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TEXTURE PROFILING WITH THE VANE: A GENERAL METHOD FOR CHARACTERISING THE RHEOLOGY OF SHEAR-SENSITIVE SOFT FOODS Alan Parker*, Florence Vigouroux Department of Food Science & Technology, Corporate R & D Division, Firmenich SA, 7 rue de la Bergère, CH-1217 MEYRIN 2 GENEVA, Switzerland *Author to contact:
[email protected]
ABSTRACT The key problem in characterising the rheology of shearsensitive soft food is that placing the sample in a conventional rheometer partially destroys the structure that we want to quantify. The vane geometry is the only solution to this problem. A high throughput, low cost methodology is described for making very reproducible measurements using the vane. A stress growth measurement at low shear rate is a rich source of rheological information that can be used to “fingerprint” samples. The results can be correlated empirically with the perceived texture of soft foods. However this data cannot be interpreted unambiguously. In particular, the yield stress cannot be determined. Three protocols are described which give more information. The results can be used together with structural modelling to give an interpretation in terms of rheological parameters, which is at least semi-quantitative.
1 INTRODUCTION Measurement of the texture of food is straightforward, in principle, in two limits: 1) for liquid foods, viscometry can be used and 2) for selfsupporting solids, texture profiling (e.g. penetrometry) can be used. However, between these two there is the important class of soft foods that pose difficult experimental problems. Soft foods include yoghurt, sauces and dairy desserts. The rich variety of their perceived textural properties is due to a mixture of viscoelasticity, thixotropy, yield and fracture. Typically, differences that are easily perceived when manipulating the food with a spoon are difficult to characterise using a rheometer. This paper explains how the vane [1] can be used as a general method for characterising the texture of soft foods. We call the methodology “Texture Profiling with the Vane”, TPV. The vane is a multi-bladed bob, which is inserted into the sample and then rotated about its axis to make rheological measurements.
Figure 1 Form of vane geometry used
When the vane is inserted into a sample, it only causes damage close to the blades. When it is rotated, the material stressed is between the unstressed solid cylinder of sample that moves with the blades and the outer wall of the recipient. Therefore, the material tested is completely undamaged by the introduction of the vane into the sample. Our first aim is pragmatic. For most purposes in the food industry, comparative measurements are sufficient. The fact that the data is not absolute is not fatal for most practical applications. The key problem in measuring the rheology of soft foods is that placing the sample in the rheometer partially destroys the structure that we want to measure. The first key point of this paper is that: 1) the only answer to this problem is the vane geometry. In consequence, whatever problems of calibration and interpretation using the vane may pose, we have to learn to live with them, as there is no alternative. Often, the vane is rotated at a constant low rate and the maximum torque is identified as proportional to the yield stress. Barnes and Nguyen [1] point out that several other definitions are possible. For yield stress fluids it is reasonable to assume that the maximum stress is proportional to the yield stress, however this is not true in general. The second key point that we want to make is that: 2) In stress growth measurements with the vane, interpretation of the maximum stress, or any other feature, as corresponding to the yield stress is an assumption, which must be justified on a case-by-case basis. This point of view can be justified by the observation that many experiments on fluids without a yield stress have shown overshoots. Moreover, realistic rheological models without a yield stress can generate curves with overshoots, in particular models that combine viscoelasticity with thixotropy [2]. In stress growth measurements of fluids with no yield stress, the “overshoot” peak is due to the superposition of two phenomena: the rising stress
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due to viscoelastic relaxation and the falling stress due to the viscosity decrease caused by thixotropy. A maximum occurs because the relaxation time for the viscoelasticity is typically much shorter than the relaxation time for thixotropy. In his review of thixotropy [3] Barnes explains overshoots in a similar way and shows schematic curves for products which are both viscoelastic and thixotropic, but without a yield stress (fig. 7 in reference [3]). Quemada’s structural approach makes these observations quantitative and allows the same model to be used to compare measurements made with different protocols. Fig. 2 shows some typical calculated overshoots for thixoelastic fluids with no yield stress. Note the similarity of these curves with the experimental data shown in fig. 4. They were calculated using the simplest model for a thixoelastic liquid: the MaxwellQuemada model [4], which has a constant elasticity. The Maxwell model has two parameters, the elasticity (G) and the viscosity (η). Quemada made the viscous element time-dependent, by substituting a thixotropic model [5]. The relaxation time in the Maxwell model is a constant given by η/G, whereas in the Maxwell-Quemada model it is timedependent, with a maximum value when the structure is complete.
changes from batch to batch and from week to week. 4) the vane provides the only practical way to follow the texture of soft foods over their shelf life, because it is the only measurement geometry that allows in-situ measurements. As we pointed out above, the varied texture of soft foods means that a single stress growth curve must be interpreted with great care. A series of measurements must be made to get more information. We use three protocols to do this: 1) make measurements at different shear rates, 2) follow the stress relaxation after stopping rotation at different points on the stress growth curve and 3) make strain growth (creep) measurements corresponding to different points on the stress growth curve. We do not use protocols involving ramps because the confounding of the experimental time scale with those of the sample makes unambiguous interpretation of the results very difficult.
2 EXPERIMENTAL We have developed the TPV methodology over a number of years. Using the various improvements described below, we routinely obtain coefficients of variation from sample-to-sample of less than 2%. The vane was custom built with four blades with a radius of 11mm, and a height of 24 mm. Vanes usually have rectangular blades, which greatly deform gelled samples, before penetrating. This shape gives poor reproducibility and leads to a long wait for sample relaxation. To minimise these problems our vane has its lower edges sharpened and angled at 30° to the horizontal to form an arrowlike point. These features make it easier to insert into rubbery or brittle samples. It enters the sample smoothly causing little deformation.
Figure 2 Overshoot curves for thixoelastic fluids with no yield stress. Calculated with constant equilibrium flow curve.
More than ten years ago, Sherwood, Meeten and co-workers [6] showed that the vane could be calibrated to determine rigorously the elastic modulus of weak solids. Because the elastic modulus is a linear property, it can be determined in an arbitrary geometry, just as a Newtonian viscosity can be. This conclusion leads to: 3) We can always obtain absolute values for the elastic modulus and the Newtonian viscosity by making measurements with the vane directly in the product as sold. A hard problem in the production of soft foods is shelf life testing. We need to track how the texture
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This vane was fitted to a Haake VT 550 viscometer and to TA instruments AR1000 and Physica MR300 stress controlled rheometers. The advantage of the Physica is that it can be used for both constant shear stress and constant shear rate measurements. Combining the two kinds of measurement is vital to complete understanding of the rheology of soft foods. Samples measured at room temperature (20C ± 1) were stored for at least one night. Those prepared in cylindrical containers were automatically centred and held in place using a three armed lens clamp (E053-038 Edmund Optics). For this study, samples were prepared in disposable plastic pots. These fitted into the outer part of a Couette geometry, which controlled the temperature at 6C, their storage temperature. The pots have an
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internal diameter of 33mm. They were filled to a depth of 35mm. The vane was positioned with its upper surface coincident with the sample surface. We found that gentle centrifugation using a swing out rotor was a good method to remove bubbles from more elastic samples. This geometry (vane + pot) was calibrated by the method of Sherwood and Meeten [6]. The torque (Γ) was measured at a range of rotation rates ( Ω ) and wetted heights of the vane, using a silicone oil of known viscosity, η. A plot of
Γ
Ωη
against wetted height should be a
straight line whose slope and extrapolation to zero torque can be used to calculate the radius and height, respectively, of the effective cylinder equivalent to the vane [7]. Fig. 3 shows the resulting plot for three rotation rates and seven unwetted heights.
as the rate at which the vane is inserted is controlled in software. However, this is not true for the VT550 viscometer. The simplest method is to raise the sample into the vane, using a small lab lift. The lift has to be chosen with care, to avoid play and to ensure that its movement is smooth and perfectly vertical. For convenience and more reproducible results, a computer-controlled lift, raised by a stepper motor was used (custom built by CAD Instrumentation, France). The start position, stop position and rate of lift were all user-defined. Control and data acquisition for the Haake viscometer and sample lift were made using a PC, running customwritten Microsoft Excel macros and Measure (National Instruments) software.
3 RESULTS & DISCUSSION 3.1 Standard protocol The basic TPV method is to rotate the vane in the sample at 0.1 rpm for a few minutes and plot torque as a function of time. Our fifth key point is: 5) Stress growth measurements with the vane provide comparative data that is a rich and unique source of information on the texture of soft foods.
The linear plot gave the following parameters: radius of effective cylinder = 10.1mm, height of effective -1 cylinder = 19.2mm, shear rate factor = 3.1rad , -3 shear stress factor = 80,700m . Note that the effective radius is smaller than the radius of the vane (11mm). In their review, Barnes and Nguyen [1] discuss several studies where an effective radius greater than the geometric radius was used, whereas Baravian et al [7] found that it was less, being approximately equal to the height of the triangle formed by adjacent blades. These differences are probably due to different gap widths. These conversion factors are only applicable to linear viscoelastic and Newtonian materials. We realise that determining the correct conversion factors for shear thinning [7], thixotropic and yield stress fluids is an important and complex issue. However, simply for convenience of presentation, we have used them to convert all the raw data into apparent shear stress and shear rate. The method of inserting the vane into the sample has a great influence on the quality of the results. For sophisticated rheometers, this is not a problem,
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Yoghurt - LC1 Apparent stress (Pa)
Figure 3 Calibration plot for vane in standard cylindrical 2 pot. Line is the best linear fit (R = 1.00)
Fig. 4 shows some typical experimental data. The overall shape is characteristic of the sample. The peak may be quite pointed, like the yoghurt, or it may be more or less rounded, like the Danette (a Danone cold-fill dairy dessert). The maximum may be at shorter or longer times. The level of the curve at long times may be higher or lower relative to the peak. In other cases, not shown, regular oscillations appear after the peak, due to fracture at large deformation. Often, these features cannot be interpreted in exact rheological terms, but they can be correlated with specific features of the texture and we have found that the raw data is a very useful tool for product development and quality control.
50
Vanilla Danette 40 30 20
Yoghurt - Bifidus
10
Chocolate Danette
0 0
40
80 120 Time (s)
160
200
Figure 4 Typical TPV data for dairy desserts. Apparent -1 shear rate = 0.03s
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3.2 Stress growth & relaxation A series of samples are used to make stress relaxation measurements that start at different points on the stress growth curve. For an ideal yield stress fluid, the relaxation curve will be horizontal below the yield stress as the sample acts as a solid. The figure below shows some typical data, obtained for Vanilla Danette.
3
80 60
0.3 40
0.03 0.003
20 0
30
0
20
2
4 6 8 Apparent Strain
10
12
Figure 6 Vanilla Danette: Stress growth for various shear rates. Number next to each curve is the apparent shear -1 rate in s .
10
0 0
50
100
150
200
250
Time (s)
Figure 5 Vanilla Danette: Stress growth with no relaxation compared with stress relaxation after five different times -1 of stress growth. Apparent shear rate = 0.03s
3.4 Strain growth and relaxation The vane is usually used with the rotation rate controlled, but it can also be used with controlled stress instruments. Fig. 7 shows strain growth and relaxation data obtained from Vanilla Danette. Even at the lowest stresses, we do not see the behaviour expected for a solid: a horizontal curve during application of stress followed by relaxation back to zero compliance. There is once again no evidence for a yield stress, even at the extremely low stresses applied here. 40
-1
We note three points: 1) The high reproducibility leads to almost perfect superposition of the data from the six separate samples. 2) Stress relaxation is always present, so even the shortest time of stress growth is sufficient to pass the yield stress, if there is one. 3) Relaxation of the sample stressed close to the maximum stress is fast compared to that of the less stressed samples. Its relaxation curve crosses those of the two samples stressed for shorter times. This feature is perfectly reproducible and we have observed it for other samples. However, we cannot interpret it at the moment.
We note that we have not reached a maximum stress that is independent of the shear rate. This observation emphasises that the yield stress cannot be assumed to be the overshoot maximum at an arbitrary low shear rate. A series of experiments is essential.
Apparent compliance (mPa )
Apparent stress (Pa)
40
Apparent Stress (Pa)
100
3.3 Stress growth as a function of shear rate This protocol is essential for correct determination of the yield stress with the vane [8]. However, the data also contains a lot of information on the sample’s thixoelastic properties [2]. Fig. 6 above shows typical measurements using the same product as for fig. 5.
24 16
30
4
20
0.04, 0.16 & 0.8 10
0 0
20
40 60 Time (s)
80
100
Figure 7 Vanilla Danette: Strain growth and relaxation. Number next to each curve is the apparent applied stress in Pa.
The data show damped oscillations, both at the start of strain growth and at the start of strain relaxation. The presence of oscillations shows that the samples
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are elastic [9]. The oscillations at the start of strain growth are shown in more detail in fig. 8 below. Apparent compliance (mPa -1)
25
24 16
20
4 15 0.04, 0.16 & 0.8
10
Although TPV has only been applied here to soft food, it obviously has much wider applications for quantifying the rheology of other soft solids such as cosmetics, paints and pharmaceutical products.
5 0 0
2
4 6 Time (s)
8
Our future work will have two main directions: i) study properties that can only be measured with the vane, e.g. changes during physical aging or studies over the shelf life; ii) Use structural modelling to fit simultaneously experimental data from the range of protocols defined here. Initially, this work may be better done on samples that do not require use of the vane, to minimise calibration problems.
10
Figure 8 Vanilla Danette: Strain growth, same data as in the previous figure, but only for short times. Number next to each curve is the apparent applied stress in Pa.
This kind of data can be modelled using the method of Baravian and Quemada [9]. They showed that oscillations in creep data could be modelled quantitatively by coupling the equation of movement of the rheometer bob to a dashpot and spring model for the sample rheology. To do this requires the bob’s inertia. The vane is a particular case, as part of the inertia is due to the sample between the blades. However, at times below 0.1s the system response is purely inertial, so this data can be used to determine the correct inertia [7] to use in the modelling.
4 CONCLUSIONS We have shown that stress growth measurements with the vane provide a rich source of information on the rheology of soft foods. The method is simple and very reproducible. It has high throughput and low cost. Our first aim is pragmatic. We show the usefulness in industrial practice of a new technique for quantifying the texture of soft foods. As described here, TPV can be used to make fast, routine measurements in circumstances where no satisfactory technique is currently available. It is very useful for product development and quality control. The second aim of obtaining a quantitative rheological interpretation of the data is a difficult task. Indeed the problem remains unsolved even for standard geometries, where converting the raw data into geometry-independent quantities is much more straightforward than in the wide gap vane geometry. We have defined three protocols that reduce the ambiguity in the interpretation of the stress growth measurement alone.
ACKNOWLEDGEMENTS It is a pleasure to acknowledge our long and fruitful collaboration with Daniel Quemada and Christophe Baravian.
REFERENCES [1] H. A. Barnes and Q. D. Nguyen, “Rotating vane rheometry - a review,” J. Non-Newtonian Fluid Mech., vol. 98, pp. 1-14, 2001. [2] D. Quemada, “Rheological modelling of complex fluids: IV: Thixotropic and "thixoelastic" behaviour. Start-up and stress relaxation, creep tests and hysteresis cycles,” Eur. Phys. J. Appl. Phys., vol. 5, pp. 191-207, 1999. [3] H. A. Barnes, “Thixotropy - a review,” J. NonNewtonian Fluid Mech., vol. 70, pp. 1-33, 1997. [4] D. Quemada, “A non-linear Maxwell model of biofluids: application to normal blood,” Biorheology, vol. 30, pp. 253-265, 1993. [5] C. Baravian, D. Quemada, and A. Parker, “Modelling thixotropy using a novel structural kinetics approach: Basis and application to a solution of iota carrageenan,” J. Texture Studies, vol. 27, pp. 371-390, 1996. [6] J. D. Sherwood and G. H. Meeten, “The use of the vane to measure the shear modulus of linear elastic solids,” J. Non-Newtonian Fluid Mech., vol. 41, pp. 101-118, 1991. [7] C. Baravian, A. Lalante, and A. Parker, “Vane rheometry with a large, finite gap,” Appl. Rheol., vol. 12, pp. 81-87, 2002. [8] P. V. Liddell and D. V. Boger, “Yield stress measurements with the vane,” J. Non-Newtonian Fluid Mech., vol. 63, pp. 235-261, 1996. [9] C. Baravian and D. Quemada, "Using instrumental inertia in controlled stress rheometry, Rheol. Acta, vol. 37, pp. 223-233, 1998.
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