Rheological Measurements of Viscous Materials for Quality Control

Increased monitoring of foodstuffs can help to establish quality attributes in real-time during the processing stage, and so permit better process control. The efficiency of a process and the quality of the product is a function of the fluid’s rheology in most process applications, which will influence multiple characteristics such as pourability, spreadability, and pumpability (Cullen, Duffy & O’Donnell, 2001).

Conventionally, quality control rheological measurements have been carried out on tomato-based products, both intermittently and offline, by utilizing simple dip-in viscometers such as the Brookfield viscometer (Barnes, 2001) and instruments such as the Bostwick Consistometer (Cullen, Duffy & O’Donnell, 2001).

The cost-effective, simple instrument – Bostwick Consistometer (BC) – is employed for monitoring product consistency in a range of foodstuffs. Yet, this instrument has certain limitations such as operator subjectivity and variability, dryness and leveling of the instrument, and separation of serums at the edge of product flow.

This device is not well suited for online consistency measurements because of this. Furthermore, laboratory viscometers are used extensively as quality control instruments predicated on simple rotational viscometry, with shear rate reliant on the type of spindle used, and the rotation speed.

For these reasons, substituting the laboratory viscometers and Bostwick Consistometer, or associating their measurements to a process viscometer, can provide continuous and real-time monitoring at the time of processing.

A wide range of viscometers are available for process control, including rotational, vibrational, and tube viscometers, while the appropriateness of these techniques have been assessed recently for the food sector (Cullen et al. 2000).

When handling complex food fluids (multiphase, particulate, fibrous, and highly viscous), these types of traditional viscometer designs can be problematic, which can result in errors because of fouling of measuring gap, wall slip, or phase separation.

An ideal viscometer design is one that eases the cleaning process in place with least possibilities of fouling, permits a fast response time, and enables excellent sample renewal to ensure that any type of measurement gathered is representative.

Many unit operations in the sector require mechanical agitation or effective mixing of fluids. The size and shape of the agitator employed will also be dependent on the properties, particularly viscosity, of the fluid to be combined.

Generally, helical ribbon agitators are used for highly viscous non-Newtonian fluids, permitting vertical mixing of the fluid and efficient mixing at the vessel wall (Rai, Devotta, and Rao, 2000), with typical operating speeds within the range of 30–100 rpm.

Enhanced process control can be attained via in-situ rheological assessment of batches, before pumping and post-mixing. Benefits include the elimination of the requirement for bypass processing lines or extra instrumentation to be in contact with the product, combined with real-time monitoring.

The employment of mixer viscometry, where high-precision measurements of impeller rotational torque and speed for a specified geometry can determine the obvious viscosity in the mixing vessel, has been well documented (Cantu-Lozano, Rao, and Gasparetto 2000; Ford and Steffe 1986).

However, trials like these are based on scale-down mixing geometries, depending on conventional off-line viscometer/rheometer measurement of torque and speed (Cullen, et al. 2000).

Only average values and approximate data can be determined because of the intricate flow patterns, and so, shear rates, in the mixing vessels, (Castell-Perez and Steffe, 1992).

The creation of a cost-effective, new, non-contact torque transducer (TorqSense, Sensor Technology Ltd, Banbury, Oxon, UK) providing accurate dynamic measurements of rotary torque over ranges of 0–10 mN⋅m to 0–10,000 N⋅m will support technology transfer of mixer viscometry to the production scale.

With regards to this torque transducer, the concept of operation involves a surface acoustic wave device which is used as a frequency-dependent strain gauge to establish the alteration in resonant frequency induced by the applied strain in the shaft. The precise measurement of shaft rotational speed using a light beam was also recorded.

The focus of this article is to evaluate the capability of a pilot plant-scale helical ribbon mixer as a rheological process control technique, using the criteria below:

  1. Determine power-law indices using the mixer viscometer technique
  2. Determine effective power-law indices from representative mixer flow curves
  3. Develop correlations between single-point mixer torque measurements and offline reference techniques

Materials and Methods

To begin with, a pilot scale helical ribbon agitator (42 L) was developed and contains a cylindrical dished-bottom stainless steel vessel, integrating a close clearance helical ribbon impeller. The geometrical configurations of this are listed in Table 1 and shown in Figure 1.

Schematic of pilot plant helical ribbon agitator

Figure 1. Schematic of pilot plant helical ribbon agitator. Image Credit: Sensor Technology Ltd

Table 1. Geometrical characteristics of helical ribbon agitator. Source: Sensor Technology Ltd

Parameter
Diameter, d (m) 0.36
Height, h (m) 0.31
Pitch, p (m) 0.18
Blade width, w (m) 0.05
Clearance, c (m) 0.01
p/d 0.5
c/d 0.027

By utilizing a non-contact rotary torque transducer (Torqsense, Sensor Technology Ltd, Banbury, Oxon, UK) in the 0–6 N⋅m range and logging with the system software and transducer interface module, both torque and speed were established.

Next, the agitator speed was varied from 35 to 70 rpm by utilizing a variable speed Heidolph (model RZR 2041) stirrer motor (AGB Scientific Ltd, Dublin). The temperature was established in the agitator and replicated on the rheometer for each sample.

Using the slope method, Newtonian fluids and Non-Newtonian fluids (see Table 2) were employed to determine the agitator’s mixer viscometer constant. Well-defined model fluids (Sigma-Aldrich Ireland Ltd, Dublin) were chosen that span the spectrum of flow behavioral indices.

Table 2. Flow characteristics of standard fluids, as determined by laboratory rheometer. Source: Sensor Technology Ltd

Fluid K n
Pa.sn -
Glycerol 5.55 0.98
Glycerol / H2O / 0.1% CMCa 8.66 0.68
0.5% Carboxymethyl cellulose 10.3 0.56
1.0% Carboxymethyl cellulose 25.5 0.49
1.5% Carboxymethyl cellulose 65.6 0.43
0.5% Guar gum 25.4 0.33
1.0% Guar gum 80.9 0.25
1.5% Guar gum 253.3 0.16

a85% mass glycerol, 15% mass water, 0.1% mass carboxymethylcellulose

To examine the effect of elasticity on torque, xanthan gum aqueous solutions (1%, 1.5%, and 2%) were used as model fluids. By adding samples and tomato paste with different inconsistency from Bostwick values of ca. 2.5 to 10.5, by dilution, the thickness of a commercial ketchup was increased.

Next, a pizza sauce which contained particulates of approximately 5.0 mm in length (Green Isle Foods, Naas, Ireland) was selected as a fluid showing more complex properties and differed in consistency across an insignificant scope of Bostwick values from ca. 4.0 to 6.0, by dilution.

Water quantities of ca. 1.5% of the total sample volume were added to attain dilution levels. These samples were combined at 20 °C for a period of 30 minutes prior to measurement. The mechanically degraded samples replicated post-mixing conditions and were believed to be time-independent and eventually modeled as power-law fluids.

Offline consistency measurements were gathered for each dilution with a Bostwick Consistometer (Christison Scientific, Gateshead, Tyne, and Ware, UK), with values taken as the distance in centimeters traveled by the sauce over 30 seconds.

On a laboratory rheometer, (Carrimed CSL2100, TA Instruments, Leatherhead, Surrey, UK), shear rate sweeps (0–300 second−1) were performed by utilizing a cone and plate geometry (4 cm and 2° acrylic cone) for samples of tomato ketchup, and a parallel plate geometry (4 cm and 1500 μm gap) for samples of pizza sauce, at batch temperatures.

For every dilution, Rheometer and BC rheometer measurements (shear rate sweeps) were then performed in triplicate and averaged.

Results and Discussion

Mixer Viscometer Constant

Figure 2 shows a linear regression analysis of the semi-logarithmic plot of (1 − n) versus (P/KΩn+1d3) that provided an excellent measure of fit (R2 = 0.99); ks – the shear rate proportionality constant – was determined from the slope of the line as 10.

This constant was established to be independent of angular velocity for speeds of 40, 50, 60, and 70 rpm with correspondingly high measures of fit.

Semi-logarithmic plot of dimensionless functions (P/KΩn+1d3) versus (1 − n) for standard fluids as listed in Table 2.

Figure 2. Semi-logarithmic plot of dimensionless functions (P/KΩn+1d3) versus (1 − n) for standard fluids as listed in Table 2. Image Credit: Sensor Technology Ltd

Power-Law Indices

Determined from the logarithmic plots of rotational speed versus mixer torque, the flow behavioral index gave similar results to those established with the laboratory rheometer, giving an average percentage variation in a 5% magnitude.

As shown in Figure 3, they also defined the transition of the fluids tested toward more Newtonian behavior across a slight range of dilutions. These outcomes show that agitators may be utilized to estimate the flow behavioral indices in situ, by establishing torque as a function of rotational speed.

Logarithmic plot of torque versus rotational speed, for tomato ketchup samples.

Figure 3. Logarithmic plot of torque versus rotational speed, for tomato ketchup samples. Image Credit: Sensor Technology Ltd

The K values are compared in Figure 4, they were determined using Equation (1) to their rheometer-quantified equivalents for a variety of dilutions. The mixer viscometer supplied consistency index values that were significantly higher, with the discrepancy inversely proportional to dilution.

(1)

Consistency index (K) as determined by the mixer viscometer, compared to their rheometer-measured equivalents, for tomato ketchup samples (BC values 4.2–6.8).

Figure 4. Consistency index (K) as determined by the mixer viscometer, compared to their rheometer-measured equivalents, for tomato ketchup samples (BC values 4.2–6.8). Image Credit: Sensor Technology Ltd

It is suggested that such a discrepancy is due to the solid fraction of tomato products, resulting in gel-like behavior or network structure (Rao and Cooley, 1992). The viscoelastic behavior of a ketchup sample is examined in Figures 5, with G′ being higher than G″ at all frequencies (ω) established.

Logarithmic plot of angular frequency (ω) versus storage (G′) and loss (G″) moduli and η (η*) for a tomato ketchup sample.

Figure 5. Logarithmic plot of angular frequency (ω) versus storage (G′) and loss (G″) moduli and η (η*) for a tomato ketchup sample. Image Credit: Sensor Technology Ltd

This shows that the properties of the sample were more solid than viscous. The decrease in complex viscosity η* exhibits the sample’s shear thinning nature. Log plots of G″ or G′ against log ω of weak gels produce true gels zero slopes and positive slopes, from a structural standpoint.

So, it can be established that the tested tomato ketchup showed weak gel-like behavior. The effect of elasticity on combining with agitators, including helical ribbons is vague, with many authors reporting decreases, increases, and no effects on torque (Castell-Perez and Steffe, 1992).

Elasticity is known to cause differences in the flow fields around the mixing impeller, and typically, it is concluded that fluids’ elastic properties are inclined to reverse secondary flows caused by centrifugal force (Castell-Perez and Steffe, 1992).

In this regard, several authors have reported an evident growth in torque because of elasticity for helical ribbons (Brito et.al. 1991; Collias and Prud’homme, 1985). As a result of elasticity, a tripling of torque for certain fluids has also been reported by the latter authors.

So, it can be concluded that this increased torque is not a function of the power-law consistency index or flow behavioral index. To examine this theory further, xanthan gum, which is a well-defined reference fluid, was circulated in the helical ribbon agitator. The fluid has a gel-like structure at higher than 1% concentrations.

The percentage changes in magnitude between the consistency index established by the mixer viscometer and its equivalents calculated by the rheometer increased from 3% at 1% concentrations to 7% and 50% at 1.5% and 2% concentrations, respectively.

So, the traditional technique for non-Newtonian fluids created by Metzner and Otto (1957) to determine power consumption in agitator systems does not consider the effects of elasticity on torque created for complex fluids such as tomato sauces. Similarly, Equation (1) does not consider this effect either.

Assessment studies carried out on the effects of elasticity on mixing, involved the utilization of elastic fluids with a constant viscosity (Boger fluids).

Changes in power consumption could also be because of changes in either viscosity or elasticity, considering that most viscoelastic fluids also have robust shear thinning properties (Castell-Perez and Steffe, 1992). Producing a correlation which includes elasticity, and also considers the differences in impeller geometry and viscosity, can be challenging.

From this assessment, it becomes clear that the Otto and Metzner correlation may no longer be valid for scaling-up on the basis of power usage for each unit volume, as detailed by Oliver et al (1984), due to the different power requirements because of the changing fluid elasticity.

The effects of elasticity on quantified torque are dependent on scale, and this could explain why such effects are not seen in the laboratory-scale studies outlined in the literature (Ford and Steffe, 1986; Castell-Perez and Steffe, 1992).

Representative Flow Curves

As determined through Equation (2) and then plotted against angular velocity, effective viscosity was modeled as a power-law function. These representative flow curves for a set of dilutions for samples of tomato ketchup are shown in Figure 6.

(2)

Representative flow curves of tomato ketchup samples for a series of dilutions (BC values 4.2–6.5).

Figure 6. Representative flow curves of tomato ketchup samples for a series of dilutions (BC values 4.2–6.5). Image Credit: Sensor Technology Ltd

Data regression analysis resulted in an effective consistency coefficient Keff and an effective flow behavioral index neff. Effective consistency was seen to correlate robustly (R2 = 0.99) against K established by the rheometer (see Figure 7), showing that the technique could well be used for process measurements of fluid consistency.

Linear correlation between effective consistency index (Keff), as determined from the mixer, against rheometer-measured consistency index values (K) for a series of dilutions of tomato ketchup samples (BC values 4.2–6.5).

Figure 7. Linear correlation between effective consistency index (Keff), as determined from the mixer, against rheometer-measured consistency index values (K) for a series of dilutions of tomato ketchup samples (BC values 4.2–6.5). Image Credit: Sensor Technology Ltd

Additionally, effective flow behavioral indices (neff) were the same numerically as those calculated above. Using this technique, one key advantage is that calibration model fluids are not required.

A flow curve is also produced for the product – instead of utilizing too many quality control procedures which could only supply single-point measurements – resulting in a more comprehensive rheological characterization. Effective consistency values correlated strongly (R2 = 0.97) against Bostwick Consistometer values.

Single-Point Measurements

Raw torque data also correlated robustly from the agitator (R2 = 0.98 and R2 = 0.99) with consistency index from the Bostwick and rheometer values, using a power-law model respectively (see Figure 8).

Correlations developed between off-line consistency index K (rheometer) and Bostwick values with torque measurements for a series of tomato ketchup sample dilutions.

Figure 8. Correlations developed between off-line consistency index K (rheometer) and Bostwick values with torque measurements for a series of tomato ketchup sample dilutions. Image Credit: Sensor Technology Ltd

These high measures of fit paired with low standard errors of prediction (denoted as a percentage of the range), less than 3% and 4% respectively, show that offline reference measurement can be predicted accurately via torque readings at a constant speed.

For the correlation created between the Bostwick values and torque readings for the samples of pizza sauce, an analogously high measure of fit (R2 = 0.98) was gathered over an extremely small consistency range, BC values 4.0–6.0 cm. In addition, BC measurements were provided in increments of 0.5 cm, the limit of the sensitivity of the instruments as stated by Cullen, Duffy, and O’Donnell (2001).

As determined from rheometer shear rate sweeps, the generation of a correlation with consistency coefficient, K, was more difficult, due to the inability of the rheometer to handle samples which were made up of large particulates, even using the parallel plate geometry with a huge gap.

Furthermore, the torque transducer was seen to be susceptible to insignificant differences in product consistency, which is characteristic of fluctuations in the sector and can handle large particulates. If multiple products or recipes must be assessed, then it is better to develop such correlations for each product.

Most frequently, quality control personnel just want to know if the product created is within the range given for daily production, the range which was generated earlier based on the understanding of the entire flow curve (Barnes, 2001).

Whether determined by single viscosity readings from laboratory viscometers or consistometers, this quality control range could be precisely predicted or substituted by mixer torque measurements, which also gives the benefits of real-time process monitoring.

Conclusions

Combined with a new torque transducer, proposed mixer viscometry techniques were examined as a process control tool to track rheological characteristics of fluid foods in a helical ribbon agitator.

Post-mixing rheological assessments of tomato-based products using representative flow curves within a pilot plant scale helical ribbon agitator, were seen to be an effective technique to achieve process viscometry measurements. Modeling effective viscosity as power-law functions also supplied similar data to results measured by rheometer.

Developing correlations with steady speed torque measurements from the agitator can help anticipate reference off-line measurement techniques. The torque transducer which was utilized exhibited susceptibility to even slight variations in product consistency.

Utilizing Equation (1), comparison of torque readings to reference non-Newtonian fluid data did not establish absolute power-law indices because of variations in elasticity. The influences of absolute power-law indices are dependent on both the scale and geometry of operation, and the viscoelastic properties of the fluid.

Design advantages of the recommended viscometry system for the sector include its ability to handle the properties of complex fluid such as particulates and fibers. Subjectivity and errors from operator variability, related to certain offline instruments, are also eliminated. Real-time process monitoring allows enhanced process control.

Furthermore, rheological measurement problems due to particle blockages or slip are avoided. Extra cleaning or instrumentation in contact with the foodstuff is no longer required. It is recommended that other low-speed impeller designs like paddles and anchors, which function in the laminar flow region, could also be used for other types of viscous fluids.

References

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This information has been sourced, reviewed and adapted from materials provided by Sensor Technology Ltd.

For more information on this source, please visit Sensor Technology Ltd.

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