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Imperfect squeezing flow viscometry of mustards with suspended particulates
Journal of Food Engineering 39 (1999) 217±226
Imperfect squeezing ¯ow viscometry of mustards with suspended particulates T. Suwonsichon, M. Peleg 1 Department of Food Science, Chenoweth Laboratory, University of Massachusetts, Agricultural Engineering Building, Amherst, MA 01003, USA Received 13 July 1998; received in revised form 29 October 1998; accepted 30 October 1998
Abstract Samples of commercial mustard and a mustard spread all with suspended particulates were placed in a wide Te¯onR container and were compressed with a wide Te¯onR plate to induce imperfect Ôsqueezing ¯owÕ. The recorded force vs. height relationships were plotted on logarithmic coordinates. The resulting curves had a clear linear part marking the region where squeezing ¯ow was dominant. The slope of this linear region was on the order of ÿ0.8 to ÿ1.0. When the upper plate was stopped at a preset height the force decayed to a level well above that which is produced by buoyancy, indicating a yield stress of a considerable magnitude. The tests reproducibility was on the order of about 10%, more than sucient to detect textural dierences between the products and to monitor the eect of the compression rate and the upper plate diameter (or gap). The textural dierences between the products were expressed in terms of apparent compressive stress at 0.5, 1 and 2 mm height and the residual apparent compressive stress after 60 and 120 s relaxation. The magnitude of all the mechanical parameters had a modest dependence on the upper plate diameter but which had no eect on their sensitivity as measures of product consistency. Increasing the compression rate from 0.1 to 0.2 mm sÿ1 had relatively small eect on the magnitude of the apparent stress which was probably due, atleast in part, to the considerable yield stress of these products. It was concluded that the imperfect squeezing ¯ow viscometry is a convenient and sensitive method to evaluate the texture of mustard and mustard products whether or not they contain seed parts. Ó 1999 Elsevier Science Ltd. All rights reserved.
1. Introduction The rheology of mustard and mustard products has received, relatively, only a little attention in the food literature (Stee, 1992; Aguilar, Rizvi, Ramivex & India, 1991a,b). The consistency of mustards has been primarily evaluated by coaxial viscosimetry with the results expressed in terms of the Herschel-Bulkly modelÕs or the power law equationÕs parameters (Stee, 1992; Aguilar, et al., 1991a,b), or by dynamic test (Aguilar, et al., 1991a,b). Characteristic values for room temperature were a ¯ow index (n) on the order of 0.2±0.4 and a consistency coecient (K) on the order of 20±60 Pasn (Stee, 1992). The yield stress of a commercial mustard was also determined by coaxial viscosimetry and compared with that determined by squeezing ¯ow in a creep array (Campanella, 1987; Campanella & Peleg, 1987a). The reported values of the yield stress were on the order of 50±80 Pa with a considerable drop after shearing. In experimental mustard prepared by Aguilar, et al. (1991a, 1 Corresponding author. Tel.: 001-413-545-5852; fax: 001-413-5451262; e-mail: [email protected]
b), it was on the order of 16±30 Pa and strongly aected by the suspended seed parts size distribution. The low reported values of the ¯ow index (n) suggest that slip might have been a factor in the rheological measurements. The considerable drop in the yield stress magnitude after shearing suggests that the latter causes a considerable structural disruption. Consequently, coaxial viscosimetry or any other method where the specimen is pressed into the narrow gap of the sensor, may not give a reliable account of the original products consistency. The presence of solid particulates can only aggravate the situation since upon shearing they tend to migrate to the center of the gap. This leaves the sensorÕs surfaces in contact with a ¯uid layer with little or no particles, a situation that is equivalent to the presence of a lubricating ®lm. In coaxial or capillary viscometry the result can be a full or partial plug ¯ow for which the standard equations for calculating the shear stress and rate are inappropriate. Lubricated squeezing ¯ow viscometry (Fig. 1) oers a way to avoid, or atleast considerably reduce, the problems posed by both structural disruption and slip. The method is based on compression, i.e., squeezing, of a
0260-8774/99/$ ± see front matter Ó 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 0 - 8 7 7 4 ( 9 8 ) 0 0 1 5 9 - 9
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T. Suwonsichon, M. Peleg / Journal of Food Engineering 39 (1999) 217±226
Fig. 1. Schematic view of an ideal squeezing ¯ow sensor: (a) before testing; (b) frictional ¯ow (note the parabolic front of the exiting liquid); (c) lubricated ¯ow (note the ¯at front of the exiting liquid).
thin layer of ¯uid between lubricated plates (Chatraei, Macosko & Winter, 1981; Soskey & Winter, 1985) to produce a plug ¯ow regime deliberately (see Fig. 1(c)). Squeezing ¯ow viscometry was introduced to food rheology by Dr. Edward Bagley of the USDA-NRRC of Peoria, IL. (Casiraghi, Bagley & Christianson, 1985) and has been applied to a variety of food products (e.g., Campanella, 1987; Campanella & Peleg, 1987b; Huang & Kokini, 1993; Ramirez-Wong, Sweat, Torres & Rooney, 1996). Since the specimen is loaded when the plates are far apart, the specimen is spared much of the disruption that occurs in conventional viscometry, where it is subjected to a high but uncontrolled shear when forced into the narrow space between the sensorÕs moving and stationary parts. Because the plates are also lubricated, or made of Te¯onR , slip is intentionally induced. Thus instead of being an artifact as in coaxial or capillary viscometry slip is a prerequisite for a proper test. The diculty with the original method is that the preparation and mounting of the specimen can be somewhat inconvenient or messy. For this reason, it has recently been proposed to use what has been called Ôimperfect lubricated squeezing ¯ow viscometryÕ (Fig. 2), where the bottom plate is replaced by a shallow container. Atleast in principle a specimen of a product like mustard can actually be formed in the container or collected from the ®lling machine and be tested virtually
intact and undisturbed. However, because of the sensor geometry, the measured forces are in¯uenced by entry eect, annular ¯ow and buoyancy. Hence the method is a compromise between accuracy and convenience. It has been demonstrated that despite of the above mentioned eects the method can be remarkably sensitive and useful for rheological characterization of foods whose slip and/or uncontrolled structural disruption are acute problems when tested by conventional methods (Honer, Gerhards & Peleg, 1997; Lorenzo, Gerhards & Peleg, 1997; Suwonsichon & Peleg, 1999). The objective of this work was to evaluate the imperfect squeezing ¯ow method as a tool to assess the consistency of mustard and mustard products which contain suspended seed parts and therefore may be dicult to test by coaxial viscometry and other traditional methods.
2. Theoretical background The force exerted by a power law ¯uid squeezed between parallel frictionless plates of the same radius at a constant displacement rate is given by (Campanella & Peleg, 1987b) n 1 F H p R2 K3 n1=2 V =H ; where F is the momentary force, H, the specimenÕs momentary height, R the plate radius, V the displacement rate (linear velocity), and K and n the ¯uidÕs consistency and ¯ow index, respectively. Thus when the force vs. height relationship is plotted on logarithmic coordinates the expected result is a straight line with a slope of ÿn. Once n has been determined, K can be calculated with Eq. (1). In frictional ¯ow, that is when the plates are not lubricated, the force-height relationship is given by ScottÕs equation which can be written in the form (Avila & Binding, 1982)
Fig. 2. Schematic view of an imperfect squeezing ¯ow sensor.
n F H 2pKRn3 = n 3 2n: 1=n V n =H 2n1 :
2
T. Suwonsichon, M. Peleg / Journal of Food Engineering 39 (1999) 217±226
The theoretical slope of the log F(H) vs. log H relationship in this case is therefore ÿ(2n+1). Since the absolute value of a shear thinning ¯uidÕs with a ¯ow index, n, must be between zero and one, 0 6 n 6 1, the absolute magnitude of the slope of the log F(H) vs. log H relationship in frictional ¯ow must be greater than one too. Thus an experimentally observed slope with an absolute magnitude smaller than one is a strong evidence that the ¯ow is of the lubricated kind. This can also be con®rmed if the exiting liquidÕs front has a rectangular shape (Fig. 1(c)) ± a characteristic of a plug ¯ow. (Had the plates provided friction the pro®le of the exiting ¯uid would have a parabolic shape as shown in Fig. 1(b)). If in a material known to have a ``structure'' the absolute magnitude of the slope of the log F(H) vs. log H relationship is close to one, its interpretation is more dicult. Since the ¯uid is certainly non-newtonian, a slope on the order ÿ1 can indicate a very high degree of plasticity, or that the above equation is inappropriate because the material has a high yield stress for example. In the case of imperfect squeezing ¯ow (Fig. 2) the measured momentary force, F(H), is also in¯uenced by the buoyancy, annular ¯ow and entry and end eects. If, however, the upper plate is suciently large and so is the gap between the upper plate and the container, then disregarding these eects can be justi®ed (Damrau & Peleg, 1997). Or in other words, with a sensor geometry of the kind used in this work (see below) Eqs. (1) and (2), if indeed valid, can in principle be used to estimate the rheological constants of the tested ¯uid (Honer, et al., 1997). The consistency of the estimates can be tested by using upper plates of dierent diameters and dierent compression rates. If for any reason neither equation is valid (see below) the consistency of dierent samples can still be compared in terms of their apparent stress at a given height i.e., r@0:5
or 1 or 2 mm
F@0:5
or 1 or 2 mm = pR
2
3
with or without correction for the buoyancy (Lorenzo, et al., 1997; Suwonsichon & Peleg, 1999). The disadvantage of such a procedure is that the magnitude of the apparent stress depends on the displacement rate at which the test is performed and the height, or heights, selected for the comparison. Nevertheless, the magnitude of the apparent stress is directly determined and therefore is not based on any assumed rheological model. It also has a signi®cant advantage over purely empirical measures of consistency determined by instruments such as the Bostwick consistometer or the ``back extrusion'' cell. Being measured in specimens having a high diameter to height ratio and expressed in stress units its magnitude is much less aected by geometric artifacts. Also the validity of the apparent stress as a consistency measure can be experimentally veri®ed by comparing the values obtained with upper plates of dierent diameters.
219
2.1. Yield stress It is dicult to determine the yield stress of a semiliquid food by squeezing ¯ow viscosimetry performed at a constant displacement rate. (As already stated this can be done in a ``creep array'' (Campanella & Peleg, 1987a) where the displacement under a constant load is monitored. However standard commercial creep testers are not readily available and therefore it is doubtful that this method will gain popularity in food research in the near future.) Nevertheless, a relative estimate of the yield stress can be obtained by determining the residual apparent stress of the specimen at a given height, or several heights, after it has been allowed to relax for a given time e.g., rapp
@ 60 or 120 s
F@
60 or 120 s = pR
2
:
4
In imperfect squeezing ¯ow, the force exerted by ¯uids without a yield stress decays to the buoyancy force almost instantaneously. The higher the yield stress and more solid the structure the higher is the absolute magnitude of the residual force (or stress). The latter, therefore, can serve as a measure of solidity ± on the pertinent time scale ± and hence as an indicator of the yield stress. Such a measure has all the advantages and disadvantages of the apparent stress at a given height, and likewise its applicability can be veri®ed by repeating the tests with sensors of dierent geometries. 3. Experimental 3.1. Materials Jars of mustard of two national brands and a mustard product all containing pieces of mustard seeds were purchased at a local supermarket and tested at an ambient temperature of 23°C. Because no attempt has been made to establish how representative the samples were of their respective manufacturerÕs product the latter are not identi®ed by name. 3.2. Mechanical testing Specimens of the mustard were gently transferred from their original container into an all Te¯onR sensor having a ¯at container 140 mm in diameter using a large spoon to minimize disruption of the original structure. They were subsequently compressed by Te¯onR upper plates 100 and 120 mm in diameter (Fig. 3) as described by Honer, et al. (1997). The initial height of all the specimens, was about 6±7 mm in all the tests. Since only data at high compression ratios were considered, i.e., when the plates separation was less than about 4 mm, the slight initial variability in the specimen height has hardly any eect on the measurements ± theoretically
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T. Suwonsichon, M. Peleg / Journal of Food Engineering 39 (1999) 217±226
Fig. 3. The all Te¯onR sensor used in this work ®lled with a mustard specimen containing seed parts.
and in practice. The compression was performed with a TA.TX2 Texture Analyzer (Texture Technologies Corp., Scarsdale, NY) equipped with a 25 kg load cell and interfaced with Gateway 2000 microcomputer. The specimens were compressed to a ®nal height of 0.5 mm at a speeds of 0.1 and 0.2 mm sÿ1 . At the end of each run the crosshead was stopped and the decaying force recorded for about 3 min before the crosshead was withdrawn. The raw data ®les were imported to and processed by the Systate 5.0 package (Systate, Inc., Evanston, IL). Each test was performed in four replicates. 3.3. Data processing The recorded raw data were converted into forceheight relationships plotted on linear and logarithmic coordinates (see below). The linear part of the logarithmic relationship was considered as representing the region of dominant squeezing ¯ow (Lorenzo, et al., 1997; Honer, et al., 1997) and its slope was determined by linear regression. The initial part of the ¯ow curves (corresponding to specimen heights of to about 4±7 mm) was considered as re¯ecting entry eects and therefore discarded. The apparent stress at a specimen height of 0.5, 1 and 2 mm, rapp@H 0:5 or 1 or 2 mm , was calculated by Eq. (3) and was used as a semi-empirical consistency measure. The force decay data were used to calculate an apparent residual stress using Eq. (6).
4. Results and discussion 4.1. The shape of the force-height relationship and the mustards consistency: Typical force-height curves of the three mustards plotted on linear and logarithmic coordinates are shown in Figs. 4 and 5. The curves were remarkably reproducible (see below) and enabled characterization of the products in terms of the various mechanical parameters listed in Table 1. The logarithmic curves had the expected characteristic shape. Their linear part allowed for clear identi®cation of the region where squeezing ¯ow had been the dominant ¯ow regime. The absolute magnitudes of the slopes of the linear parts of the logarithmic curves of the dierent mustards are listed in Table 1. The typical values were on the order of ÿ1.0 to ÿ0.8. Had these values corresponded to the ¯ow index, n, as in an ideal lubricated squeezing ¯ow, they would imply that the mustards were newtonian or almost newtonian ¯uids which obviously they are not. This was clearly evident in their response to a rate change and in their relaxation pattern (Fig. 6). Also had there been an appreciable friction between the specimens and the sensors surfaces the slope should have been much closer to ÿ3 than to ÿ1. A slope of ÿ1 is the theoretical lower limit of a power law ¯uid in frictional ¯ow and it would imply ideal plasticity with no rate sensitivity. This possibility too ought to have been ruled out (see Table 1) and hence neither Eqs. (1) nor (2) were used to calculate
T. Suwonsichon, M. Peleg / Journal of Food Engineering 39 (1999) 217±226
221
Fig. 4. Typical force ± height relationships in the imperfect squeezing ¯ow of the three mustards ± linear scale.
Fig. 5. Typical force ± height relationships in the imperfect squeezing ¯ow of three mustards ± logarithmic scale. (Note that the region where squeezing ¯ow was dominant can be clearly identi®ed from the linear part of plots.)
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T. Suwonsichon, M. Peleg / Journal of Food Engineering 39 (1999) 217±226
Fig. 6. Typical relaxation curves of the three mustards tested. (Note the considerable residual stress even after 3 min.) Table1 Rheological parameters of commercial mustard determined by lubricated imperfect squeezing ¯ow Brand
Diameter (mm)
Speed (mm sÿ1 )
Slope
r 2 mm (kPa)
r 1 mm (kPa)
r @ t0s (kPa)
r @ t60s (kPa)
r @ t120s (kPa)
A
100
0.1 0.2 0.1 0.2
ÿ0.9 0.01 ÿ1.0 0.02 ÿ0.8 0.02 ÿ0.9 0.02
1.43 0.01 1.66 0.09 1.72 0.06 1.97 0.03
2.59 0.28 3.23 0.23 3.11 0.06 3.63 0.07
4.60 0.05 5.66 0.32 4.82 0.15 5.51 0.09
1.33 0.05 1.52 0.17 1.64 0.17 1.61 0.07
1.30 0.05 1.49 0.16 1.59 0.16 1.56 0.06
0.1 0.2 0.1 0.2
ÿ0.8 0.01 ÿ0.9 0.02 ÿ0.8 0.02 ÿ0.9 0.02
1.52 0.16 1.83 0.02 1.95 0.03 2.22 0.14
2.67 0.30 3.38 0.5 3.44 0.07 3.96 0.18
4.70 0.41 5.94 0.09 5.37 0.13 5.93 0.21
1.89 0.19 2.31 0.06 2.36 0.06 2.30 0.09
1.86 0.19 2.28 0.06 2.31 0.06 2.26 0.09
0.1 0.2 0.1 0.2
ÿ0.9 0.02 ÿ1.0 0.01 ÿ0.9 0.02 ÿ1.0 0.01
1.05 0.16 1.36 0.02 1.49 0.16 1.62 0.02
1.98 0.28 2.65 0.05 2.74 0.26 3.09 0.05
4.01 0.58 5.17 0.18 4.72 0.32 5.16 0.18
1.73 0.23 2.12 0.07 2.27 0.19 2.20 0.07
1.68 0.23 2.04 0.05 2.21 0.18 2.14 0.05
120
B
100 120
C
100 120
the mustards consistency coecient (K). Instead the apparent stresses at three selected heights (2, 1 and 0.5 mm) which had been determined directly were used as empirical measures consistency. 4.2. The tests reproducibility Despite the crudeness of the experimental array, the samples preparation and the specimens loading proce-
dure the measurements and the rheological parameters which they provided were remarkably reproducible (Table 1). This was irrespective of the product, the upper plateÕs diameter and the displacement rate. The measurements were sensitive enough to distinguish, clearly and consistently, between the three products irrespective of the test conditions as shown in Figs. 7 and 8. A similar degree of reproducibility has been observed in other products evaluated by this method (Lorenzo, et al.,
T. Suwonsichon, M. Peleg / Journal of Food Engineering 39 (1999) 217±226
223
Fig. 7. Comparison of the relative consistency of the three mustards on the basis of their apparent stress at three heights as determined with a sensor having an upper plate 100 mm in diameter.
1997; Honer, et al., 1997; Suwonsichon & Peleg, 1999). This demonstrates that since the plates are wide and the specimen height very small in comparison, any irregularity in the upper surface of the specimen at the beginning of the test can have only a very minor eect of the results. That there was a certain degree of textural variability among the samples also cannot be ruled out, and the same can be said about the specimens handling before testing. Nevertheless even the cumulative error produced by these factors had little in¯uence on the methodÕs ability to provide a consistent comparison between the products (Figs. 7 and 8). Whatever this error was it was smaller than the eect of the sensorÕs geometry and that of the compression rate (Table 1). 4.3. Diameter eects The apparent stresses determined with a sensor having an upper plate 120 mm in diameter were consistently higher than those obtained with an upper plate having 100 mm in diameter. The magnitude of the dierence
was generally on the order of about 30%. Similar differences were observed in other products (Honer, et al., 1997; Lorenzo, et al., 1997; Suwonsichon & Peleg, 1999). One can surmise that the higher values are more representative of the mustards actual consistency. This is because as the diameter of the plate increases the relative role of the annular ¯ow in the gap, and that of end effects diminishes (Damrau & Peleg, 1997). This implies that the wider the sensor and its gap the more reliable the measurement is. However, when the sensor is enlarged it becomes more dicult to guarantee that the upper plate and the containerÕs bottom are perfectly parallel, which can cause a signi®cant error. It therefore appears that a sensor with dimensions of those which were used in this work, although by no means, ideal is at least an acceptable practical compromise. (That the plates of the experimental sensors were indeed parallel to the containerÕs bottom was checked with a level.) An additional factor that ought to be considered in machines of the kind used in this work is that as the plates diameter is increased the absolute magnitude of
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Fig. 8. Comparison of the relative consistency of the three mustards on the basis of their apparent stress at three heights as determined with a sensor having an upper plate 120 mm in diameter.
the forces also increases. If the machine and/or sensor have even a slight compliance the tests results would be distorted. Compensation for such an eect can be done through programming, but it would always be safer to use a machine and sensor which are as rigid as possible.
ative magnitude of the ®rst component is re¯ected in the residual force, or stress, after relaxation and the second in the dissipated portion (see Fig. 6). According to this hypothesis the ratio between the forces when the speed is doubled, RF , would be approximately
4.4. Rate eects
RF F 2V =F V H const x 1 ÿ x2m ;
In the ideal case of lubricated squeezing ¯ow and according to Eq. (1), doubling the testing speed, V, for ¯uids with n 1 (the absolute magnitude of the slope of the log F(H) vs. log H relationship) will double the force at any given specimen height, H. According to Eq. (3) (ideal frictional ¯ow) if the absolute magnitude of the slope is one then 2n + 1 1 and n 0, which implies that there would be no rate eect al all. As can be seen in Table 1 neither was the case in the tested mustards. Doubling the speed from 0.1 to 0.2 mm sÿ1 did cause an appreciable increase in the force level but not to the extent predicted by Eq. (1). A hypothesis consistent with this observation is that the measured total force had a deformation and rate dependent components. The rel-
5
or m log RF ÿ x= 1 ÿ x= log 2;
6
where x is the fraction of the residual force after relaxation, 1 ÿ x the fraction of the dissipated force and m (0 6 m 6 1) a constant serving as a ``¯ow index'' of sort. (Special cases according to this equation are; a newtonian ¯uid (x 0, m 1) where RF 2, a ``bingham like ¯uid'' (x x0 , m 1) where RF x0 + 2(1ÿx0 ) and a ``pseudoplastic'' (``power law'') ¯uid without a yield stress (x 0, m m) where RF 2m .) Application of this model to the experimental ratios derived from Table 1 showed that the value of m, in all three products, was in the range of 0.2±0.6. The relation of this empirical index to the ¯ow index in shear is un-
T. Suwonsichon, M. Peleg / Journal of Food Engineering 39 (1999) 217±226
225
clear at this point but it is not unreasonable to expect that they will have a numerical value on the same order of magnitude. A true test of the hypothesis is whether the value of m remains the same for other speed ratios but this was outside the scope of this work. (When silicon oils were tested with the same cells, the forces ratio for speeds of 0.1, 0.2, 0.4, and 0.6 mm sÿ1 were 1 (by de®nition), 2.0, 3.7 and 5.6, respectively. Considering the test geometry these values can be considered as being close to the theoretical values of 1, 2, 4 and 6 for newtonian liquids squeezed between parallel plates of same diameter.) Obviously Eq. (5) is only an empirical approximation because it is based on the assumption that the residual stress after relaxation is rate independent. Although this was evidently the case where the data were obtained using the 120 mm upper plate (Table 1), there were a few noticeable discrepancies in the data obtained with the 100 mm plates (see Table). Also, although not observed in this study there is at least a theoretical possibility that deformation at an increased rate can cause more intensive structural damage and hence that the residual stress after relaxation will be inherently rate dependent. That this may happen in mustard at rates much higher than those used in this work is a possibility that cannot be ruled out. But as
stated this aspect was not investigated in the present study and hence it remains a conjecture and a topic for future research.
Fig. 9. Comparison of the relative consistency of the three mustards on the basis of their residual apparent stress after relaxation determined with a sensor having an upper plate 100 mm in diameter.
Fig. 10. Comparison of the relative consistency of the three mustards on the basis of their residual apparent stress after relaxation determined with a sensor having an upper plate 120 mm in diameter.
4.5. Yield stress A residual stress after relaxation ± well above the level caused by buoyancy ± is a clear indication that the tested ¯uid has a yield stress of considerable magnitude (Lorenzo, et al., 1997; Suwonsichon & Peleg, 1999). Fig. 6 and Table 1 show that all three mustard products indeed had an appreciable yield stress. (The buoyancy corresponding to the conditions under which the curves that appear in Fig. 6 were determined is on the order of 1N well below that of the residual force which was on the order of 10±35N). The residual apparent stresses of the three products tested are reported in Table 1 and are compared graphically in Figs. 9 and 10. The table and ®gures show that the products with the higher apparent stress at a given height, i.e., having a stronger consistency, also had a higher residual apparent stress after relaxation, i.e., a higher yield stress. The same was observed in products as variable as tomato concentrates (Lorenzo, et al., 1997) and refried beans (Suwonsichon
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T. Suwonsichon, M. Peleg / Journal of Food Engineering 39 (1999) 217±226
& Peleg, 1999) which is consistent with the notion that both the yield stress and consistency are a manifestation of the strength and integrity of the same microstructure or gel network. Comparison between the products on the basis of their residual stresses after relaxation (Figs. 9 and 10) gave the same ranking as that based on the apparent stress at any given height (Figs. 7 and 8). It therefore appears that at least for the products tested in this work all the mechanical parameters could be used interchangeably as consistency measures. Acknowledgements Contribution of the Massachusetts Agricultural Experiment Station at Amherst. The support of the work by the USDA-NRICGP, under Grant No. 9502429, is gratefully acknowledged. The authors also express their thanks to the Royal Thai Government for its support of T.S. References Aguilar, C., Rizvi, S. S. H., Ramirex, J. F., & Inda, A. (1991a). Rheological behavior of processed mustard I. Eect of milling treatment. J. Texture Studies, 22, 59±84. Aguilar, C., Rizvi, S. S. H., Ramirex, J. F., & Inda, A. (1991b). Rheological behavior of processed mustard II. Storage eects of milling treatment. J. Texture Studies, 22, 85±103. Avila, F., & Binding, D. M. (1982). Normal and reverse squeezing ¯ow. J. Non-Newtonian Fluid Mech., 11, 111±126.
Campanella, O. H. (1987). Rheological properties of semi-liquid foods. Ph D. Thesis, University of Massachusetts, Amherst. Campanella, O. H., & Peleg, M. (1987a). Determination of the yield stress of semi-liquid foods from squeezing ¯ow data. J. Food Sci. 52, 214±215 and 217. Campanella, O. H., & Peleg, M. (1987b). Squeezing ¯ow viscosimetry of peanut butter. J. Food Sci., 52, 180±184. Casiraghi, E. M., Bagley, E. B., & Christianson, D. D. (1985). Behavior of mozzarella cheddar and processed cheese spread in lubricated and bonded uniaxial compression. J. Texture Studies, 16, 281±301. Chatraei, S. H., Macosko, C. W., & Winter, H. H. (1981). Lubricate squeezing ¯ow. A new biaxial extension rheometer. J. Rheol., 25, 433±443. Damrau, E., & Peleg, M. (1997). Imperfect squeezing ¯ow viscosimetry of Newtonian liquids ± theoretical and practical considerations. J. Texture Studies, 28, 187±204. Honer, B., Gerhards, C., & Peleg, M. (1997). Imperfect lubricated squeezing ¯ow viscometry for foods. Rheol. Acta, 36, 686±693. Huang, H., & Kokini, J. L. (1993). Measurement of braxial extentional viscosity of wheat ¯our dough. J. Rheol., 37, 879±891. Lorenzo, M. A., Gerhards, C., & Peleg, M. (1997). Imperfect squeezing ¯ow viscosimetry of selected tomato products. J. Texture Studies, 28, 543±567. Ramõrez-Wong, B., Sweat, V. E., Torres, P. I., & Rooney, L. W. (1996). Evaluation of rheological properties of fresh corn masa using squeezing ¯ow viscometry : Biaxial extensional viscosity. J. Texture Studies, 27, 185±198. Soskey, P. R., & Winter, H. H. (1985). Equibiaxial extension of two polymer melts: Polystyrene and low density polyethylene. J. Rheol., 29, 493±517. Stee, J. F. (1992). Rheological Methods in Food Engineering. New York: Freeman Press. Suwonsichon, T., & Peleg, M. (1999). Imperfect squeezing ¯ow viscometry for commercial refried beans. Food Sci. Technol. Intnl. (in press).
Imperfect squeezing ¯ow viscometry of mustards with suspended particulates T. Suwonsichon, M. Peleg 1 Department of Food Science, Chenoweth Laboratory, University of Massachusetts, Agricultural Engineering Building, Amherst, MA 01003, USA Received 13 July 1998; received in revised form 29 October 1998; accepted 30 October 1998
Abstract Samples of commercial mustard and a mustard spread all with suspended particulates were placed in a wide Te¯onR container and were compressed with a wide Te¯onR plate to induce imperfect Ôsqueezing ¯owÕ. The recorded force vs. height relationships were plotted on logarithmic coordinates. The resulting curves had a clear linear part marking the region where squeezing ¯ow was dominant. The slope of this linear region was on the order of ÿ0.8 to ÿ1.0. When the upper plate was stopped at a preset height the force decayed to a level well above that which is produced by buoyancy, indicating a yield stress of a considerable magnitude. The tests reproducibility was on the order of about 10%, more than sucient to detect textural dierences between the products and to monitor the eect of the compression rate and the upper plate diameter (or gap). The textural dierences between the products were expressed in terms of apparent compressive stress at 0.5, 1 and 2 mm height and the residual apparent compressive stress after 60 and 120 s relaxation. The magnitude of all the mechanical parameters had a modest dependence on the upper plate diameter but which had no eect on their sensitivity as measures of product consistency. Increasing the compression rate from 0.1 to 0.2 mm sÿ1 had relatively small eect on the magnitude of the apparent stress which was probably due, atleast in part, to the considerable yield stress of these products. It was concluded that the imperfect squeezing ¯ow viscometry is a convenient and sensitive method to evaluate the texture of mustard and mustard products whether or not they contain seed parts. Ó 1999 Elsevier Science Ltd. All rights reserved.
1. Introduction The rheology of mustard and mustard products has received, relatively, only a little attention in the food literature (Stee, 1992; Aguilar, Rizvi, Ramivex & India, 1991a,b). The consistency of mustards has been primarily evaluated by coaxial viscosimetry with the results expressed in terms of the Herschel-Bulkly modelÕs or the power law equationÕs parameters (Stee, 1992; Aguilar, et al., 1991a,b), or by dynamic test (Aguilar, et al., 1991a,b). Characteristic values for room temperature were a ¯ow index (n) on the order of 0.2±0.4 and a consistency coecient (K) on the order of 20±60 Pasn (Stee, 1992). The yield stress of a commercial mustard was also determined by coaxial viscosimetry and compared with that determined by squeezing ¯ow in a creep array (Campanella, 1987; Campanella & Peleg, 1987a). The reported values of the yield stress were on the order of 50±80 Pa with a considerable drop after shearing. In experimental mustard prepared by Aguilar, et al. (1991a, 1 Corresponding author. Tel.: 001-413-545-5852; fax: 001-413-5451262; e-mail: [email protected]
b), it was on the order of 16±30 Pa and strongly aected by the suspended seed parts size distribution. The low reported values of the ¯ow index (n) suggest that slip might have been a factor in the rheological measurements. The considerable drop in the yield stress magnitude after shearing suggests that the latter causes a considerable structural disruption. Consequently, coaxial viscosimetry or any other method where the specimen is pressed into the narrow gap of the sensor, may not give a reliable account of the original products consistency. The presence of solid particulates can only aggravate the situation since upon shearing they tend to migrate to the center of the gap. This leaves the sensorÕs surfaces in contact with a ¯uid layer with little or no particles, a situation that is equivalent to the presence of a lubricating ®lm. In coaxial or capillary viscometry the result can be a full or partial plug ¯ow for which the standard equations for calculating the shear stress and rate are inappropriate. Lubricated squeezing ¯ow viscometry (Fig. 1) oers a way to avoid, or atleast considerably reduce, the problems posed by both structural disruption and slip. The method is based on compression, i.e., squeezing, of a
0260-8774/99/$ ± see front matter Ó 1999 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 0 - 8 7 7 4 ( 9 8 ) 0 0 1 5 9 - 9
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Fig. 1. Schematic view of an ideal squeezing ¯ow sensor: (a) before testing; (b) frictional ¯ow (note the parabolic front of the exiting liquid); (c) lubricated ¯ow (note the ¯at front of the exiting liquid).
thin layer of ¯uid between lubricated plates (Chatraei, Macosko & Winter, 1981; Soskey & Winter, 1985) to produce a plug ¯ow regime deliberately (see Fig. 1(c)). Squeezing ¯ow viscometry was introduced to food rheology by Dr. Edward Bagley of the USDA-NRRC of Peoria, IL. (Casiraghi, Bagley & Christianson, 1985) and has been applied to a variety of food products (e.g., Campanella, 1987; Campanella & Peleg, 1987b; Huang & Kokini, 1993; Ramirez-Wong, Sweat, Torres & Rooney, 1996). Since the specimen is loaded when the plates are far apart, the specimen is spared much of the disruption that occurs in conventional viscometry, where it is subjected to a high but uncontrolled shear when forced into the narrow space between the sensorÕs moving and stationary parts. Because the plates are also lubricated, or made of Te¯onR , slip is intentionally induced. Thus instead of being an artifact as in coaxial or capillary viscometry slip is a prerequisite for a proper test. The diculty with the original method is that the preparation and mounting of the specimen can be somewhat inconvenient or messy. For this reason, it has recently been proposed to use what has been called Ôimperfect lubricated squeezing ¯ow viscometryÕ (Fig. 2), where the bottom plate is replaced by a shallow container. Atleast in principle a specimen of a product like mustard can actually be formed in the container or collected from the ®lling machine and be tested virtually
intact and undisturbed. However, because of the sensor geometry, the measured forces are in¯uenced by entry eect, annular ¯ow and buoyancy. Hence the method is a compromise between accuracy and convenience. It has been demonstrated that despite of the above mentioned eects the method can be remarkably sensitive and useful for rheological characterization of foods whose slip and/or uncontrolled structural disruption are acute problems when tested by conventional methods (Honer, Gerhards & Peleg, 1997; Lorenzo, Gerhards & Peleg, 1997; Suwonsichon & Peleg, 1999). The objective of this work was to evaluate the imperfect squeezing ¯ow method as a tool to assess the consistency of mustard and mustard products which contain suspended seed parts and therefore may be dicult to test by coaxial viscometry and other traditional methods.
2. Theoretical background The force exerted by a power law ¯uid squeezed between parallel frictionless plates of the same radius at a constant displacement rate is given by (Campanella & Peleg, 1987b) n 1 F H p R2 K3 n1=2 V =H ; where F is the momentary force, H, the specimenÕs momentary height, R the plate radius, V the displacement rate (linear velocity), and K and n the ¯uidÕs consistency and ¯ow index, respectively. Thus when the force vs. height relationship is plotted on logarithmic coordinates the expected result is a straight line with a slope of ÿn. Once n has been determined, K can be calculated with Eq. (1). In frictional ¯ow, that is when the plates are not lubricated, the force-height relationship is given by ScottÕs equation which can be written in the form (Avila & Binding, 1982)
Fig. 2. Schematic view of an imperfect squeezing ¯ow sensor.
n F H 2pKRn3 = n 3 2n: 1=n V n =H 2n1 :
2
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The theoretical slope of the log F(H) vs. log H relationship in this case is therefore ÿ(2n+1). Since the absolute value of a shear thinning ¯uidÕs with a ¯ow index, n, must be between zero and one, 0 6 n 6 1, the absolute magnitude of the slope of the log F(H) vs. log H relationship in frictional ¯ow must be greater than one too. Thus an experimentally observed slope with an absolute magnitude smaller than one is a strong evidence that the ¯ow is of the lubricated kind. This can also be con®rmed if the exiting liquidÕs front has a rectangular shape (Fig. 1(c)) ± a characteristic of a plug ¯ow. (Had the plates provided friction the pro®le of the exiting ¯uid would have a parabolic shape as shown in Fig. 1(b)). If in a material known to have a ``structure'' the absolute magnitude of the slope of the log F(H) vs. log H relationship is close to one, its interpretation is more dicult. Since the ¯uid is certainly non-newtonian, a slope on the order ÿ1 can indicate a very high degree of plasticity, or that the above equation is inappropriate because the material has a high yield stress for example. In the case of imperfect squeezing ¯ow (Fig. 2) the measured momentary force, F(H), is also in¯uenced by the buoyancy, annular ¯ow and entry and end eects. If, however, the upper plate is suciently large and so is the gap between the upper plate and the container, then disregarding these eects can be justi®ed (Damrau & Peleg, 1997). Or in other words, with a sensor geometry of the kind used in this work (see below) Eqs. (1) and (2), if indeed valid, can in principle be used to estimate the rheological constants of the tested ¯uid (Honer, et al., 1997). The consistency of the estimates can be tested by using upper plates of dierent diameters and dierent compression rates. If for any reason neither equation is valid (see below) the consistency of dierent samples can still be compared in terms of their apparent stress at a given height i.e., r@0:5
or 1 or 2 mm
F@0:5
or 1 or 2 mm = pR
2
3
with or without correction for the buoyancy (Lorenzo, et al., 1997; Suwonsichon & Peleg, 1999). The disadvantage of such a procedure is that the magnitude of the apparent stress depends on the displacement rate at which the test is performed and the height, or heights, selected for the comparison. Nevertheless, the magnitude of the apparent stress is directly determined and therefore is not based on any assumed rheological model. It also has a signi®cant advantage over purely empirical measures of consistency determined by instruments such as the Bostwick consistometer or the ``back extrusion'' cell. Being measured in specimens having a high diameter to height ratio and expressed in stress units its magnitude is much less aected by geometric artifacts. Also the validity of the apparent stress as a consistency measure can be experimentally veri®ed by comparing the values obtained with upper plates of dierent diameters.
219
2.1. Yield stress It is dicult to determine the yield stress of a semiliquid food by squeezing ¯ow viscosimetry performed at a constant displacement rate. (As already stated this can be done in a ``creep array'' (Campanella & Peleg, 1987a) where the displacement under a constant load is monitored. However standard commercial creep testers are not readily available and therefore it is doubtful that this method will gain popularity in food research in the near future.) Nevertheless, a relative estimate of the yield stress can be obtained by determining the residual apparent stress of the specimen at a given height, or several heights, after it has been allowed to relax for a given time e.g., rapp
@ 60 or 120 s
F@
60 or 120 s = pR
2
:
4
In imperfect squeezing ¯ow, the force exerted by ¯uids without a yield stress decays to the buoyancy force almost instantaneously. The higher the yield stress and more solid the structure the higher is the absolute magnitude of the residual force (or stress). The latter, therefore, can serve as a measure of solidity ± on the pertinent time scale ± and hence as an indicator of the yield stress. Such a measure has all the advantages and disadvantages of the apparent stress at a given height, and likewise its applicability can be veri®ed by repeating the tests with sensors of dierent geometries. 3. Experimental 3.1. Materials Jars of mustard of two national brands and a mustard product all containing pieces of mustard seeds were purchased at a local supermarket and tested at an ambient temperature of 23°C. Because no attempt has been made to establish how representative the samples were of their respective manufacturerÕs product the latter are not identi®ed by name. 3.2. Mechanical testing Specimens of the mustard were gently transferred from their original container into an all Te¯onR sensor having a ¯at container 140 mm in diameter using a large spoon to minimize disruption of the original structure. They were subsequently compressed by Te¯onR upper plates 100 and 120 mm in diameter (Fig. 3) as described by Honer, et al. (1997). The initial height of all the specimens, was about 6±7 mm in all the tests. Since only data at high compression ratios were considered, i.e., when the plates separation was less than about 4 mm, the slight initial variability in the specimen height has hardly any eect on the measurements ± theoretically
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Fig. 3. The all Te¯onR sensor used in this work ®lled with a mustard specimen containing seed parts.
and in practice. The compression was performed with a TA.TX2 Texture Analyzer (Texture Technologies Corp., Scarsdale, NY) equipped with a 25 kg load cell and interfaced with Gateway 2000 microcomputer. The specimens were compressed to a ®nal height of 0.5 mm at a speeds of 0.1 and 0.2 mm sÿ1 . At the end of each run the crosshead was stopped and the decaying force recorded for about 3 min before the crosshead was withdrawn. The raw data ®les were imported to and processed by the Systate 5.0 package (Systate, Inc., Evanston, IL). Each test was performed in four replicates. 3.3. Data processing The recorded raw data were converted into forceheight relationships plotted on linear and logarithmic coordinates (see below). The linear part of the logarithmic relationship was considered as representing the region of dominant squeezing ¯ow (Lorenzo, et al., 1997; Honer, et al., 1997) and its slope was determined by linear regression. The initial part of the ¯ow curves (corresponding to specimen heights of to about 4±7 mm) was considered as re¯ecting entry eects and therefore discarded. The apparent stress at a specimen height of 0.5, 1 and 2 mm, rapp@H 0:5 or 1 or 2 mm , was calculated by Eq. (3) and was used as a semi-empirical consistency measure. The force decay data were used to calculate an apparent residual stress using Eq. (6).
4. Results and discussion 4.1. The shape of the force-height relationship and the mustards consistency: Typical force-height curves of the three mustards plotted on linear and logarithmic coordinates are shown in Figs. 4 and 5. The curves were remarkably reproducible (see below) and enabled characterization of the products in terms of the various mechanical parameters listed in Table 1. The logarithmic curves had the expected characteristic shape. Their linear part allowed for clear identi®cation of the region where squeezing ¯ow had been the dominant ¯ow regime. The absolute magnitudes of the slopes of the linear parts of the logarithmic curves of the dierent mustards are listed in Table 1. The typical values were on the order of ÿ1.0 to ÿ0.8. Had these values corresponded to the ¯ow index, n, as in an ideal lubricated squeezing ¯ow, they would imply that the mustards were newtonian or almost newtonian ¯uids which obviously they are not. This was clearly evident in their response to a rate change and in their relaxation pattern (Fig. 6). Also had there been an appreciable friction between the specimens and the sensors surfaces the slope should have been much closer to ÿ3 than to ÿ1. A slope of ÿ1 is the theoretical lower limit of a power law ¯uid in frictional ¯ow and it would imply ideal plasticity with no rate sensitivity. This possibility too ought to have been ruled out (see Table 1) and hence neither Eqs. (1) nor (2) were used to calculate
T. Suwonsichon, M. Peleg / Journal of Food Engineering 39 (1999) 217±226
221
Fig. 4. Typical force ± height relationships in the imperfect squeezing ¯ow of the three mustards ± linear scale.
Fig. 5. Typical force ± height relationships in the imperfect squeezing ¯ow of three mustards ± logarithmic scale. (Note that the region where squeezing ¯ow was dominant can be clearly identi®ed from the linear part of plots.)
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Fig. 6. Typical relaxation curves of the three mustards tested. (Note the considerable residual stress even after 3 min.) Table1 Rheological parameters of commercial mustard determined by lubricated imperfect squeezing ¯ow Brand
Diameter (mm)
Speed (mm sÿ1 )
Slope
r 2 mm (kPa)
r 1 mm (kPa)
r @ t0s (kPa)
r @ t60s (kPa)
r @ t120s (kPa)
A
100
0.1 0.2 0.1 0.2
ÿ0.9 0.01 ÿ1.0 0.02 ÿ0.8 0.02 ÿ0.9 0.02
1.43 0.01 1.66 0.09 1.72 0.06 1.97 0.03
2.59 0.28 3.23 0.23 3.11 0.06 3.63 0.07
4.60 0.05 5.66 0.32 4.82 0.15 5.51 0.09
1.33 0.05 1.52 0.17 1.64 0.17 1.61 0.07
1.30 0.05 1.49 0.16 1.59 0.16 1.56 0.06
0.1 0.2 0.1 0.2
ÿ0.8 0.01 ÿ0.9 0.02 ÿ0.8 0.02 ÿ0.9 0.02
1.52 0.16 1.83 0.02 1.95 0.03 2.22 0.14
2.67 0.30 3.38 0.5 3.44 0.07 3.96 0.18
4.70 0.41 5.94 0.09 5.37 0.13 5.93 0.21
1.89 0.19 2.31 0.06 2.36 0.06 2.30 0.09
1.86 0.19 2.28 0.06 2.31 0.06 2.26 0.09
0.1 0.2 0.1 0.2
ÿ0.9 0.02 ÿ1.0 0.01 ÿ0.9 0.02 ÿ1.0 0.01
1.05 0.16 1.36 0.02 1.49 0.16 1.62 0.02
1.98 0.28 2.65 0.05 2.74 0.26 3.09 0.05
4.01 0.58 5.17 0.18 4.72 0.32 5.16 0.18
1.73 0.23 2.12 0.07 2.27 0.19 2.20 0.07
1.68 0.23 2.04 0.05 2.21 0.18 2.14 0.05
120
B
100 120
C
100 120
the mustards consistency coecient (K). Instead the apparent stresses at three selected heights (2, 1 and 0.5 mm) which had been determined directly were used as empirical measures consistency. 4.2. The tests reproducibility Despite the crudeness of the experimental array, the samples preparation and the specimens loading proce-
dure the measurements and the rheological parameters which they provided were remarkably reproducible (Table 1). This was irrespective of the product, the upper plateÕs diameter and the displacement rate. The measurements were sensitive enough to distinguish, clearly and consistently, between the three products irrespective of the test conditions as shown in Figs. 7 and 8. A similar degree of reproducibility has been observed in other products evaluated by this method (Lorenzo, et al.,
T. Suwonsichon, M. Peleg / Journal of Food Engineering 39 (1999) 217±226
223
Fig. 7. Comparison of the relative consistency of the three mustards on the basis of their apparent stress at three heights as determined with a sensor having an upper plate 100 mm in diameter.
1997; Honer, et al., 1997; Suwonsichon & Peleg, 1999). This demonstrates that since the plates are wide and the specimen height very small in comparison, any irregularity in the upper surface of the specimen at the beginning of the test can have only a very minor eect of the results. That there was a certain degree of textural variability among the samples also cannot be ruled out, and the same can be said about the specimens handling before testing. Nevertheless even the cumulative error produced by these factors had little in¯uence on the methodÕs ability to provide a consistent comparison between the products (Figs. 7 and 8). Whatever this error was it was smaller than the eect of the sensorÕs geometry and that of the compression rate (Table 1). 4.3. Diameter eects The apparent stresses determined with a sensor having an upper plate 120 mm in diameter were consistently higher than those obtained with an upper plate having 100 mm in diameter. The magnitude of the dierence
was generally on the order of about 30%. Similar differences were observed in other products (Honer, et al., 1997; Lorenzo, et al., 1997; Suwonsichon & Peleg, 1999). One can surmise that the higher values are more representative of the mustards actual consistency. This is because as the diameter of the plate increases the relative role of the annular ¯ow in the gap, and that of end effects diminishes (Damrau & Peleg, 1997). This implies that the wider the sensor and its gap the more reliable the measurement is. However, when the sensor is enlarged it becomes more dicult to guarantee that the upper plate and the containerÕs bottom are perfectly parallel, which can cause a signi®cant error. It therefore appears that a sensor with dimensions of those which were used in this work, although by no means, ideal is at least an acceptable practical compromise. (That the plates of the experimental sensors were indeed parallel to the containerÕs bottom was checked with a level.) An additional factor that ought to be considered in machines of the kind used in this work is that as the plates diameter is increased the absolute magnitude of
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Fig. 8. Comparison of the relative consistency of the three mustards on the basis of their apparent stress at three heights as determined with a sensor having an upper plate 120 mm in diameter.
the forces also increases. If the machine and/or sensor have even a slight compliance the tests results would be distorted. Compensation for such an eect can be done through programming, but it would always be safer to use a machine and sensor which are as rigid as possible.
ative magnitude of the ®rst component is re¯ected in the residual force, or stress, after relaxation and the second in the dissipated portion (see Fig. 6). According to this hypothesis the ratio between the forces when the speed is doubled, RF , would be approximately
4.4. Rate eects
RF F 2V =F V H const x 1 ÿ x2m ;
In the ideal case of lubricated squeezing ¯ow and according to Eq. (1), doubling the testing speed, V, for ¯uids with n 1 (the absolute magnitude of the slope of the log F(H) vs. log H relationship) will double the force at any given specimen height, H. According to Eq. (3) (ideal frictional ¯ow) if the absolute magnitude of the slope is one then 2n + 1 1 and n 0, which implies that there would be no rate eect al all. As can be seen in Table 1 neither was the case in the tested mustards. Doubling the speed from 0.1 to 0.2 mm sÿ1 did cause an appreciable increase in the force level but not to the extent predicted by Eq. (1). A hypothesis consistent with this observation is that the measured total force had a deformation and rate dependent components. The rel-
5
or m log RF ÿ x= 1 ÿ x= log 2;
6
where x is the fraction of the residual force after relaxation, 1 ÿ x the fraction of the dissipated force and m (0 6 m 6 1) a constant serving as a ``¯ow index'' of sort. (Special cases according to this equation are; a newtonian ¯uid (x 0, m 1) where RF 2, a ``bingham like ¯uid'' (x x0 , m 1) where RF x0 + 2(1ÿx0 ) and a ``pseudoplastic'' (``power law'') ¯uid without a yield stress (x 0, m m) where RF 2m .) Application of this model to the experimental ratios derived from Table 1 showed that the value of m, in all three products, was in the range of 0.2±0.6. The relation of this empirical index to the ¯ow index in shear is un-
T. Suwonsichon, M. Peleg / Journal of Food Engineering 39 (1999) 217±226
225
clear at this point but it is not unreasonable to expect that they will have a numerical value on the same order of magnitude. A true test of the hypothesis is whether the value of m remains the same for other speed ratios but this was outside the scope of this work. (When silicon oils were tested with the same cells, the forces ratio for speeds of 0.1, 0.2, 0.4, and 0.6 mm sÿ1 were 1 (by de®nition), 2.0, 3.7 and 5.6, respectively. Considering the test geometry these values can be considered as being close to the theoretical values of 1, 2, 4 and 6 for newtonian liquids squeezed between parallel plates of same diameter.) Obviously Eq. (5) is only an empirical approximation because it is based on the assumption that the residual stress after relaxation is rate independent. Although this was evidently the case where the data were obtained using the 120 mm upper plate (Table 1), there were a few noticeable discrepancies in the data obtained with the 100 mm plates (see Table). Also, although not observed in this study there is at least a theoretical possibility that deformation at an increased rate can cause more intensive structural damage and hence that the residual stress after relaxation will be inherently rate dependent. That this may happen in mustard at rates much higher than those used in this work is a possibility that cannot be ruled out. But as
stated this aspect was not investigated in the present study and hence it remains a conjecture and a topic for future research.
Fig. 9. Comparison of the relative consistency of the three mustards on the basis of their residual apparent stress after relaxation determined with a sensor having an upper plate 100 mm in diameter.
Fig. 10. Comparison of the relative consistency of the three mustards on the basis of their residual apparent stress after relaxation determined with a sensor having an upper plate 120 mm in diameter.
4.5. Yield stress A residual stress after relaxation ± well above the level caused by buoyancy ± is a clear indication that the tested ¯uid has a yield stress of considerable magnitude (Lorenzo, et al., 1997; Suwonsichon & Peleg, 1999). Fig. 6 and Table 1 show that all three mustard products indeed had an appreciable yield stress. (The buoyancy corresponding to the conditions under which the curves that appear in Fig. 6 were determined is on the order of 1N well below that of the residual force which was on the order of 10±35N). The residual apparent stresses of the three products tested are reported in Table 1 and are compared graphically in Figs. 9 and 10. The table and ®gures show that the products with the higher apparent stress at a given height, i.e., having a stronger consistency, also had a higher residual apparent stress after relaxation, i.e., a higher yield stress. The same was observed in products as variable as tomato concentrates (Lorenzo, et al., 1997) and refried beans (Suwonsichon
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T. Suwonsichon, M. Peleg / Journal of Food Engineering 39 (1999) 217±226
& Peleg, 1999) which is consistent with the notion that both the yield stress and consistency are a manifestation of the strength and integrity of the same microstructure or gel network. Comparison between the products on the basis of their residual stresses after relaxation (Figs. 9 and 10) gave the same ranking as that based on the apparent stress at any given height (Figs. 7 and 8). It therefore appears that at least for the products tested in this work all the mechanical parameters could be used interchangeably as consistency measures. Acknowledgements Contribution of the Massachusetts Agricultural Experiment Station at Amherst. The support of the work by the USDA-NRICGP, under Grant No. 9502429, is gratefully acknowledged. The authors also express their thanks to the Royal Thai Government for its support of T.S. References Aguilar, C., Rizvi, S. S. H., Ramirex, J. F., & Inda, A. (1991a). Rheological behavior of processed mustard I. Eect of milling treatment. J. Texture Studies, 22, 59±84. Aguilar, C., Rizvi, S. S. H., Ramirex, J. F., & Inda, A. (1991b). Rheological behavior of processed mustard II. Storage eects of milling treatment. J. Texture Studies, 22, 85±103. Avila, F., & Binding, D. M. (1982). Normal and reverse squeezing ¯ow. J. Non-Newtonian Fluid Mech., 11, 111±126.
Campanella, O. H. (1987). Rheological properties of semi-liquid foods. Ph D. Thesis, University of Massachusetts, Amherst. Campanella, O. H., & Peleg, M. (1987a). Determination of the yield stress of semi-liquid foods from squeezing ¯ow data. J. Food Sci. 52, 214±215 and 217. Campanella, O. H., & Peleg, M. (1987b). Squeezing ¯ow viscosimetry of peanut butter. J. Food Sci., 52, 180±184. Casiraghi, E. M., Bagley, E. B., & Christianson, D. D. (1985). Behavior of mozzarella cheddar and processed cheese spread in lubricated and bonded uniaxial compression. J. Texture Studies, 16, 281±301. Chatraei, S. H., Macosko, C. W., & Winter, H. H. (1981). Lubricate squeezing ¯ow. A new biaxial extension rheometer. J. Rheol., 25, 433±443. Damrau, E., & Peleg, M. (1997). Imperfect squeezing ¯ow viscosimetry of Newtonian liquids ± theoretical and practical considerations. J. Texture Studies, 28, 187±204. Honer, B., Gerhards, C., & Peleg, M. (1997). Imperfect lubricated squeezing ¯ow viscometry for foods. Rheol. Acta, 36, 686±693. Huang, H., & Kokini, J. L. (1993). Measurement of braxial extentional viscosity of wheat ¯our dough. J. Rheol., 37, 879±891. Lorenzo, M. A., Gerhards, C., & Peleg, M. (1997). Imperfect squeezing ¯ow viscosimetry of selected tomato products. J. Texture Studies, 28, 543±567. Ramõrez-Wong, B., Sweat, V. E., Torres, P. I., & Rooney, L. W. (1996). Evaluation of rheological properties of fresh corn masa using squeezing ¯ow viscometry : Biaxial extensional viscosity. J. Texture Studies, 27, 185±198. Soskey, P. R., & Winter, H. H. (1985). Equibiaxial extension of two polymer melts: Polystyrene and low density polyethylene. J. Rheol., 29, 493±517. Stee, J. F. (1992). Rheological Methods in Food Engineering. New York: Freeman Press. Suwonsichon, T., & Peleg, M. (1999). Imperfect squeezing ¯ow viscometry for commercial refried beans. Food Sci. Technol. Intnl. (in press).