Rheol Acta (2000) 39: 452±460 Ó Springer-Verlag 2000

Maria G. Corradini Veronique Stern Thongchai Suwonsichon Micha Peleg

Received: 1 November 1999 Accepted: 2 May 2000

M. G. Corradini á V. Stern T. Suwonsichon á M. Peleg (&) Department of Food Science Chenoweth Laboratory University of Massachusetts Amherst, MA 01003, USA Fax: 001-413 545 1262 e-mail: [email protected]

ORIGINAL CONTRIBUTION

Squeezing ¯ow of semi liquid foods between parallel Te¯on coated plates

Abstract Samples of commercial tomato paste, low fat mayonnaise and mustard about 6±8 mm thick were squeezed to 0.8 mm at various speeds between 5 mm min)1 and 25 mm min)1 between Te¯on-coated parallel plates 127 mm in diameter using an Instron UTM Model 5542. All the log force vs log height relationships had a clearly identi®ed linear region. This indicated that a dominant squeezing ¯ow regime was achieved at about 3 mm height, and that the machine has the proper sti€ness to perform the tests. The stress level at a pre-selected height in this region is a measure of consistency, sensitive enough to distinguish between products of di€erent brands. The residual stress after relaxation for about 2 min was on order of 10±50% of the initial stress, an indication that all three foods have a considerable structural integrity. In all three products there was a considerable discrepancy between the observed rate e€ects and

Introduction Lubricated squeezing ¯ow viscometry (Chatraei et al. 1981; Soskey and Winter 1985) was introduced to foods testing in the mid1980s (Casiraghi et al. 1985) and has since been applied to a variety of semiliquid food products (e.g., Campanella and Peleg 1987; Campanella et al. 1987; Bagley et al. 1990; Huang and Kokini 1993; Raminez Wong et al. 1996). The method o€ers a practical solution to two major

predictions based on a pseudoplastic (power law) model. It could be described by the empirical relation (Fv1 ) FR)/(Fv2 ) FR) ˆ (V1/V2)m where Fv1 and Fv2 are the forces at the given displacement reached at speeds v1 and v2 respectively, FR is the residual force after relaxation (found to be practically rate independent), and m is a constant of the order of 0.15±0.33, independent of the compression velocities ratio but characteristic of the food and brand. The calculated elongational viscosity was not a unique function of biaxial strain rate. To a certain extent, this was probably due to imperfect lubrication. But it was also a manifestation of these products considerable structural integrity which cannot be accounted for by models developed for ideal liquids. Key words Squeezing ¯ow á Viscometry á Elongational viscosity á Texture á Mayonnaise á Mustard á Tomato concentrates

problems that beset food viscometry, namely slip, and the inadvertent disruption of the specimen's structure upon its insertion into the narrow gap of conventional rheometers (Lorenzo et al. 1997; Ho€ner et al. 1997; Suwonsichon and Peleg 1999a±d). The mathematical analysis of ideal frictionless and frictional ¯ows of Newtonian liquids is well developed and so is that of pseudoplastic ¯uids having a power law state equation. The force-height relationship of a ¯uid pressed between parallel lubricated plates of an equal diameter moving

453

at a constant speed V (Fig. 1) is given by the following expressions. For a Newtonian ¯uid with a viscosity, l, (Chatraei et al. 1981; Soskey and Winter 1985): F ˆ 3plR2 V=H

…1†

and for a pseudoplastic ¯uid with a consistency, K, and ¯ow index n, (Campanella and Peleg 1987; Lee and Peleg 1990): …n‡1†=2

Fˆ3

2

pKR (V/H)

n

…2†

where F is the force, R the plates radius, and H the specimen's momentary height. Equations (1) and (2) entail that the slope of the log F vs log H relationship in lubricated squeezing ¯ow with the geometry shown in Fig. 1 is 1.0 if the liquid is Newtonian, and n < 1.0, if it is pseudoplastic. [The corresponding values for fully frictional ¯ow are 3.0 (Leider and Bird 1974a, b) and 2n + 1, respectively (Campanella 1987; Lee and Peleg 1990)]. In principle, once the frictionless character of the ¯ow has been established and the nature of the liquid determined from the slope of the log F vs log H relationship, the Newtonian viscosity, l, or the consistency and ¯ow index, K and n, can be calculated using

Fig. 1 Schematic view of a lubricated squeezing ¯ow sensor

Fig. 2 Schematic view of the expected elongational viscosity vs biaxial strain rate relationship of an ideal pseudoplastic ¯uid

Eqs. 1 or 2 as the case might be. A lubricated squeezing ¯ow test of the kind shown schematically in Fig. 1 also allows one, at least in principle, to calculate the ¯uid's elongational or biaxial viscosity, lb, as a function of the biaxial strain rate e_b , i.e., (Chatraei et al. 1981) e_b ˆ V=…2H†

…3†

and lb ˆ 2HF=…pR2 V†

…4†

By de®nition, a Newtonian ¯uid has no rate sensitivity in both shear and squeezing ¯ows. Hence, and as these equations also imply, the plot of lb vs e_b should be a horizontal straight line i.e., lb = 6l. For an ideal pseudoplastic ¯uid with a ¯ow index n the plot of lb vs e_b is expected to be curved. However, the log lb vs log e_b in this case should be a descending straight line with a slope of 1±n. The apparent elongational viscosity of a pseudoplastic ¯uid, like its apparent shear viscosity, is supposed to be a material property, albeit a rate dependent one. If so, the magnitude of lb is expected to be solely a function of the biaxial strain rate, e_b but not of the height-speed combination that has produced it. Or, in other words, under ideal test conditions the plots of lb vs e_b obtained in tests performed at di€erent constant speeds, Vs, should have the features shown schematically in Fig. 2. Newtonian and ideal pseudoplastic ¯uids are by de®nition liquids that, at rest, i.e., when the strain rate is zero, cannot retain stress. Thus, once the motion of the upper plate is topped in a squeezing ¯ow experiment, the force would be expected to drop instantaneously to zero. In reality, of course, the force never drops instantaneously. There is always a time delay, primarily determined by the crosshead deceleration and the system's response time. If accurately measured, the force may not drop to zero exactly

454

because of surface tension e€ects at the ¯uid's edge. But again, in most cases, this is only a negligible secondary e€ect that does not in¯uence the results interpretation. When certain foods were tested in an imperfect squeezing ¯ow array ± that is where a lower plate is replaced by a shallow container (Ho€ner et al. 1997) ± considerable deviations from the described behavior were observed (Suwonsichon and Peleg 1999a±c). The deviations were of such a magnitude that they could not be caused by annular ¯ow, buoyancy, structural disruption, and/or a faulty instrument. That all these factors could be safely excluded as being the cause of the discrepancies was con®rmed by comparison of the food results to those of mineral oils tested with the same sensor (see below). The deviations therefore were more likely due to that the Te¯on plates did not provide the desired degree of lubrication, failure of the power law model to describe these foods rheological properties, or both. Although Te¯on does not provide ideal lubrication, a Te¯on coating is probably still the most practical and e€ective way to obtain non-sticky surfaces, especially in sensors to be used in routine industrial quality control. It has therefore become necessary to reexamine the performance of squeezing ¯ow viscometry using Te¯on coated plates as a practical tool to assess the consistency of semiliquid foods. The objective of this work was to evaluate the e€ects of the test conditions, especially those of the displacement rate, on the measured rheological parameters of three common commercial food products.

Materials and methods Materials and sample preparation Commercial mustard, low fat mayonnaise, and tomato concentrate of di€erent national brands were purchased at a local supermarket. They were stored in the laboratory and tested immediately after their container had been opened, at an ambient temperature of about 22 °C. Because no e€ort was made to establish how representative the samples were of their respective manufacturers' products they are only identi®ed by a letter. It has been previously realized (Suwonsichon and Peleg 1999c) that careful transfer of a semiliquid food specimen from the container to the squeezing ¯ow sensor using a large spoon, or wide spatula, causes only very slight damage to its internal structure, if at all, and hence has a negligible e€ect on test results (see below). The same applies to an uneven specimen height at the beginning of the test. Because a fully developed squeezing ¯ow regime is only obtained when the specimen height is squeezed to about 3 mm (see below) any initial irregularity only a€ects the transient ¯ow regime. With these considerations in mind, the foods were gently removed from their containers using a wide shallow spoon and placed, almost intact, at the bottom plate of the sensor to form a specimen having an initial height of 6±8 mm. In a separate set of experiments, three silicon oils having di€erent viscosities, Viscosil 5 M, 10 M, and 12 M (General Electric, Waterford, NY), were tested as reference ¯uids. Instrumentation All the food samples were compressed between Te¯on coated steel plates 127 mm in diameter, mounted on an Instron UTM model 5542 (Instron Corp., Canton, MA) with a

500-Newton load cell, interfaced with a Gateway 2000 computer. The compression rates were 5, 10, 15, 20, and 25 mm min)1, and the ®nal specimen height was set to 0.8 mm in all the experiments. After this height had been reached, the specimen was allowed to relax for little more than 2 min prior to the crosshead withdrawal. The digitized force-height and force-time relationships, in the compression and stress relaxation stages respectively, were recorded and saved. They were subsequently analyzed and plotted using the Systat 8.0 statistical package (Systat Inc., Evanston, IL). The mineral oils were tested in an imperfect array (i.e., with a sensor in which the ¯at bottom plate had been replaced by a shallow Te¯on container, to avoid spilling) as described by Ho€ner et al. (1997). All the tests were performed in 4±5 replicates and their results are reported as mean values with the corresponding standard deviation in parentheses.

Results and discussions Typical experimental force-height relationships at two compression rates and corresponding relaxation curves of the three products are shown in Figs. 3±5. Examples of the logarithmic plots of the force height relationship are shown in Figs. 6±8. They all had a linear region starting at a corresponding height of about 3±4 mm. Thus all the data points obtained at a specimen height above this range were considered as re¯ecting transient e€ects and consequently discarded. The absence of any visible curvature in the small height region is also an indication that the Instron UTM has the proper rigidity to perform such tests and that, unlike certain other instruments used in food research, correction for the machine's own compliance is not needed. The slopes of the log F vs log H relationships were in the range of 0.9± 1.2 in all three products and appeared to be rate independent (see Tables 1±3). The textural consistency of the tested products was primarily expressed in the absolute magnitude of the developed stresses. It could be assessed by comparison of the stress magnitude at a preselected height or heights, in the region where squeezing ¯ow was prominent, i.e., where the log F vs log H relationship was clearly linear. Obviously, the smaller the specimen's height the larger the corresponding stress. Hence, lowering the ®nal specimen's height makes the apparent stress a more sensitive measure of the ¯uid's consistency. Nevertheless, the specimen's height cannot be reduced inde®nitely. When it reaches levels considerably smaller than about 1 mm, any imperfection in the plates' parallel alignment can cause an appreciable distortion of the results. As shown in Tables 1±3, the tests' reproducibility, despite the crudeness of the specimen loading procedure, was on the order of about 10% or less when expressed as a coecient of variation (i.e., the standard deviation divided by the mean). The reproducibility of the results was about the same as that found in mineral oils (see below) and seems to represent the overall accuracy of the method. Since mineral oils have no internal structure, a similar reproducibility in

455

Fig. 3 Typical force vs time curves of commercial tomato paste (Brands A and B) squeezed at two speeds (5 and 25 mm min)1)

foods that do is a clear indication that transferring these foods from their containers by the described procedure caused only negligible damage to their microstructure. Had any appreciable damage been caused, it would have been impossible to reproduce it in detail, and the scatter of the results should have increased dramatically. One must conclude, therefore, that the specimens were indeed tested practically intact, and that the method was suciently sensitive not only to distinguish between the foods but also to monitor di€erences between products of di€erent brands (Tables 1±3). The typical stress relaxation pattern of the compressed specimens is shown in Figs. 3±5. In all three products the samples retained a considerable residual stress after more than 2 min. The magnitude of the residual stress was on the order of 10±50% of the initial stress, and was only slightly a€ected by the preceding Fig. 4 Typical force vs time curves of commercial low fat mayonnaise (Brands A and B) squeezed at two speeds (5 and 25 mm min)1)

compression rate if at all (Tables 1±3). In comparison with the initial stress decay rate, the one observed after 1±3 min was extremely small. Thus the residual stress level, at a given height and time, could also be considered as a measure of the structural integrity of the food in question (Suwonsichon and Peleg 1999a±c). The existence of a considerable residual stress was most probably an indication that, on the experimental time scale, all three foods have a considerable yield stress. [This is of course also evident from the fact that small quantities of these products do not continuously ¯ow under their own weight.] The rate insensitivity or practical insensitivity of the residual stress may also indicate that compression between Te¯on plates in itself causes relatively little damage to the specimens' internal structure. This was not totally unexpected because, ideally, frictionless compression does not produce shear.

456

Fig. 5 Typical force vs time curves of commercial mustard (Brand A and B) squeezed at two speeds (5 and 25 mm min)1)

Had the tested foods been pseudoplastic ¯uids, the rate e€ects should have been predicted by Eq. (2). This was

obviously not the case in all three products (Tables 1±3), and the disagreement cannot be explained as being caused just by a slight deviation from pseudoplasticity. The magnitude of the discrepancy suggests that all the samples had partial solidity, a characteristic consistent with the considerable residual stress after relaxation. The rate e€ect was therefore assessed in the following manner. It was assumed that the stress has two major components; one the residual stress after-relaxation which represented

Fig. 6 Typical force vs height relationships of tomato paste (Brands A and B) plotted on logarithmic coordinates. (Note the linear region)

Fig. 7 Typical force vs height relationships of low fat mayonnaise (Brands A and B) plotted on logarithmic coordinates. (Note the linear region)

[A partial support for this observation comes from the results of tests in which the specimens were subjected to successive compression cycles.] Characterization of the rate e€ects

457

the specimen's solidity, and the other (the dissipated stress) which is expected to be rate dependent. The solid part is not an elastic component in the conventional sense, i.e., its magnitude is not proportional to the displacement. It represents, at least in principle, the ability of the deformed structure to maintain or recover its integrity after the ¯ow. It is reminiscent of a yield stress of sheared liquid observed after the shearing seizes. According to this oversimpli®ed model the relation between forces recorded at the same height at two di€erent speeds V1 and V2, can be approximated by an empirical relationship (Corradini and Peleg 2000): …FV2

Fig. 8 Typical force vs height relationships of mustard (Brands A and B) plotted on logarithmic coordinates. (Note the linear region)

FR † ˆ …V2 =V1 †m

FR †=…FV1

…5†

where FV2 and FV1 are the forces measured at speeds V1 and V2 respectively, FR is the residual unrelaxed force at the corresponding height, (assumed to be roughly constant), and m a constant. Special cases according to this crude model are a Newtonian liquid where FR ˆ 0 and m ˆ 1 and hence FV2/FV1 ˆ V2/V1, and an ideal pseudoplastic ¯uid where FR ˆ 0 and m ˆ n, the ¯ow index and hence FV2/FV1 ˆ (V2/V1)n. The value of FR was directly determined from the stress relaxation curves. As shown in Tables 1 and 3, in almost all cases it indeed remained fairly constant at the

Table 1 Rheological parameters of tomato paste (Brands A and B) Brand

Speed (mm min)l)

Slope

A

5 10 15 20 25

)0.99 )0.95 )0.93 )0.92 )0.91

‹ ‹ ‹ ‹ ‹

B

5 10 15 20 25

)1.03 )0.99 )1.03 )0.99 )0.99

‹ ‹ ‹ ‹ ‹

App. stress @2 mm (kPa)

App. stress @1 mm (kPa)

App. stress @0.8 mm (kPa)

App. stress @60 s (kPa)

App. stress @120 s (kPa)

0.01 0.01 0.02 0.03 0.05

6.4 7.4 7.9 8.4 8.6

‹ ‹ ‹ ‹ ‹

0.2 0.4 0.4 0.4 0.3

12.8 14.3 15.2 16.0 16.4

‹ ‹ ‹ ‹ ‹

0.4 0.6 0.8 0.5 0.4

15.6 17.4 18.3 19.3 19.8

‹ ‹ ‹ ‹ ‹

0.5 0.7 0.8 0.3 0.6

4.3 4.2 4.2 4.2 4.1

‹ ‹ ‹ ‹ ‹

0.3 0.2 0.3 0.2 0.1

4.0 3.9 3.9 3.9 3.7

‹ ‹ ‹ ‹ ‹

0.3 0.2 0.3 0.2 0.2

0.04 0.03 0.03 0.05 0.02

4.2 4.6 4.9 5.1 5.1

‹ ‹ ‹ ‹ ‹

0.2 0.6 0.4 0.2 0.6

8.9 9.8 10.1 10.9 11.0

‹ ‹ ‹ ‹ ‹

0.2 0.4 0.5 0.6 0.6

11.1 11.9 12.5 13.3 13.4

‹ ‹ ‹ ‹ ‹

0.5 0.5 0.6 0.7 0.7

3.1 2.8 2.9 2.5 2.7

‹ ‹ ‹ ‹ ‹

0.4 0.3 0.2 0.1 0.3

2.9 2.6 2.7 2.3 2.6

‹ ‹ ‹ ‹ ‹

0.4 0.2 0.3 0.2 0.3

Table 2 Rheological parameters of low fat mayonnaise (Brands A and B) Brand

Speed (mm min)l)

Slope

A

5 10 15 20 25

)0.96 )0.98 )0.99 )1.01 )1.03

‹ ‹ ‹ ‹ ‹

0.04 0.01 0.01 0.01 0.03

3.7 4.1 4.4 4.5 4.6

‹ ‹ ‹ ‹ ‹

0.1 0.1 0.1 0.1 0.1

7.3 8.0 8.7 9.0 9.4

‹ ‹ ‹ ‹ ‹

0.1 0.1 0.3 0.2 0.1

8.9 9.8 10.8 11.3 11.8

‹ ‹ ‹ ‹ ‹

B

5 10 15 20 25

)1.06 )1.08 )1.07 )1.06 )1.08

‹ ‹ ‹ ‹ ‹

0.02 0.01 0.01 0.01 0.01

4.1 4.7 5.1 5.4 5.7

‹ ‹ ‹ ‹ ‹

0.1 0.1 0.1 0.1 0.3

8.2 9.8 10.7 11.3 11.9

‹ ‹ ‹ ‹ ‹

0.2 0.2 0.1 0.2 0.1

10.2 12.3 13.4 14.1 14.9

‹ ‹ ‹ ‹ ‹

App. stress @2 mm (kPa)

App. stress @1 mm (kPa)

App. stress @0.8 mm (kPa)

App. stress @60 s (kPa)

App. stress @120 s (kPa)

0.2 0.1 0.4 0.2 0.1

4.6 4.5 4.6 4.4 4.4

‹ ‹ ‹ ‹ ‹

0.2 0.1 0.2 0.1 0.1

4.5 4.5 4.6 4.4 4.4

‹ ‹ ‹ ‹ ‹

0.2 0.1 0.2 0.1 0.1

0.2 0.3 0.3 0.2 0.2

3.2 3.0 3.0 2.9 2.9

‹ ‹ ‹ ‹ ‹

0.3 0.1 0.1 0.1 0.1

3.1 3.0 2.9 2.8 2.8

‹ ‹ ‹ ‹ ‹

0.3 0.1 0.1 0.1 0.1

458

Table 3 Rheological parameters of mustard (Brands A and B) Brand

Speed (mm min)l)

Slope

App. stress @2 mm (kPa)

App. stress @1 mm (kPa)

A

5 10 15 20 25

)1.05 ‹ 0.01 )1.07 ‹ 0.02 )1.07 ‹ 0.02 )l.07 ‹ 0.01 )1.10 ‹ 0.02

1.2 1.4 1.5 1.6 1.7

‹ ‹ ‹ ‹ ‹

0.1 0.1 0.1 0.1 0.1

2.4 2.9 3.2 3.4 3.5

‹ ‹ ‹ ‹ ‹

0.1 0.2 0.1 0.1 0.1

3.0 3.6 3.9 4.2 4.4

‹ ‹ ‹ ‹ ‹

B

5 10 15 20 25

)1.14 )1.16 )1.16 )1.20 )1.23

1.4 1.6 1.7 1.8 2.0

‹ ‹ ‹ ‹ ‹

0.1 0.1 0.1 0.1 0.1

3.0 3.4 3.7 4.1 4.6

‹ ‹ ‹ ‹ ‹

0.2 0.2 0.2 0.3 0.2

3.8 4.5 4.9 5.4 5.9

‹ ‹ ‹ ‹ ‹

‹ ‹ ‹ ‹ ‹

0.07 0.04 0.03 0.05 0.03

range of the speeds tried. If Eq. (5) truly captures the rate e€ect, then the magnitude of m should be independent of the speeds ratio. This could be veri®ed by comparing the magnitudes of the calculated m values from tests performed at di€erent compression rates. The value of m can be conveniently calculated from m ˆ log‰…FV2

FR †=…FV1

FR †Š= log‰V2 =V1 Š

App. stress @60 s (kPa)

App. stress @120 s (kPa)

0.1 0.2 0.2 0.1 0.1

0.7 0.7 0.6 0.5 0.3

‹ ‹ ‹ ‹ ‹

0.04 0.06 0.07 0.04 0.06

0.7 0.7 0.6 0.5 0.3

‹ ‹ ‹ ‹ ‹

0.04 0.05 0.07 0.04 0.07

0.2 0.2 0.2 0.3 0.2

0.8 0.7 0.6 0.6 0.6

‹ ‹ ‹ ‹ ‹

0.07 0.05 0.06 0.06 0.03

0.8 0.6 0.6 0.6 0.6

‹ ‹ ‹ ‹ ‹

0.05 0.04 0.05 0.07 0.03

compression rate, but characteristic of the product and brand. The m values were all on the order of 0.15±0.33, well below the characteristic ¯ow index of typical pseudoplastic ¯uids. They may therefore indicate that the ¯ow pattern of the three foods tested was primarily governed by their plasticity (see below).

…6†

Calculated values of m for four speeds ratios (corresponding to speeds 5, 10, 15, 10, and 25 mm min)1) are listed in Table 4. In all six cases, the resulting values were fairly constant, i.e., practically independent of the Table 4 Mean magnitudes of the index m calculated from di€erent tests Mayonnaise

App. stress @0.8 mm (kPa)

Speed ratio

Tomato paste

Mustard

1 2 3 4

0.21 0.19 0.20 0.19

0.13 0.14 0.17 0.15

0.27 0.33 0.31 0.31

0.37 0.33 0.31 0.31

0.32 0.29 0.29 0.29

0.29 0.28 0.30 0.32

Mean

0.20

0.15

0.31

0.33

0.30

0.30

Brand A Brand B Brand A Brand B Brand A Brand B

Rate e€ects on mineral oils The observed behavior of the three foods, as already stated, was very unlikely to be a result of instrumental artifacts. Support for this view comes from tests performed on three silicone oils which are summarized in Table 5. The coecient of variation in these tests was on the same order of magnitude, i.e., it rarely exceeded 10% and in most cases was below 5%. Being Newtonian or approximately Newtonian, the oils were not expected to slip, and the stress at a given height was expected to be proportional to the compression rate. As can be seen in the table, this was indeed the case. The slight deviations from the theoretical values can be attributed to buoyancy, annular ¯ow, and end e€ects which were created by replacing the bottom plate with a shallow container.

Table 5 E€ect of speed on the apparent stress of squeezed silicone oils (Force @ 1 mm (N) of silicone oils of various viscosities) Speed (mm s)1)

5M Plates diameter

l0M Plates diameter

12 M Plates diameter

100 mm

120 mm

100 mm

120 mm

100 mm

120 mm

0.1

7.3 ‹ 0.78 (1.0)a

12.7 ‹ 0.99 (1.0)

11.9 ‹ 0.49 (1.0)

20.3 ‹ 0.71 (1.0)

15.1 ‹ 0.14 (1.0)

23.1 ‹ 1.41 (1.0)

0.2

14.2 ‹ 0.21 (1.9)

20.1 ‹ 0.14 (1.6)

23.9 ‹ 0.99 (2.0)

41.1 ‹ 1.63 (2.0)

31.0 ‹ 2.83 (2.1)

47.4 ‹ 0.57 (2.1)

0.4

29.8 ‹ 0.35 (4.1)

42.0 ‹ 1.41 (3.3)

45.3 ‹ 0.42 (3.8)

80.3 ‹ 0.42 (4.0)

53.0 ‹ 0.00 (3.5)

91.3 ‹ 2.47 (4.0)

0.6

48.6 ‹ 2.26 (6.5)

76.8 ‹ 1.70 (6.0)

66.7 ‹ 2.62 (5.6)

112.5 ‹ 0.71 (5.5)

73.8 ‹ 1.77 (5.0)

120.52 ‹ 2.12 (5.2)

a

Ratio of force at the indicated speed to force at 0.1 mm s)1 under the same testing conditions.

459

Fig. 9 Typical apparent elongational viscosity vs strain rate relationships of tomato paste (Brands A and B) squeezed at three di€erent speeds (5, 15, and 25 mm min)1)

Fig. 10 Typical apparent elongational viscosity vs strain rate relationship of low fat mayonnaise (Brands A and B) squeezed at three di€erent speeds (5, 15, and 25 mm min)1)

Fig. 11 Typical apparent elongational viscosity vs strain rate relationship of mustard (Brands A and B)

460

Elongational viscosity Typical plots of calculated elongational viscosity vs the biaxial strain rate relationships of the three foods studied in this work are shown in Figs. 9±11. They clearly demonstrate that in, all the samples, the elongational viscosity calculated with Eq. (4) was not a unique function of the strain rate when calculated using Eq. (3) (compare to Fig. 2). Qualitatively the observed behavior re¯ects an intermediate ¯ow pattern between that of pure plasticity …lb / 1=e_b † and pseudoplasticity …lb / 1=e_1b n † and hence is consistent with the observed rate dependence of the stresses (see above). But since imperfect lubrication could also be a factor, at least theoretically, a direct relationship between the two could not be established. (If frictional forces are signi®cant, a shear free deformation is no more the case and Eqs. (3) and (4) may become irrelevant.)

Conclusion Squeezing ¯ow between wide Te¯on-coated plates seems to be a convenient and practical method to assess the consistency of semiliquid foods primarily because they leave the specimen practically intact. Despite the described tests' crudeness, the reproducibility of their results was sucient to monitor

di€erences and similarities between products and brands. The three foods tested all have a rate dependence and stress relaxation pattern that depart considerably from those expected from a typical pseudoplastic ¯uid. The rate e€ects can be characterized by an empirical model based on the assumption that only a portion of the stress, that which relaxes when the ¯ow is halted, has a power law relationship with the compression rate. The validity of this hypothesis was veri®ed experimentally, and it was found that the power is on the order of 0.15±0.33 and characteristic of the product and brand. Plots of elongational viscosity vs biaxial strain rate relationships calculated using the standard equations for lubricated squeezing ¯ow demonstrated that the apparent elongational viscosity is not a unique function of the strain rate as expected from ideal ¯uids. This can be primarily attributed to these foods' structural integrity and considerable plasticity, and partially attributed to the existence of a certain degree of friction between the specimen and plates, despite the fact that the latter had a Te¯on coating. Acknowledgements The support of the work by the USDANRICGP under grant No. 9502429 is gratefully acknowledged. The authors also express their thanks to the Instron Corporation for contributing the coated plates for the study, to the General Electric Corporation for donating the silicone oils, and to the Fulbright program for its support of M.G. Corradini.

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