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Flow behaviour of soy protein isolate melt with low and intermediate moisture levels at an elevated temperature
Journal of Food Engineering18 ( 1993) 1- 11
Flow Behaviour of Soy Protein Isolate Melt with Low and Intermediate Moisture Levels at an Elevated Temperature Nobuyuki Hayashi, Isao Hayakawa & Yusaku Fujio* Department of Food Science and Technology, Faculty of Agriculture, Kyushu University, 6- lo- 1, Hakozaki, Higashi-ku, Fukuoka 8 12, Japan (Received 25 October 199 1; accepted 19 December
199 1)
ABSTRACT The flow behaviour of moisturized (20-70% d. b.) soy protein isolate@PI) melt at 140°C was markedly dependent on its moisture content. By regression analysis,the Herschel-Bulkley power-law model was successfully fitted to the measured data over the range 3 = lo3 to 5 x IO4s-l. The discontinuity of the regression coecients observed at 41-54% d.b. moisture range suggested a difference in melt flow mechanism at the opposite sides of this moisture range. At the lower moisture content (20-41% d.b.), SPI melt could flow unisotropically,but at higher moisture content (54-70% d.b.), the free watercould act as a lubricant.
INTRODUCTION In extrusion cooking, protein molecules change to a molten state and behave as a fluid, like synthetic polymers, at an elevated temperature which is generally far higher than the protein denaturation temperature. At this time, irreversible and complex changes such as unfolding and disulphide-disulphide interactions take place in the protein molecules. These physicochemical interactions make it difficult to analyse the melt rheology of bio-polymers. However, much research has been carried out to evaluate the flow properties of food materials at elevated temperatures using extruders (Chen et al., 1978; Jao et al., 1978; Bhattacharya & Hanna, 1986). Although these investigations provided important infor*To whom correspondence
should be addressed. 1 Joumal of Food Engineering 0260-8774/92/$05.00 Publishers Ltd, England. Printed in Great Britain
- Q 1992
Elsevier
Science
N. Hayashi, I. Hayakawa, Y. Fuji0
2
mation about extrusion cooking, further fundamental studies on the flow properties of bio-polymer melt, especially protein melt, were considered necessary in order to obtain basic information about the thermomechanical properties. Therefore the flow properties of soy protein isolate (SPI) melt at an elevated temperature ( 14OaC) have been studied using a capillary tube viscometer. As a result, the large dependency of the flow properties of SPI melt on its moisture content has been determined as, at higher moisture contents (70% d.b.), SPI melt possesses flow properties that can be defined by the power-law model (Hayashi et al., 1991), but at lower than 40% d.b. moisture it changes to an unknown type of plastic fluid (Fuji0 et al., 1991). In the present paper, the flow properties of various moisture level SPI melts (20-70% water, dry basis) at an elevated temperature (140°C) have been studied and the flow properties fitted to the Herschel-Bulkley power-law model by regression analysis.
MATERIALS
AND METHODS
Soy protein isolate Soy protein isolate (SPI) powder containing 87.7% d.b. protein (Kjeldahl nitrogen x 5.71) and 57% moisture was obtained from Ajinomoto Co. Ltd. (Tokyo, Japan). The moisture content of the SPI was adjusted to 20, 30, 41, 54 and 70% d.b. according to the procedure described previously (Hayashi et al., 1990a; Fuji0 et al., 1991). Extrusion viscometry Extrusion viscometq was performed at 140°C which is higher than the flow starting temperature of the lowest moisturized SPI sample (20% d.b.) (Fuji0 et al., 1991). The capillary tube viscometer used, which was designed in the authors’ laboratory and assembled by Shinmeiwa Co. Ltd. (Tokyo, Japan), were as detailed in previous papers (Hayashi et al., 1990b; Fuji0 et al., 1991). The moisturized SPI powder (4-O g) was moulded into a cylindrical shape (l-08 cm in diameter and about 3 cm in length) using a hand press and inserted into the sample reservoir. After pre-heating for 20 min, the sample was extruded through a capillary tube or an orifice die at a selected constant plunger travelling speed (Fig. 1). The capillary tube used was O-75 mm in radius (R) and 20 mm in length (15 ); thus the corresponding L/R ratio was 26.7. Plunger travelling speed and the resultant pressure drop were measured for a given capillary tube
Flow properties of moisturized SPI melt
kW4 (b)
(4 Fig. 1.
Design of experimental dies: (a) capillary tube die; (b) orifice die. Arrow indicates flow direction. x9 = 1.5 mm.
(APc, MPa) or an orifice die (A&
MPa). APc and APO were measured over as broad a range as possible by applying various plunger speeds, i.e. various volume flow rate, Q (m3 s-l). End effect correction was done by subtracting APO from APc at the same value of Q. This gives APd ( = APc - APO) which indicates the pressure drop at the capillary tube wall. The validity of this correction method for SPI melt, particularly on 70% d.b. moisture, was already investigated and a satisfactory result was obtained (Hayashi et al., 1991). The volumetric flow rate, Q, and APd were converted into apparent shear rates (pa,, s-l) by using the equation: (3, = 4Q/3rR3), and th e s h ear stress at the capillary tube wall (t,, MPa) according to the equation; r, = A Pd X R/2 L . Regression analysis The Herschel-Bulkley power-law model (Skelland, 1967) was applied to measured data in order to characterize the flow properties of SPI melt, described by the following equation: tw=
q)+(q’x &)”
where to (MPa) is the yield stress, i.e. the minimum shear stress required for flow; n (dimensionless) is the flow behaviour index which is a measure of the departure from Newtonian flow; 7’ (MPa”” s) is the consistency index, but only when n = 1, and has the dimensions of viscosity. If the fluid is a Bingham fluid then r, # 0 (Holdsworth, 1971). Barnes and Walters (1985) recently questioned the concept of a yield stress. It is true that, from a purely theoretical point of view, most
4
N. Hayashi, I. Hayakawa, Y. Fuji0
materials will not exhibit a yield stress when they are given a sufficiently long time for flow starting. However, Ofoli et al. (1987) mentioned that the yield stress concept is useful in process modelling because of the dependence of all food processes on strict time limitations. In the present study the experimental time range was significantly shorter than that required to support the theoretical view point of Barnes and Walters. Therefore, a yield stress parameter has been included in the present model. Since the model equation is intrinsically non-linear, the ordinary regression method for linear equations is not applicable. Therefore, the successive approximative calculation was performed iteratively at each moisture content using a computer (PC-98OlVX, Nippon Electric Co. Ltd., Tokyo, Japan) to find the regression coefficients that minimize the residual sum of squares (Williams, 1959; Draper & Smith, 1966; Snedecor & Cochran, 1989).
RESULTS Measured data Figure 2 shows the observed volumetric flow rates, Q (m3 s-r), and resultant APc or APO (MPa) on a log-log scale. The volumetric flow rate of the SPI melt varied between 6 x 10s6 to 2 x 10-s m3 s-l depending on the plunger speed. The pressure drop at the capillary tube wall, APd, was calculated from these results and is shown in Fig. 3. As seen in Fig. 3, a change in moisture content drastically affected the relationship between Q and APd, i.e. the pressure drop required to achieve the same flow rate was remarkably decreased by a small increase in moisture content. Flow curves for moisturized SPI melt Apparent shear rate, y,, and shear stress at the capillary tube wall, tw, were calculated from Q and APd, respectively. The flow curves, p, versus z,, for SPI melt with various moisture contents are shown on logarithmic scales in Fig. 4 and on ordinary scales in Fig. 5. The good linearity on logarithmic scales was observed at 70 and 54% d.b. moisturized SPI melts over the full experimental range and also in 20, 30 and 41% d.b. samples at shear rates higher than 3 X 10 s-i. This linearity observed on logarithmic scales means that these fluids could be the power-law fluids. On the other hand, as seen in Fig. 5, the non-linearity
t
102
2
E,
-
10' =
: 9
100
lo-’
=
.L
10-e
lo-'
10*
lO4
Cl Cm3esec-11
(4
m 8
2 9
10’
I
100
lo-' lo-'
I
I
1
I
, I I,,
,
,
,
,
, ,
10-r
,(,
104
(
,
(
,
,
,a
10"
Cl CmGec-‘I
(b)
Fig. 2. Relationship between Q and measured pressure drop for SPI melt with various moisture contents at 140°C: (a) capillary tube (A&); (b) orifice die (APO). Moisture content (% d.b.): 0,20; l, 30; A, 41; A, 54; q,70.
N. Hayashi, I. Hayakawa, Y. Fuji0
10’
10-l 10-a
I
10-
Q [ma-set-’
Fig. 3.
1111~
lo-’
1
Relationship between Q and APd for SPI melt with various moisture contents at 140°C. Moisture content (% d.b.): 0,20; l,30; A, 41; A, 54; 0,70.
observed on linear scales means that they could be non-Bingham plastics within the shear rate range of the present experiment. Additionally, some yield stress was observed as the intercept on the ordinate. These results supported the fitting of the data to the Herschel-Bulkley power-law model. Regression curves Calculated regression coefficients, r,, 7’ and n obtained by the successive approximate regression are shown in Table 1. A close agreement between regression curves and measured data was obtained as can be seen in Fig. 4. The values of the residual sum of squares, the degree of freedom and the sufficiently small mean square residual are also shown in Table 1. By using the obtained flow behaviour index (n), the Rabinowitsch correction (Harper & Sahrigi, 1965; Skelland, 1967; Clark, 1978; Padmanabhan & Bhattacharya, 1989) was performed in order to determine the real shear rate at the capillary tube wall, p,, using the following equation:
The calculated flow curves, pWversus rWare shown in Fig. 6.
Flow properties of moisturized SPI melt
-100
-
IO
P
r’
10-l
7
Fig. 4. Flow curves for SPI melt with various moisture contents at 140°C on double logarithmic scales. Symbols indicate measured values and the solid line the regression curve. Moisture content (% d.b.): 0,20; l,30; A, 41; A, 54; q,70.
0.8
0.6
0.4
0.2
0 0
10000
)‘el Fig. 5.
20000 [set-‘1
Flow curves for SPI melt with various moisture contents at 140°C on ordinary scales. Moisture content (% d.b.): 0,20; l,30; A, 41; A, 54; q,70.
N, Hayashi, I. Hayakawa, Y. Fuji0
8
The relationship between regression coefficients and moisture content As shown in Table 1, regression coefficients, r,, q’ and n, showed discontinuous relationships with the moisture content. The yield stress, r,, decreased linearly as the moisture content increased and became negligibly small at 54 and 71% d.b. moisture content. The value of q’ decreased with moisture content and a rapid decrease was observed between 41 and 54% d.b. of moisture content. The rheology index, n, was almost constant for the low moisture samples, however it decreased rapidly at higher than 41% d.b. of moisture content. These results indicated not only the large dependency of flow properties of SPI melt
TABLE 1 Regression Coefficients and Regression Errors for the Equation Moisture content %d. b.
20 30 41 54 70
Yield stress, %” (MPa)
623 x 3.73 x 2.37~ 1.96 x 4.90x
lo-? lo-’ lo-’ 1O-3 10-j
Consktency coeficient ?+ (MPa’l” s)
3.99 2.00 1.11 1.02 1.79
x x x x x
Flow behaviour index, n
10m5 lo-? 10ms lo-” 10-7
0.670 0.680 0.675 0.430 0.360
Sum of squares of the residuals
1-27x 9.77 x 3.03 x 1.70 x 1,26x
lo-? 10-j 10-j 10-j lo-”
rW= r0 + (7’ x p,)” Degrees of freedom
21 21 21 21 21
Mean square residual
5-99 4.65 1.44 8.07 5.99
x x x x x
10-j 10-j 10-j 1O-6 10-h
“Minimum shear stress required for flow.
Fig. 6. Rabinowitsch corrected flow curves for SPI melt with various moisture contents at 140°C on double logarithmic scales. Moisture content (% d.b.): a, 20; b, 30; c, 41; d, 54; e, 70.
Flow properties of moisturized SPI melt
9
on moisture content, but also the discontinuous change of melt flow behaviour of SPI in the moisture content ranging from 41 to 54% d.b.
DISCUSSION The Herschel-Bulkley power-law model successfully expressed the melt flow behaviour of SPI in the range 20 to 70% d.b. moisture at 140°C. A large dependency of equation coefficients, e.g. to, 7’ and n on moisture content and a discontinuous change at moisture contents between 41 to 54% d.b. were observed. These results suggest that the melt flow mechanism of SPI could be different at the opposite ends of the 41-54% d.b. moisture region. This moisture range at which the discontinuity of regression coefficients was observed (41%-54% moisture range) was almost equal to the maximum bound water range of soy protein, reported as 25% to 50% (Muffett & Snyder, 1980; Tanteeratarm et al., 1990). The moisture region was also equal to the moisture content at which the flow line style in the reservoir changed and the secondary circular flow at the capillary entrance region occurred (Hayashi et al., 1990b). These results lead to a hypothesis that the flow properties of SPI melt are largely affected by the water state in the melt. The free water that was observed in samples with a moisture higher than 41% d.b. may act as a lubricant among the molten state protein molecules while bound water could not act as a lubricant even at such elevated temperatures as 140°C. Consequently, the flow behaviour of SPI melt could be markedly affected not only by the moisture content but also the water state in the sample. As a result, the discontinuous change of regression coefficients could occur at the transition moisture region at which the water state in the sample changes. Moreover, the change in flow behaviour index, n, with moisture content was contrary to the expectation that a lower moisture sample indicates a lower n value because of its further transformation into a non-Newtonian fluid. However, n showed a constant value at lower moisture contents (20-41% d.b.) and it decreased at higher moisture contents (54-70% d.b.). The unexpected large n value obtained with a less moisturized sample suggested the unexpected pressure drop occurred not only at the capillary tube wall but also somewhere else. For example, there could be considerable friction between molten SPI molecules. Therefore, the low moisturized SPI melt having no free water could flow unisotropically in the capillary tube. On the other hand, the result showing a remarkable decrease in n at the higher moisture range is contrary to the general rule. However, the n value of the SPI melt could
10
N, Hayashi, I. Hayakawa, Y. Fuji0
be expected to increase again at a much higher unknown moisture content. Unfortunately, the pressure drops given by SPI melt with higher than 70% d.b. moisture were too small to be measured accurately using the authors’ extrusion viscometer. Future studies will be focused on improving the viscometer, thus clarifying the flow properties of SPI melt higher than 70% d.b. moisture, and also investigating the water state in molten SPI at an elevated temperature.
REFERENCES Barnes, H. A. & Walters, K. (1985). The yield stress myth? Rheol. Acta, 24,
323-6. Bhattacharya, M. & Hanna, M. A. ( 1986). Viscosity modeling of dough in extrusion. J. Food Technol., 21, 167-74. Chen, A. H., Jao, Y. C., Larkin, J. W. & Goldstein, W. E. ( 1978). Rheological model of soy dough in extrusion. J. Food Process Eng., 2,337-42. Clark, J. P. (1978). Dough rheology in extrusion cooking. Food Technology, 32, 73-6. Draper, N. R. & Smith, H. ( 1966). An introduction to nonlinear estimation. In Applied RegressionAnalysis.John Wiley & Sons, New York, pp. 263-304. Fujio, Y., Hayashi, N. & Hayakawa, I. ( 199 1). Effect of moisture content on flow behaviour of molten soy-protein isolate under an elevated temperature. Znt.J. Food&i. Techno!., 26,45-51. Harper, J. C. & Sahrtgi, A. F. E. (1965). Viscometric behavior of tomato concentrates. J. Food Sci., 30,470-6. Hayashi, N., Hayakawa, I. & Fujio, Y. ( 1990a). Flow patterns in soybean protein isolate melt in the reservoir of an extrusion viscometer. J. Fat. Agr., Kyushu Univ.,35,59-64. Hayashi, N., Hayakawa, I. & Fujio, Y. (1990b). Development and evaluation of an extrusion viscometer for polymer melt. J. Fat. Agr., Kyushu Univ., 35, 73-9. Hayashi, N., Hayakawa, I. & Fujio, Y. ( 1991). Entrance effect correction on the flow of moisturized soy protein isolate melt in an extrusion viscometer. Znf.J. Food Sci. Technol., 26,567-74. Holdsworth, S. D. (1971). Applicability of rheological models to the interpretation of flow and processing behaviour of fluid food products. J. Texture S&dies, 2,393-418. Jao, Y. C., Chen, A. H., Lewandowski, D. & Irwin, W. E. ( 1978). Engineering analysis of soy dough rheolo in extrusion. J. Food Process Eng., 2,97- 112. Muffett, D. J. & Snyder, H. E. ?1980). Measurement of unfrozen and free water in soy proteins by differential scanning calorimetry. Journal of Agricultural Food Chemistry,28,1303-5. Ofoli, R. Y., Morgan, R. G. & Steffe, J. F. (1987). A generalized rheological model for inelastic fluid foods. J. Texture Studies, l&213-30. Padmanabhan, M. & Bhattacharya, M. ( 1989). Analysis of pressure drop in extruder dies. J. Food Sci., 54,709-13.
Flow properties of moisturized SPI melt
11
SkeIland, A. H. P. (1967). Determination of flow properties. In Non-Newtonian Flow and Heat Transfer. John Wiley & Sons, New York, pp. 68-108. Snedecor, G. W. & Cochran, W. G. ( 1989). Nonlinear relations. In Statistical Methods, 8th edn. Iowa State University Press, IA, pp. 398-4 15. Tanteeratarm, K., Wei, L. S., Steinberg, M. P. & Yamashita, N. (1990). Bound water associated with 7s and 11s soy proteins determined by vapor sorption isotherms and pulsed NMR. Journal of Food Science, 55,130-2. Williams, E. J. ( 1959). Regression equations requiring iterative calculation. In Regression Analysis, John Wiley & Sons, New York, pp. 59-7 1.
Flow Behaviour of Soy Protein Isolate Melt with Low and Intermediate Moisture Levels at an Elevated Temperature Nobuyuki Hayashi, Isao Hayakawa & Yusaku Fujio* Department of Food Science and Technology, Faculty of Agriculture, Kyushu University, 6- lo- 1, Hakozaki, Higashi-ku, Fukuoka 8 12, Japan (Received 25 October 199 1; accepted 19 December
199 1)
ABSTRACT The flow behaviour of moisturized (20-70% d. b.) soy protein isolate@PI) melt at 140°C was markedly dependent on its moisture content. By regression analysis,the Herschel-Bulkley power-law model was successfully fitted to the measured data over the range 3 = lo3 to 5 x IO4s-l. The discontinuity of the regression coecients observed at 41-54% d.b. moisture range suggested a difference in melt flow mechanism at the opposite sides of this moisture range. At the lower moisture content (20-41% d.b.), SPI melt could flow unisotropically,but at higher moisture content (54-70% d.b.), the free watercould act as a lubricant.
INTRODUCTION In extrusion cooking, protein molecules change to a molten state and behave as a fluid, like synthetic polymers, at an elevated temperature which is generally far higher than the protein denaturation temperature. At this time, irreversible and complex changes such as unfolding and disulphide-disulphide interactions take place in the protein molecules. These physicochemical interactions make it difficult to analyse the melt rheology of bio-polymers. However, much research has been carried out to evaluate the flow properties of food materials at elevated temperatures using extruders (Chen et al., 1978; Jao et al., 1978; Bhattacharya & Hanna, 1986). Although these investigations provided important infor*To whom correspondence
should be addressed. 1 Joumal of Food Engineering 0260-8774/92/$05.00 Publishers Ltd, England. Printed in Great Britain
- Q 1992
Elsevier
Science
N. Hayashi, I. Hayakawa, Y. Fuji0
2
mation about extrusion cooking, further fundamental studies on the flow properties of bio-polymer melt, especially protein melt, were considered necessary in order to obtain basic information about the thermomechanical properties. Therefore the flow properties of soy protein isolate (SPI) melt at an elevated temperature ( 14OaC) have been studied using a capillary tube viscometer. As a result, the large dependency of the flow properties of SPI melt on its moisture content has been determined as, at higher moisture contents (70% d.b.), SPI melt possesses flow properties that can be defined by the power-law model (Hayashi et al., 1991), but at lower than 40% d.b. moisture it changes to an unknown type of plastic fluid (Fuji0 et al., 1991). In the present paper, the flow properties of various moisture level SPI melts (20-70% water, dry basis) at an elevated temperature (140°C) have been studied and the flow properties fitted to the Herschel-Bulkley power-law model by regression analysis.
MATERIALS
AND METHODS
Soy protein isolate Soy protein isolate (SPI) powder containing 87.7% d.b. protein (Kjeldahl nitrogen x 5.71) and 57% moisture was obtained from Ajinomoto Co. Ltd. (Tokyo, Japan). The moisture content of the SPI was adjusted to 20, 30, 41, 54 and 70% d.b. according to the procedure described previously (Hayashi et al., 1990a; Fuji0 et al., 1991). Extrusion viscometry Extrusion viscometq was performed at 140°C which is higher than the flow starting temperature of the lowest moisturized SPI sample (20% d.b.) (Fuji0 et al., 1991). The capillary tube viscometer used, which was designed in the authors’ laboratory and assembled by Shinmeiwa Co. Ltd. (Tokyo, Japan), were as detailed in previous papers (Hayashi et al., 1990b; Fuji0 et al., 1991). The moisturized SPI powder (4-O g) was moulded into a cylindrical shape (l-08 cm in diameter and about 3 cm in length) using a hand press and inserted into the sample reservoir. After pre-heating for 20 min, the sample was extruded through a capillary tube or an orifice die at a selected constant plunger travelling speed (Fig. 1). The capillary tube used was O-75 mm in radius (R) and 20 mm in length (15 ); thus the corresponding L/R ratio was 26.7. Plunger travelling speed and the resultant pressure drop were measured for a given capillary tube
Flow properties of moisturized SPI melt
kW4 (b)
(4 Fig. 1.
Design of experimental dies: (a) capillary tube die; (b) orifice die. Arrow indicates flow direction. x9 = 1.5 mm.
(APc, MPa) or an orifice die (A&
MPa). APc and APO were measured over as broad a range as possible by applying various plunger speeds, i.e. various volume flow rate, Q (m3 s-l). End effect correction was done by subtracting APO from APc at the same value of Q. This gives APd ( = APc - APO) which indicates the pressure drop at the capillary tube wall. The validity of this correction method for SPI melt, particularly on 70% d.b. moisture, was already investigated and a satisfactory result was obtained (Hayashi et al., 1991). The volumetric flow rate, Q, and APd were converted into apparent shear rates (pa,, s-l) by using the equation: (3, = 4Q/3rR3), and th e s h ear stress at the capillary tube wall (t,, MPa) according to the equation; r, = A Pd X R/2 L . Regression analysis The Herschel-Bulkley power-law model (Skelland, 1967) was applied to measured data in order to characterize the flow properties of SPI melt, described by the following equation: tw=
q)+(q’x &)”
where to (MPa) is the yield stress, i.e. the minimum shear stress required for flow; n (dimensionless) is the flow behaviour index which is a measure of the departure from Newtonian flow; 7’ (MPa”” s) is the consistency index, but only when n = 1, and has the dimensions of viscosity. If the fluid is a Bingham fluid then r, # 0 (Holdsworth, 1971). Barnes and Walters (1985) recently questioned the concept of a yield stress. It is true that, from a purely theoretical point of view, most
4
N. Hayashi, I. Hayakawa, Y. Fuji0
materials will not exhibit a yield stress when they are given a sufficiently long time for flow starting. However, Ofoli et al. (1987) mentioned that the yield stress concept is useful in process modelling because of the dependence of all food processes on strict time limitations. In the present study the experimental time range was significantly shorter than that required to support the theoretical view point of Barnes and Walters. Therefore, a yield stress parameter has been included in the present model. Since the model equation is intrinsically non-linear, the ordinary regression method for linear equations is not applicable. Therefore, the successive approximative calculation was performed iteratively at each moisture content using a computer (PC-98OlVX, Nippon Electric Co. Ltd., Tokyo, Japan) to find the regression coefficients that minimize the residual sum of squares (Williams, 1959; Draper & Smith, 1966; Snedecor & Cochran, 1989).
RESULTS Measured data Figure 2 shows the observed volumetric flow rates, Q (m3 s-r), and resultant APc or APO (MPa) on a log-log scale. The volumetric flow rate of the SPI melt varied between 6 x 10s6 to 2 x 10-s m3 s-l depending on the plunger speed. The pressure drop at the capillary tube wall, APd, was calculated from these results and is shown in Fig. 3. As seen in Fig. 3, a change in moisture content drastically affected the relationship between Q and APd, i.e. the pressure drop required to achieve the same flow rate was remarkably decreased by a small increase in moisture content. Flow curves for moisturized SPI melt Apparent shear rate, y,, and shear stress at the capillary tube wall, tw, were calculated from Q and APd, respectively. The flow curves, p, versus z,, for SPI melt with various moisture contents are shown on logarithmic scales in Fig. 4 and on ordinary scales in Fig. 5. The good linearity on logarithmic scales was observed at 70 and 54% d.b. moisturized SPI melts over the full experimental range and also in 20, 30 and 41% d.b. samples at shear rates higher than 3 X 10 s-i. This linearity observed on logarithmic scales means that these fluids could be the power-law fluids. On the other hand, as seen in Fig. 5, the non-linearity
t
102
2
E,
-
10' =
: 9
100
lo-’
=
.L
10-e
lo-'
10*
lO4
Cl Cm3esec-11
(4
m 8
2 9
10’
I
100
lo-' lo-'
I
I
1
I
, I I,,
,
,
,
,
, ,
10-r
,(,
104
(
,
(
,
,
,a
10"
Cl CmGec-‘I
(b)
Fig. 2. Relationship between Q and measured pressure drop for SPI melt with various moisture contents at 140°C: (a) capillary tube (A&); (b) orifice die (APO). Moisture content (% d.b.): 0,20; l, 30; A, 41; A, 54; q,70.
N. Hayashi, I. Hayakawa, Y. Fuji0
10’
10-l 10-a
I
10-
Q [ma-set-’
Fig. 3.
1111~
lo-’
1
Relationship between Q and APd for SPI melt with various moisture contents at 140°C. Moisture content (% d.b.): 0,20; l,30; A, 41; A, 54; 0,70.
observed on linear scales means that they could be non-Bingham plastics within the shear rate range of the present experiment. Additionally, some yield stress was observed as the intercept on the ordinate. These results supported the fitting of the data to the Herschel-Bulkley power-law model. Regression curves Calculated regression coefficients, r,, 7’ and n obtained by the successive approximate regression are shown in Table 1. A close agreement between regression curves and measured data was obtained as can be seen in Fig. 4. The values of the residual sum of squares, the degree of freedom and the sufficiently small mean square residual are also shown in Table 1. By using the obtained flow behaviour index (n), the Rabinowitsch correction (Harper & Sahrigi, 1965; Skelland, 1967; Clark, 1978; Padmanabhan & Bhattacharya, 1989) was performed in order to determine the real shear rate at the capillary tube wall, p,, using the following equation:
The calculated flow curves, pWversus rWare shown in Fig. 6.
Flow properties of moisturized SPI melt
-100
-
IO
P
r’
10-l
7
Fig. 4. Flow curves for SPI melt with various moisture contents at 140°C on double logarithmic scales. Symbols indicate measured values and the solid line the regression curve. Moisture content (% d.b.): 0,20; l,30; A, 41; A, 54; q,70.
0.8
0.6
0.4
0.2
0 0
10000
)‘el Fig. 5.
20000 [set-‘1
Flow curves for SPI melt with various moisture contents at 140°C on ordinary scales. Moisture content (% d.b.): 0,20; l,30; A, 41; A, 54; q,70.
N, Hayashi, I. Hayakawa, Y. Fuji0
8
The relationship between regression coefficients and moisture content As shown in Table 1, regression coefficients, r,, q’ and n, showed discontinuous relationships with the moisture content. The yield stress, r,, decreased linearly as the moisture content increased and became negligibly small at 54 and 71% d.b. moisture content. The value of q’ decreased with moisture content and a rapid decrease was observed between 41 and 54% d.b. of moisture content. The rheology index, n, was almost constant for the low moisture samples, however it decreased rapidly at higher than 41% d.b. of moisture content. These results indicated not only the large dependency of flow properties of SPI melt
TABLE 1 Regression Coefficients and Regression Errors for the Equation Moisture content %d. b.
20 30 41 54 70
Yield stress, %” (MPa)
623 x 3.73 x 2.37~ 1.96 x 4.90x
lo-? lo-’ lo-’ 1O-3 10-j
Consktency coeficient ?+ (MPa’l” s)
3.99 2.00 1.11 1.02 1.79
x x x x x
Flow behaviour index, n
10m5 lo-? 10ms lo-” 10-7
0.670 0.680 0.675 0.430 0.360
Sum of squares of the residuals
1-27x 9.77 x 3.03 x 1.70 x 1,26x
lo-? 10-j 10-j 10-j lo-”
rW= r0 + (7’ x p,)” Degrees of freedom
21 21 21 21 21
Mean square residual
5-99 4.65 1.44 8.07 5.99
x x x x x
10-j 10-j 10-j 1O-6 10-h
“Minimum shear stress required for flow.
Fig. 6. Rabinowitsch corrected flow curves for SPI melt with various moisture contents at 140°C on double logarithmic scales. Moisture content (% d.b.): a, 20; b, 30; c, 41; d, 54; e, 70.
Flow properties of moisturized SPI melt
9
on moisture content, but also the discontinuous change of melt flow behaviour of SPI in the moisture content ranging from 41 to 54% d.b.
DISCUSSION The Herschel-Bulkley power-law model successfully expressed the melt flow behaviour of SPI in the range 20 to 70% d.b. moisture at 140°C. A large dependency of equation coefficients, e.g. to, 7’ and n on moisture content and a discontinuous change at moisture contents between 41 to 54% d.b. were observed. These results suggest that the melt flow mechanism of SPI could be different at the opposite ends of the 41-54% d.b. moisture region. This moisture range at which the discontinuity of regression coefficients was observed (41%-54% moisture range) was almost equal to the maximum bound water range of soy protein, reported as 25% to 50% (Muffett & Snyder, 1980; Tanteeratarm et al., 1990). The moisture region was also equal to the moisture content at which the flow line style in the reservoir changed and the secondary circular flow at the capillary entrance region occurred (Hayashi et al., 1990b). These results lead to a hypothesis that the flow properties of SPI melt are largely affected by the water state in the melt. The free water that was observed in samples with a moisture higher than 41% d.b. may act as a lubricant among the molten state protein molecules while bound water could not act as a lubricant even at such elevated temperatures as 140°C. Consequently, the flow behaviour of SPI melt could be markedly affected not only by the moisture content but also the water state in the sample. As a result, the discontinuous change of regression coefficients could occur at the transition moisture region at which the water state in the sample changes. Moreover, the change in flow behaviour index, n, with moisture content was contrary to the expectation that a lower moisture sample indicates a lower n value because of its further transformation into a non-Newtonian fluid. However, n showed a constant value at lower moisture contents (20-41% d.b.) and it decreased at higher moisture contents (54-70% d.b.). The unexpected large n value obtained with a less moisturized sample suggested the unexpected pressure drop occurred not only at the capillary tube wall but also somewhere else. For example, there could be considerable friction between molten SPI molecules. Therefore, the low moisturized SPI melt having no free water could flow unisotropically in the capillary tube. On the other hand, the result showing a remarkable decrease in n at the higher moisture range is contrary to the general rule. However, the n value of the SPI melt could
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N, Hayashi, I. Hayakawa, Y. Fuji0
be expected to increase again at a much higher unknown moisture content. Unfortunately, the pressure drops given by SPI melt with higher than 70% d.b. moisture were too small to be measured accurately using the authors’ extrusion viscometer. Future studies will be focused on improving the viscometer, thus clarifying the flow properties of SPI melt higher than 70% d.b. moisture, and also investigating the water state in molten SPI at an elevated temperature.
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323-6. Bhattacharya, M. & Hanna, M. A. ( 1986). Viscosity modeling of dough in extrusion. J. Food Technol., 21, 167-74. Chen, A. H., Jao, Y. C., Larkin, J. W. & Goldstein, W. E. ( 1978). Rheological model of soy dough in extrusion. J. Food Process Eng., 2,337-42. Clark, J. P. (1978). Dough rheology in extrusion cooking. Food Technology, 32, 73-6. Draper, N. R. & Smith, H. ( 1966). An introduction to nonlinear estimation. In Applied RegressionAnalysis.John Wiley & Sons, New York, pp. 263-304. Fujio, Y., Hayashi, N. & Hayakawa, I. ( 199 1). Effect of moisture content on flow behaviour of molten soy-protein isolate under an elevated temperature. Znt.J. Food&i. Techno!., 26,45-51. Harper, J. C. & Sahrtgi, A. F. E. (1965). Viscometric behavior of tomato concentrates. J. Food Sci., 30,470-6. Hayashi, N., Hayakawa, I. & Fujio, Y. ( 1990a). Flow patterns in soybean protein isolate melt in the reservoir of an extrusion viscometer. J. Fat. Agr., Kyushu Univ.,35,59-64. Hayashi, N., Hayakawa, I. & Fujio, Y. (1990b). Development and evaluation of an extrusion viscometer for polymer melt. J. Fat. Agr., Kyushu Univ., 35, 73-9. Hayashi, N., Hayakawa, I. & Fujio, Y. ( 1991). Entrance effect correction on the flow of moisturized soy protein isolate melt in an extrusion viscometer. Znf.J. Food Sci. Technol., 26,567-74. Holdsworth, S. D. (1971). Applicability of rheological models to the interpretation of flow and processing behaviour of fluid food products. J. Texture S&dies, 2,393-418. Jao, Y. C., Chen, A. H., Lewandowski, D. & Irwin, W. E. ( 1978). Engineering analysis of soy dough rheolo in extrusion. J. Food Process Eng., 2,97- 112. Muffett, D. J. & Snyder, H. E. ?1980). Measurement of unfrozen and free water in soy proteins by differential scanning calorimetry. Journal of Agricultural Food Chemistry,28,1303-5. Ofoli, R. Y., Morgan, R. G. & Steffe, J. F. (1987). A generalized rheological model for inelastic fluid foods. J. Texture Studies, l&213-30. Padmanabhan, M. & Bhattacharya, M. ( 1989). Analysis of pressure drop in extruder dies. J. Food Sci., 54,709-13.
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