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Rheology of raspberry juices
Journal of Food Engineering 6 (1987) 269-289
Rheology of Raspberry Juices A. Ibarz and J. Pagan Departament de Qutica i Indlistries AgroaIimentaries, Escola Tknica Superior d’Enginyers Agrbnoms de Lleida, Universitat PoIitknica de Catalunya, Avinguda Alcalde Rovira Roure, 177,25006-Lleida, Spain (Received 29 April 1986; revised version received 10 July 1986; accepted 22 October 1986)
ABSTRACT This paper reports a study of the rheological behaviour of different concentrations of raspberry juice at different temperatures. The behaviour is pseudoplastic at higher concentrations and lower temperatures, although at low concentrations and in some cases at high temperatures the behaviour is Newtonian. The effect of temperature and soluble solids content on the consistency coefficient was also studied: an equation was derived which describes the combined effect of these two variablesfor two different models and over the range of temperatures and concentrations studied.
NOMENCLATURE Constant in eqn (5) (dimensionless) Constant in eqn (6) (“Brix-‘) Constant in eqn (7) (dimensionless) Constant in eqn (8) (“Brix- 1) Concentration in soluble solids (“Brix) Activation energy of the flux (kcal g-mall I Consistency coefficient (Pa s “) Constant in eqn (4) (Pa s”) Constant in eqn (5) (Pa s” “BrixA1) Constant in eqn (6) (Pa sfl) Constant in eqn (7) (Pa sN0BriYA3) Constant in eqn (8) (Pa s”) Flow behaviour index (dimensionless) 269 Journal
of Food
Engineering
0260-8774/87/$03.50
Publishers Ltd, England, 1987. Printed in Great Britain
- 0
Elsevier
Applied
Science
270
A. Iban, J. Pugh
Gas constant (kcal g-malli K-r) Temperature (“C or K) Shear rate (s-l) Coefficient of viscosity (Pa s) Apparent coefficient of viscosity (Pa s) Shear stress (Pa)
1 INTRODUCTION The raspberry (Rubus idzeus) is a bush fruit of the rosaceous family (strawberry, bilberry, etc.), a native of Europe, whose economic importance is increasing not least because of the use of raspberry products in the food industry. The most important raspberry products are juices, flavours, colours, anthocyanins for therapeutic purposes, jams and other preserves. As raspberry juices can be marketed at different concentrations, their physical and chemical properties at different concentrations and temperatures are of primary importance. Clear juices, free from pectin and pulp in suspension, are Newtonian for which: z=)7j
(1)
where t is the shear stress, f the shear rate and q the coefficient of viscosity. However undepectinized juices are pseudo-plastic (Saravacos, 1970; Holdsworth, 1971; Vitali et al., 1974; Rao, 1977; Rao et al., 1984) and their rheological behaviour can be described by the power law t= zq+
(2)
where K is the consistency coefficient and y1is the flow behaviour index. The apparent coefficient of viscosity is given by the expression:
It is to be noted that the value of the apparent coefficient of viscosity depends on the shear rate, so there is not one single characteristic coefficient of viscosity for this type of fluid, only one referred to a particular shear rate.
Rheology of raspbeny juices
271
2 EXPERIMENTAL 2.1 Preparation of the samples The juices were obtained in the laboratory from fruit of the Zeva 1 variety. The fruit was crushed and a pulp obtained which was then filtered on standard paper. The resulting juice was 11”Brix and from this, juice of 41”Brix was obtained by concentration in an evaporator. In this juice the pectin content, as galacturonic acid, was 0.500 g kg- l juice. From this concentrated juice, juices of 15, 20, 25, 30 and 35‘Brix were obtained by diluting with distilled water. The juices were not depectinized as pectin present would be expected to affect the rheological behaviour. 2.2 Rheological measurements The rheological measurements were carried out on a Rotovisco RV 12 (Haake) viscometer, equipped with a M 500~type measurement attachment which can transmit a maximum torque of 4.90 N-cm, an NV-type pair of coaxial cylinders and a thermostatic bath to control the working temperature within the range 5-60°C (see Ibarz et aE.,Fig. 1, this issue). Rotor speeds were variable in the range l-5 12 rpm which enabled rheograms (shear stress r against shear rate p) to be constructed. Readings were taken at increasing rotor speeds until maximum speed was reached, after which it was gradually reduced. With Newtonian and pseudo-plastic liquids, the curves obtained at increasing and decreasing speeds coincided, whereas in thixotropic liquids, the descending curve was below the ascending one. In some cases, it was not possible to evaluate the shear stress at low rotational speeds, whereas in others difficulty occurred at high speeds in that the readings were off the scale of the instrument. Values for K and II were obtained from the experimental values for the corresponding shear stress and shear rate according to eqn (2).
3
RESULTS
AND DISCUSSION
The experimental results of shear stress r against shear rate f are displayed on log-log scales for the different concentrations and temperatures (Figs l-10).
272
A. Iban, J. Pagdn
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Rheology of raspberryjuices
273
(Pa 1
2
l_
lo_
lOO_
Fig. 3.
Flow curves for raspberry juice of different soluble solids contents at 15°C.
Rheology of raspberryjuices
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Rheology of raspberryjuices
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-5 VI
‘0
8
-8
-0
”
Fig. 7.
Flow curves for raspberry juice of different soluble solids contents at 35°C.
., 9. fl (7 1,
35 “c
-x.25 A 30 v 35 0 41
'Brtx
15
n 20
.
(Pa 1
2
l_
lo_
lOO_
Fig. 8.
0 $1 fl 1' (1
Flow curves for raspberry juice of different soluble solids contents at 45°C.
45 “c
0 41
a 25 A 30 v35
'Brix
15
n 20
.
280
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Rheology ofraspberryjuices
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These experimental results were fitted by the least-squares method to the linearized form of eqn (2) (taken in logarithmic form) which enabled values for K and n for the different samples to be obtained. Tables l-6 give the results of these: both the fittings and the estimates of the curve and origin were significant at the 95% level. It is observed from these results that, for juice of a particular concentration, K and y1decreased as the temperature rose. At a given temperature, K increased with increase in soluble solids content, whereas n tended to decrease. In general the lower the concentration and the higher the temperature, the more Newtonian the behaviour of the juice.
TABLE 1
Flow Behaviour Constants at Different Temperatures T (“c:) 5 10
15 20 25 30 35 45 55 60
for 1YBrix Raspberry Juice
n
K (Pa s”)
r
0.90 + 0.04 0.92 + 0.03 0.93 * 0.03 0.94 zk0.03 O-96 IL0.03 0.96 + 0.03 0,99 f 0.02 1.01 f 0.04 1.00 Ik 0.07 1.02 AZ0.08
0.029 k 0.006 0.022 f 0.005 0.017 f 0.002 0.014 f 0.002 O*OlOk 0.002 0.009 + 0.002 0.006 f 0.003 0.004 Ik 0.00 1 0.003 f 0.002 0.002 + 0.00 1
0.997 0.999 0.999 0.999 0.999 0.999 0.998 0.999 0.998 0.999
TABLE 2
Flow Behaviour Constants at Different Temperatures T CV 5 10 15 20 25 30 35 45 55 60
for 2O”Brix Raspberry Juice
n
K (Pa s”)
r
0.90 III0.04 0.92 + 0.04 0.94 f 0.03 0.94 + 0.04 O-96 f 0.04 0.96 f 0.03 0.99 f 0.05 0.99 Ik 0.03 1.01 f 0.04 1.00 f 0.04
0.058 f 0.011 0.045 + 0.009 0.032 I!Z0.008 0.030 f 0.007 O-023 i O-004 0.019 f 0.003 0.014 a 0.007 0.0 11 * 0.003 0.0 10 f 0.004 0.008 * 0.002
0.997 0.998 0997 0.998 O-998 0.999 0.995 0.999 0.996 0.998
Rheology of raspberryjuices
283
TABLE 3 Flow Behaviour Constants at Different Temperatures for 25”Brix Raspberry Juice
5 10 15 20 25 30 35 45 55 60
n
K (Pa s”)
r
0.76 ?I O-03 086 I!I0.05 0.9 1 zk0.06 O-94 zk0.04 0.94 + 0.06 O-95 f o-04 1.00 f 0.06 1.00 k O-06 1.00 f o-04 l-01 + 0.04
0.344 Lko-040 0.169 zk0.040 0.111 f 0.036 0.072 k O-024 0.064 f O-021 o-050 f o-01 1 0.033 f o-012 0.024 f 0.008 0.02 1 + O-006 0019 *o-o07
0.999 0.995 O-996 0.998 O-994 O-998 o-995 0.997 0.997 0997
TABLE 4 Flow Behaviour Constants at Different Temperatures for 30”Brix Raspberry Juice
T0 5 10 15 20 25 30 35 45 55 60
3.1
n
K (Pa s”)
r
0.74 + 0.04 O-82 IL0.05 081 + 0.03 0.90 * 0.05 O-91 + 0.06 0.9 1 SfI0.05 O-92 + O-07 0.95 k 0.07 0.95 f 0.06 0.96 IL0.04
0.739 + 0.153 0.437 f 0.090 0.365 zk0.059 0.202 k O-052 0.142 If:O-047 0.124-10-038 0.101 fO-045 0.067 f 0.030 0.049 + 0.0 19 0.040 zk0.007
0.995 O-996 0.998 0.995 0.990 0.995 0.990 0993 0995 0.998
The effect of temperature
The viscosity of liquids usually decreases with increase in temperature. In the case of Newtonian fluids, an Arrhenius-type equation is generally used to show the influence of temperature on viscosity. In the case of non-Newtonian fluids, the apparent coefficient of viscosity at a fixed shear rate is used instead of the coefficient of viscosity; for power law fluids, the consistency coefficient is normally used (Rao ez al., 1984), such that: K= K, exp(E,/RT)
(4)
284
A. Zban, J. Pugh TABLE 5 Flow Behaviour Constants at Different Temperatures for 35”Brix Raspberry Juice II 0.69 + 0.03 O-72 k 0.04 0.80 + 0.04 0.79 + 0.04 0.79 + 0.04 086 + o-05 0.87 k 0.03 0.91 f o-05 0.92 f 0.05 0.95 Y!I0.04
5 10 15 20 25 30 35 45 55 60
K (Pa 9’)
r
1.858 k 0.263 1.299 k 0.233 0.805 -t 0.142 0.673 k 0.131 0.561_+ O-125 0.344 zk0072 0.283 zk0.043 0.167 IIZ0036 0.116 f 0027 0.084 f 0.025
o-997 0.996 0.996 0.996 0.994 0.996 0.999 0.997 0.997 0.995
TABLE 6 Flow Behaviour Constants at Different Temperatures for 41”Brix Raspberry Juice n
T CC) 5 10 15 20 25 30 35 45 55 60
0.59 0.64 0.66 0.68 0.73 0.75 0.79 0.88 0.87 0.88
* 0.03 zk0.04 k 0.03 f 0.03 k 0.04 + 0.03 Ik0.03 k 0.05 f 0.04 f. 0.05
K (Pa s”)
r
6.248 f 0.742 4.295 k 0.569 3.361 k 0.457 2.569 k 0,377 1.614f0.268 1.340 f 0.195 0.952 + O-134 0.457 zko-094 0.347 k 0.070 0.302 k 0.060
0.997 0,997 0.997 o-997 0.995 0.997 0.997 0.996 0.997 0.997
in which K, is a constant, E, is the activation energy of flow in kcal g-mol- t; R is the gas constant and Tis the temperature in Kelvin. When In K is plotted against l/Ta straight line is obtained. Figure 11 shows such straight lines for the juices of different concentrations. From the slopes of these straight lines, it is possible to obtain the values for the activation energies in each case. The general tendency is for the activation energy to increase as the soluble solids content increases.
Rheology of raspberryjuices
285
286
A. Ibatz, J. Pagh
I ,
0.001
Fig. 13.
10
Effect of concentration
I
20
on the consistency coefficient. Exponential
I
30
10
model.
;krix)
i
IS A 20 v 25 n 30 c35 *45 v 55 + 60
0 0
* )’ 1’ 1’ r> * Y +
)’
A. Ibarz, J. Pa&in
288
3.2
The effect of concentration
In order to relate soluble solids concentration to viscosity at a given temperature, different types of equation were tested. One of these was of power form (Harper and El-Sahrigi, 1965; Rao et al., 1984). K= K, CA’
(5)
However, Rao et al. (1984) found an exponential-type relationship between concentration and the viscosity of concentrated apple juice: K= K2 exp(A,C)
(6)
Cis the concentration and K,, K2, A, and A, are constants. Figure 12 shows the change with concentration according to the power model, and Fig. 13 that according to the exponential model. The latter gives the better fit.
TABLE
7
Combined Effect of Temperature and Concentration on the Consistency Coefficient of Raspberry Juices”
Power model: K = K, C”’ exp K,=2.076~
10-15Pas”“Brix~“’
A 3 = 5.0 18 dimensionless E, = 9.06 kcal g-mol- ’
r2 = 0.97 1
K,=1.198~
lo-“‘Pas”
A,=O-196”Brix-’ L, = 9.06 kcal g-mol r’ =
’
0.90 1
“Units: Consistency coefficient in Pas”; Cin “Brix; temperature in degrees Kelvin.
Rheology of raspberryjuices
3.3
289
The combined effect of temperature and concentration
A single equation combining the effects of temperature and concentration on the coefficient would be useful. To this end, the different models tested were combined into the following expressions: K = K, CAZexp & i K= K, exp +*+A
(
(7)
i
C i
In order to obtain the values of the different constants in these equations, the linear forms, after taking logarithms, were fitted by linear multiple regression. Table 7 shows these values. It should be emphasized that the constants of eqns (7) and (8) are applicable only to the range of temperatures and concentration studied. The values for the activation energies E, for the combined models are the averages of the values for all the samples studied.
REFERENCES Harper, J. C. and El-Sahrigi, A. F. ( 1965). Viscometric behaviour of tomato concentrates. J. Food&i., 30,470. Holdsworth, S. D. ( 1971). Applicability of rheological models to the interpretation of flow and processing behaviour of fluid food products. J. Texture Studies, 2,393-418. Rao, M. A. (1977). Rheology of liquid foods - A review. J. Texture Studies, 8, 135-68. Rao, M. A., Cooley, M. J. and Vitali, A. A. (1984). Flow properties of concentrated juices at low temperatures. Food Technol., 38 (3), 113-19. Saravacos, G. D. (1970). Effect of temperature on viscosity of fruit juices and purees. J. FoodSci., 35,122-5. Vitali, A. A., Roig, S. M. and Rao, M. A. (1974). Viscosity behaviour of concentrated passion fruit juice. Confructu, 19 (5), 20 1.
Rheology of Raspberry Juices A. Ibarz and J. Pagan Departament de Qutica i Indlistries AgroaIimentaries, Escola Tknica Superior d’Enginyers Agrbnoms de Lleida, Universitat PoIitknica de Catalunya, Avinguda Alcalde Rovira Roure, 177,25006-Lleida, Spain (Received 29 April 1986; revised version received 10 July 1986; accepted 22 October 1986)
ABSTRACT This paper reports a study of the rheological behaviour of different concentrations of raspberry juice at different temperatures. The behaviour is pseudoplastic at higher concentrations and lower temperatures, although at low concentrations and in some cases at high temperatures the behaviour is Newtonian. The effect of temperature and soluble solids content on the consistency coefficient was also studied: an equation was derived which describes the combined effect of these two variablesfor two different models and over the range of temperatures and concentrations studied.
NOMENCLATURE Constant in eqn (5) (dimensionless) Constant in eqn (6) (“Brix-‘) Constant in eqn (7) (dimensionless) Constant in eqn (8) (“Brix- 1) Concentration in soluble solids (“Brix) Activation energy of the flux (kcal g-mall I Consistency coefficient (Pa s “) Constant in eqn (4) (Pa s”) Constant in eqn (5) (Pa s” “BrixA1) Constant in eqn (6) (Pa sfl) Constant in eqn (7) (Pa sN0BriYA3) Constant in eqn (8) (Pa s”) Flow behaviour index (dimensionless) 269 Journal
of Food
Engineering
0260-8774/87/$03.50
Publishers Ltd, England, 1987. Printed in Great Britain
- 0
Elsevier
Applied
Science
270
A. Iban, J. Pugh
Gas constant (kcal g-malli K-r) Temperature (“C or K) Shear rate (s-l) Coefficient of viscosity (Pa s) Apparent coefficient of viscosity (Pa s) Shear stress (Pa)
1 INTRODUCTION The raspberry (Rubus idzeus) is a bush fruit of the rosaceous family (strawberry, bilberry, etc.), a native of Europe, whose economic importance is increasing not least because of the use of raspberry products in the food industry. The most important raspberry products are juices, flavours, colours, anthocyanins for therapeutic purposes, jams and other preserves. As raspberry juices can be marketed at different concentrations, their physical and chemical properties at different concentrations and temperatures are of primary importance. Clear juices, free from pectin and pulp in suspension, are Newtonian for which: z=)7j
(1)
where t is the shear stress, f the shear rate and q the coefficient of viscosity. However undepectinized juices are pseudo-plastic (Saravacos, 1970; Holdsworth, 1971; Vitali et al., 1974; Rao, 1977; Rao et al., 1984) and their rheological behaviour can be described by the power law t= zq+
(2)
where K is the consistency coefficient and y1is the flow behaviour index. The apparent coefficient of viscosity is given by the expression:
It is to be noted that the value of the apparent coefficient of viscosity depends on the shear rate, so there is not one single characteristic coefficient of viscosity for this type of fluid, only one referred to a particular shear rate.
Rheology of raspbeny juices
271
2 EXPERIMENTAL 2.1 Preparation of the samples The juices were obtained in the laboratory from fruit of the Zeva 1 variety. The fruit was crushed and a pulp obtained which was then filtered on standard paper. The resulting juice was 11”Brix and from this, juice of 41”Brix was obtained by concentration in an evaporator. In this juice the pectin content, as galacturonic acid, was 0.500 g kg- l juice. From this concentrated juice, juices of 15, 20, 25, 30 and 35‘Brix were obtained by diluting with distilled water. The juices were not depectinized as pectin present would be expected to affect the rheological behaviour. 2.2 Rheological measurements The rheological measurements were carried out on a Rotovisco RV 12 (Haake) viscometer, equipped with a M 500~type measurement attachment which can transmit a maximum torque of 4.90 N-cm, an NV-type pair of coaxial cylinders and a thermostatic bath to control the working temperature within the range 5-60°C (see Ibarz et aE.,Fig. 1, this issue). Rotor speeds were variable in the range l-5 12 rpm which enabled rheograms (shear stress r against shear rate p) to be constructed. Readings were taken at increasing rotor speeds until maximum speed was reached, after which it was gradually reduced. With Newtonian and pseudo-plastic liquids, the curves obtained at increasing and decreasing speeds coincided, whereas in thixotropic liquids, the descending curve was below the ascending one. In some cases, it was not possible to evaluate the shear stress at low rotational speeds, whereas in others difficulty occurred at high speeds in that the readings were off the scale of the instrument. Values for K and II were obtained from the experimental values for the corresponding shear stress and shear rate according to eqn (2).
3
RESULTS
AND DISCUSSION
The experimental results of shear stress r against shear rate f are displayed on log-log scales for the different concentrations and temperatures (Figs l-10).
272
A. Iban, J. Pagdn
-0
1
/““I 8
’
’
1 0
I”“I’
’
’
l”“I’
’
’
I
2
0
Rheology of raspberryjuices
273
(Pa 1
2
l_
lo_
lOO_
Fig. 3.
Flow curves for raspberry juice of different soluble solids contents at 15°C.
Rheology of raspberryjuices
I
I”“1 8
’
’
’
0
I”“[’
’
’
I”“”
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’
, m 7
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276
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’
’
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’
’
-.
0
Rheology of raspberryjuices
277
-5 VI
‘0
8
-8
-0
”
Fig. 7.
Flow curves for raspberry juice of different soluble solids contents at 35°C.
., 9. fl (7 1,
35 “c
-x.25 A 30 v 35 0 41
'Brtx
15
n 20
.
(Pa 1
2
l_
lo_
lOO_
Fig. 8.
0 $1 fl 1' (1
Flow curves for raspberry juice of different soluble solids contents at 45°C.
45 “c
0 41
a 25 A 30 v35
'Brix
15
n 20
.
280
A. Ibarz, J. Pagh
-0
8
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-0
Rheology ofraspberryjuices
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’
I
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l”“I’
’
’
l”“1”
281
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-.
0
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A. Ibarz, J. Pagh
282
These experimental results were fitted by the least-squares method to the linearized form of eqn (2) (taken in logarithmic form) which enabled values for K and n for the different samples to be obtained. Tables l-6 give the results of these: both the fittings and the estimates of the curve and origin were significant at the 95% level. It is observed from these results that, for juice of a particular concentration, K and y1decreased as the temperature rose. At a given temperature, K increased with increase in soluble solids content, whereas n tended to decrease. In general the lower the concentration and the higher the temperature, the more Newtonian the behaviour of the juice.
TABLE 1
Flow Behaviour Constants at Different Temperatures T (“c:) 5 10
15 20 25 30 35 45 55 60
for 1YBrix Raspberry Juice
n
K (Pa s”)
r
0.90 + 0.04 0.92 + 0.03 0.93 * 0.03 0.94 zk0.03 O-96 IL0.03 0.96 + 0.03 0,99 f 0.02 1.01 f 0.04 1.00 Ik 0.07 1.02 AZ0.08
0.029 k 0.006 0.022 f 0.005 0.017 f 0.002 0.014 f 0.002 O*OlOk 0.002 0.009 + 0.002 0.006 f 0.003 0.004 Ik 0.00 1 0.003 f 0.002 0.002 + 0.00 1
0.997 0.999 0.999 0.999 0.999 0.999 0.998 0.999 0.998 0.999
TABLE 2
Flow Behaviour Constants at Different Temperatures T CV 5 10 15 20 25 30 35 45 55 60
for 2O”Brix Raspberry Juice
n
K (Pa s”)
r
0.90 III0.04 0.92 + 0.04 0.94 f 0.03 0.94 + 0.04 O-96 f 0.04 0.96 f 0.03 0.99 f 0.05 0.99 Ik 0.03 1.01 f 0.04 1.00 f 0.04
0.058 f 0.011 0.045 + 0.009 0.032 I!Z0.008 0.030 f 0.007 O-023 i O-004 0.019 f 0.003 0.014 a 0.007 0.0 11 * 0.003 0.0 10 f 0.004 0.008 * 0.002
0.997 0.998 0997 0.998 O-998 0.999 0.995 0.999 0.996 0.998
Rheology of raspberryjuices
283
TABLE 3 Flow Behaviour Constants at Different Temperatures for 25”Brix Raspberry Juice
5 10 15 20 25 30 35 45 55 60
n
K (Pa s”)
r
0.76 ?I O-03 086 I!I0.05 0.9 1 zk0.06 O-94 zk0.04 0.94 + 0.06 O-95 f o-04 1.00 f 0.06 1.00 k O-06 1.00 f o-04 l-01 + 0.04
0.344 Lko-040 0.169 zk0.040 0.111 f 0.036 0.072 k O-024 0.064 f O-021 o-050 f o-01 1 0.033 f o-012 0.024 f 0.008 0.02 1 + O-006 0019 *o-o07
0.999 0.995 O-996 0.998 O-994 O-998 o-995 0.997 0.997 0997
TABLE 4 Flow Behaviour Constants at Different Temperatures for 30”Brix Raspberry Juice
T0 5 10 15 20 25 30 35 45 55 60
3.1
n
K (Pa s”)
r
0.74 + 0.04 O-82 IL0.05 081 + 0.03 0.90 * 0.05 O-91 + 0.06 0.9 1 SfI0.05 O-92 + O-07 0.95 k 0.07 0.95 f 0.06 0.96 IL0.04
0.739 + 0.153 0.437 f 0.090 0.365 zk0.059 0.202 k O-052 0.142 If:O-047 0.124-10-038 0.101 fO-045 0.067 f 0.030 0.049 + 0.0 19 0.040 zk0.007
0.995 O-996 0.998 0.995 0.990 0.995 0.990 0993 0995 0.998
The effect of temperature
The viscosity of liquids usually decreases with increase in temperature. In the case of Newtonian fluids, an Arrhenius-type equation is generally used to show the influence of temperature on viscosity. In the case of non-Newtonian fluids, the apparent coefficient of viscosity at a fixed shear rate is used instead of the coefficient of viscosity; for power law fluids, the consistency coefficient is normally used (Rao ez al., 1984), such that: K= K, exp(E,/RT)
(4)
284
A. Zban, J. Pugh TABLE 5 Flow Behaviour Constants at Different Temperatures for 35”Brix Raspberry Juice II 0.69 + 0.03 O-72 k 0.04 0.80 + 0.04 0.79 + 0.04 0.79 + 0.04 086 + o-05 0.87 k 0.03 0.91 f o-05 0.92 f 0.05 0.95 Y!I0.04
5 10 15 20 25 30 35 45 55 60
K (Pa 9’)
r
1.858 k 0.263 1.299 k 0.233 0.805 -t 0.142 0.673 k 0.131 0.561_+ O-125 0.344 zk0072 0.283 zk0.043 0.167 IIZ0036 0.116 f 0027 0.084 f 0.025
o-997 0.996 0.996 0.996 0.994 0.996 0.999 0.997 0.997 0.995
TABLE 6 Flow Behaviour Constants at Different Temperatures for 41”Brix Raspberry Juice n
T CC) 5 10 15 20 25 30 35 45 55 60
0.59 0.64 0.66 0.68 0.73 0.75 0.79 0.88 0.87 0.88
* 0.03 zk0.04 k 0.03 f 0.03 k 0.04 + 0.03 Ik0.03 k 0.05 f 0.04 f. 0.05
K (Pa s”)
r
6.248 f 0.742 4.295 k 0.569 3.361 k 0.457 2.569 k 0,377 1.614f0.268 1.340 f 0.195 0.952 + O-134 0.457 zko-094 0.347 k 0.070 0.302 k 0.060
0.997 0,997 0.997 o-997 0.995 0.997 0.997 0.996 0.997 0.997
in which K, is a constant, E, is the activation energy of flow in kcal g-mol- t; R is the gas constant and Tis the temperature in Kelvin. When In K is plotted against l/Ta straight line is obtained. Figure 11 shows such straight lines for the juices of different concentrations. From the slopes of these straight lines, it is possible to obtain the values for the activation energies in each case. The general tendency is for the activation energy to increase as the soluble solids content increases.
Rheology of raspberryjuices
285
286
A. Ibatz, J. Pagh
I ,
0.001
Fig. 13.
10
Effect of concentration
I
20
on the consistency coefficient. Exponential
I
30
10
model.
;krix)
i
IS A 20 v 25 n 30 c35 *45 v 55 + 60
0 0
* )’ 1’ 1’ r> * Y +
)’
A. Ibarz, J. Pa&in
288
3.2
The effect of concentration
In order to relate soluble solids concentration to viscosity at a given temperature, different types of equation were tested. One of these was of power form (Harper and El-Sahrigi, 1965; Rao et al., 1984). K= K, CA’
(5)
However, Rao et al. (1984) found an exponential-type relationship between concentration and the viscosity of concentrated apple juice: K= K2 exp(A,C)
(6)
Cis the concentration and K,, K2, A, and A, are constants. Figure 12 shows the change with concentration according to the power model, and Fig. 13 that according to the exponential model. The latter gives the better fit.
TABLE
7
Combined Effect of Temperature and Concentration on the Consistency Coefficient of Raspberry Juices”
Power model: K = K, C”’ exp K,=2.076~
10-15Pas”“Brix~“’
A 3 = 5.0 18 dimensionless E, = 9.06 kcal g-mol- ’
r2 = 0.97 1
K,=1.198~
lo-“‘Pas”
A,=O-196”Brix-’ L, = 9.06 kcal g-mol r’ =
’
0.90 1
“Units: Consistency coefficient in Pas”; Cin “Brix; temperature in degrees Kelvin.
Rheology of raspberryjuices
3.3
289
The combined effect of temperature and concentration
A single equation combining the effects of temperature and concentration on the coefficient would be useful. To this end, the different models tested were combined into the following expressions: K = K, CAZexp & i K= K, exp +*+A
(
(7)
i
C i
In order to obtain the values of the different constants in these equations, the linear forms, after taking logarithms, were fitted by linear multiple regression. Table 7 shows these values. It should be emphasized that the constants of eqns (7) and (8) are applicable only to the range of temperatures and concentration studied. The values for the activation energies E, for the combined models are the averages of the values for all the samples studied.
REFERENCES Harper, J. C. and El-Sahrigi, A. F. ( 1965). Viscometric behaviour of tomato concentrates. J. Food&i., 30,470. Holdsworth, S. D. ( 1971). Applicability of rheological models to the interpretation of flow and processing behaviour of fluid food products. J. Texture Studies, 2,393-418. Rao, M. A. (1977). Rheology of liquid foods - A review. J. Texture Studies, 8, 135-68. Rao, M. A., Cooley, M. J. and Vitali, A. A. (1984). Flow properties of concentrated juices at low temperatures. Food Technol., 38 (3), 113-19. Saravacos, G. D. (1970). Effect of temperature on viscosity of fruit juices and purees. J. FoodSci., 35,122-5. Vitali, A. A., Roig, S. M. and Rao, M. A. (1974). Viscosity behaviour of concentrated passion fruit juice. Confructu, 19 (5), 20 1.