefficient
In Table 1 values of density of clarified
cashew juices are shown with different soluble
solids content (concentration) measured at
different temperatures. The statistical analysis
showed that the concentration and temperature
had a significant effect on density at a 95%
confidence level.
It was found from these results that density
of cashew juice decreased linearly with the
temperature increase and concentration
decrease. This result is in agreement with
depectined and clarified peach juice and orange
juice (Ramos & Ibarz, 1998), guava juice
(Shamsudin et al., 2005), Malus floribunda
juice (Cepeda & Villarán, 1999) and Brazilian
orange juice (Telis-Romero et al., 1998). The
multiple regression of density as a function of
concentration, Cs (ºBrix), and temperature, T
(ºC), in the range studied is shown in Eq. (5).
Figure 1 shows the response surface obtained
from Eq. (5).
Table 1. Density of cashew juices
º Brix
11.2
2.4
1.2
0.8
5
1040.16
1004.94
1000.23
996.22
20
1039.29
1004.12
998.47
996.76
Temperature (ºC)
35
50
1035.05
1025.27
997.62
990.31
992.63
983.07
993.92
983.31
  996.49  0.096T  0,0038T 2  4.03C
65
1014.48
985.52
979.09
979.17
R2 = 0,974
80
1010.93
972.28
969.08
967.89
(5)
s
Revista Brasileira de Produtos Agroindustriais, Campina Grande, v.11, n.1, p.35-42, 2009
38
Thermophysical properties of cashew juice at different concentrations and temperatures
Bonomo et al.
Figure 1. Density as function of temperature and concentration.
Calculated data from the equations of
Constenla et al. (1989), Alvarado and Romero
(1989) and the adjusted ones in this work are
nearly coincident with the experimental data
(Figure 2). For all equations the error was lower
than 2%.
Equation 3 was used in Eq. (1) to obtain the
thermal expansion coefficient (). In Table 2,
values of thermal expansion are shown for
different
concentrations
at
different
temperatures. From these results was verified
that thermal expansion coefficient of cashew
juice increased linearly with the temperature
increase and concentration decrease.
Effect of temperature on viscosity
Values of viscosity are shown in Table 3. It
was observed that its values increase with
concentration and decrease with temperature
elevation. This decrease in apparent viscosity
with increase in temperature and decrease in
concentration has also been reported by Vitali
and Rao (1984) (orange juice), Hernandez et al.
(1995) (orange juice) and Shamsudin et al.
(2005) (guava juice).
According to Constenla et al. (1989) the
solution viscosity is a function of the
intermolecular
forces
and
water-solute
interactions that restrict the molecular motion.
These forces depend upon intermolecular
spacings and the strength of the hydrogen
bonds, and are affected by changes in both
concentration and temperature (Azoubel et. al.,
2005).
The model that best fitted with the
experimental values was a polynomial type,
where the viscosity varies with the square of the
temperature and linearly with concentration.
The equation obtained by the least squares
method, with determination coefficient of
0.949, significant at a probability level of 99%,
is presented in the Equation 6. Figure 3 shows
the response surface obtained from Eq. (6).
Revista Brasileira de Produtos Agroindustriais, Campina Grande, v.11, n.1, p.35-42, 2009
Thermophysical properties of cashew juice at different concentrations and temperatures
Bonomo et al.
39
Figure 2. Density of cashew juice at 5 ºC.
Table 2. Thermal expansion coefficient of cashew juices
ºBrix
0.8
1.2
2.4
11.2
5
1.34 x10-04
1.34 x10-04
1.33 x10-04
1.29X10-04
20
2.49X10-04
2.49X10-04
2.47X10-04
2.39X10-04
Temperature (ºC)
35
50
3.65X10-04
4.83X10-04
3.64X10-04
4.82X10-04
-04
3.63X10
4.80X10-04
-04
3.50X10
4.63X10-04
65
6.04X10-04
6.03X10-04
6.00X10-04
5.79X10-04
80
7.27X10-04
7.26X10-04
7.23X10-04
6.97X10-04
Table 3. Viscosity of cashew juices
ºBrix
11.2
2.4
1.2
0.8
5
3.420
1.270
1.180
1.080
20
2.180
0.801
0.927
0.864
Temperature (ºC)
35
50
1.530
1.120
0.565
0.421
0.645
0.767
0.621
0.464
65
0.851
0.325
0.620
0.364
  1.32  3.39  10 2 T  2.78  10 4 T 2  1.84  10 1 C s  2.17  10 3 TC s
80
0.611
0.243
0.295
0.302
(6)
Revista Brasileira de Produtos Agroindustriais, Campina Grande, v.11, n.1, p.35-42, 2009
40
Thermophysical properties of cashew juice at different concentrations and temperatures
Bonomo et al.
Figure 3. Viscosity as function of temperature and concentration.
The effect of temperature on the viscosity
follows the Arrhenius-Guzman equation with
R2 values greater than 0.96. Magnitudes of
activation energy for flow related to apparent
viscosity and temperature ranged from (12.512
to 18.673) kJ.mol-1, while the corresponding
magnitudes of constant  ranged from
(5.337x10-6 to 1.057x10-3) mPa.s (Table 4).
The R2 for all cases were greater than 0.96.
This increase in activation energy with
increase in concentration has also been
reported by Nindo et al. (2007) (blueberry
puree), Cepeda & Villarán (1999) (Malus
floribunda juice).
Table 4. Fitting parameters for the Arrhenius-Guzman equation to predict the variation of viscosity of
cashew juice with absolute temperature.
ºBrix
Ea (kJ.mol-1)
Ea/R (K)
R2
 (mPa.s)
-6
5.337x10
12.512
1505.0
0.991
0.8
2.669x10-6
13.942
1677.0
0.963
1.2
5.150x10-4
17.600
2117.0
0.992
2.4
1.057x10-3
18.673
2246.0
0.998
11.2
CONCLUSIONS
From this study, it was found that the
physical properties of cashew juice were
concentration and temperature dependent. The
effect of temperature and concentration on
density and viscosity can be described by a
linear equation that could be useful for
preliminary equipment design. The activation
energy Ea increased with total solids content.
These results can be applied in process with
cashew juice which involves flow and heat
transfer.
Revista Brasileira de Produtos Agroindustriais, Campina Grande, v.11, n.1, p.35-42, 2009
Thermophysical properties of cashew juice at different concentrations and temperatures
BIBLIOGRAPHIC REFERENCES
Alvarado, J. D., Romero, C. H. Physical
properties of fruits: I – density and viscosity
of juices as functions of soluble solids and
content and temperature. Latin American
Applied Research, v.19 n.15, p. 15-21,
1989.
Azoubel, P. M., Cipriani, D. C., El-Aouar, A.
A., Antonio, G. C., Murr, F. E. X. Effect of
concentration on the physical properties of
cashew
juice.
Journal
of
Food
Engineering, v.66, p. 413-417, 2005.
Bird, R. B., Stewart, W. E., Lightfoot, E. N.
Transport phenomena p.3-33. John Wiley &
Sons, Inc., New York. 1960.
Cepeda, E., Villarán, M. C. Density and
viscosity of Malus floribunda juice as a
function of concentration and temperature.
Journal of Food Engineering, v.41, p. 103107, 1999.
Choi, Y., Okos, M. R.. The thermal properties
of tomato juice concentrate. Transactions of
the ASAE, v.26, p. 305–311, 1983.
Constenla, D. T., Lozano, J. E., Crapiste, G. H..
Thermophysical properties of clarified apple
juice as a function of concentration and
temperature. Journal of Food Science, v.54,
p. 663-668, 1989.
Silva, K. D. da, Collares, F. P., Finzer, J. R. D..
A simple and rapid method for estimating
the content of solids in industrialized cashew
juice. Food Chemistry, v.50, p. 247–250,
2000.
Hernandez, E., Chen, C. S., Johnson, J., Carter,
R. D.. Viscosity changes in orange juice
after ultrafiltration and evaporation. Journal
of Food Engineering, v.25, n.3, p. 387396,1995.
Magerramov, M. A., Abdulagatov, A. I.,
Azizov, N. D., Abdulagatov, I. M. Effect of
temperature, concentration, and pressure on
the viscosity of pomegranate and pear juice
concentrates.
Journal
of
Food
Engineering, v.80, p. 476-489, 2007.
Nindo, C. I., Tang, J., Powers, J. R., Takhar, P.
S. Rheological properties of blueberry puree
Bonomo et al.
41
for processing applications. Food Science
and
Technology
/LebensmittelWissenschaft + Technologie, v.40, p. 292299, 2007.
Ramos, A. M., Ibarz, A. Density of juice and
fruit puree as a function of soluble solids
content and temperature. Journal of Food
Engineering, v.35, p. 57-63, 1998.
Ribeiro Júnior, J. I. (2001). Análises
estatísticas no SAEG (pp. 169-226). UFV,
Viçosa.
Saravacos, G. D. Effect of temperature on
viscosity of fruit juices and purees. Journal
of Food Science, v.35, p. 122-123,1970.
Shamsudin, R., Mohamed, I. O., Yaman, N. K.
M. Thermophysical properties of Thai
seedless guava juice as affected by
temperature and concentration. Journal of
Food Engineering, v.66, p. 395-399,2005.
Tansakul, A., Chaisawang, P. Thermophysical
properties of coconut milk. Journal of Food
Engineering, v.73, p. 276-280, 2006.
Telis-Romero, J., Telis, V. R. N., Gabas, A. L.,
Yamashita, F. Thermophysical properties of
Brazilian orange juice as affected by
temperature and water content. Journal of
Food Engineering, v.38, p. 27-40, 1998.
Vitali, A. A., Rao, M. J. Flow concentrated of
low-pulp concentrated orange juice: effect of
temperature and concentration. Journal of
Food Science, v.49, p. 882-888, 1984.
Zainal, B. S., Rahman, R. A., Ariff, A. B.,
Saari, B. N., Asbi, B. A. Effects of
temperature on the physical properties of
pink guava juice at two different
concentrations.
Journal
of
Food
Engineering, v.43, p. 55-59, 2000.
Zuritz, C. A., Puntes, E. M., Mathey, H. H.,
Pérez, E. H., Gascón, A., Rubio, L. A.,
Crullo, C. A., Chernikoff, R. E., Cabeza, M.
S. Density, viscosity and coefficient of
thermal expansion of clear grape juice at
different soluble solid concentrations and
temperatures.
Journal
of
Food
Engineering, v.71, p.143-149, 2005.
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42
Thermophysical properties of cashew juice at different concentrations and temperatures
Bonomo et al.
Nomenclature
Ea
activation energy (kJ.mol-1)
P
pressure (Pa)
T
temperature (ºC)
t
the flow off time of the sample (s)
n
viscosimeter characteristic constant (m2s-2)
R
gas constant (kJ.mol-1.K-1)
Greek letters

thermal expansion coefficient

density (kg.m-3)

cinematic viscosity (m2s-1)

apparent viscosity (mPa.s)

constant (mPa.s)
Revista Brasileira de Produtos Agroindustriais, Campina Grande, v.11, n.1, p.35-42, 2009