Keywords: DCR, Rheology, Yield stress, Time-dependency, Thixotropy, Wall slip
RH146
Abstract
Viscometers are commonly used for formulation and quality testing of complex fluids in industries such as pharmaceutical, food, cosmetics, or petrochemical. However, viscometers often present limitations such as restricted measurement range and limited insights into complex fluids. With the introduction of the Discovery™ Core Rheometer, TA Instruments™ has embarked on a mission to facilitate the transition from single-point viscosity measurements to the powerful tool of rheology across various industries. This note aims to familiarize new Core Rheometer users with the core principles of rheology and facilitate this transition. It focuses on characterizing yield stress and time-dependent materials, helping the user get the best out of using the Core Rheometer and RheoGuide™ Software, especially for those who are new to using rheometers.
Introduction
Complex fluids, such as emulsions, foams, and gels, have wide applications in a variety of industries, including food, cosmetics, and pharmaceuticals. These materials exhibit unique properties due to their intricate microstructures and do not have constant viscosity, which can lead to behaviors like shear thinning, viscoelasticity, and thixotropy. Viscometers often lack a sufficient shear rate range and sensitivity to perform a comprehensive viscosity assessment of complex fluids. The complexity can be seen in Figure 1, which shows the viscosity profile of four different materials over a wide range of shear rates.
If shampoo, soap, or syrup were to be assessed at a shear rate = 50 1/s, a value within the common range of viscometers, it would be observed that shampoo and hand soap show very similar viscosities, while syrup has a higher viscosity. Using a rheometer over a wide range of shear rates reveals that although shampoo and syrup show different viscosities at = 50 1/s, they exhibit the same viscosity at much lower shear rates resembling rest or startup flow. Conversely, shampoo and hand soap samples show different viscosities at rest or startup flow, while they appear similar at a shear rate of = 50 1/s.
If a single-point viscosity evaluation is performed at a range of 10–20 1/s for syrup and topical ointment samples, similar viscosity values would be obtained. However, one of these materials is a Newtonian fluid and the other a shear-thinning non-Newtonian material, which would not be discerned from this single point measurement. Newtonian fluids, like water and some oils, have a constant viscosity that doesn't change with the shear rate at a given temperature. In contrast, non-Newtonian fluids, such as ketchup and a cornstarch-water mixture, have a viscosity that varies with the shear rate; they can become thinner or thicker depending on the rate at which they are sheared. For example, ketchup becomes runnier when squeezed, and cornstarch in water becomes more solid when rapidly sheared. This difference in flow behavior based on shear rate is the key distinction between Newtonian and non-Newtonian fluids. To comprehensively study these materials, a rheometer must be used. In addition to viscosity, rheometers can also assess viscoelasticity, time-dependency, and yield stress—critical attributes of non-Newtonian (complex) fluids like emulsions, dispersions, polymers, gels, and pastes. These properties are often overlooked in industry but are crucial for understanding how materials will behave under different conditions, such as during processing or end-use [1]. Comprehensive studies of non-Newtonian fluids are important for various applications, from food processing to the application of cosmetics and topical pharmaceuticals, as understanding these properties helps design efficient systems and create products tailored for the end user.
Time-dependent yield stress materials are abundant in nature and industrial processes. Examples include clays, light metal alloys, paints and inks, adhesives, gelled waxy crude oils, drilling muds, fresh cement pastes, food products, biological fluids, ferrofluids, some lubricants, gypsum paste, and many other slurries, emulsions, suspensions, and foams. Yield stress materials have a specific stress threshold, beyond which they begin to deform plastically. Plastic deformation refers to material undergoing permanent deformation when a force is applied. Below this point, they behave elastically and return to their original microstructure status when the stress is removed. Thus, in time-dependent yield stress materials, yield stress is a function of structure and, therefore, of time [2, 3, 4]. Precisely characterizing the timedependency and yield stress of materials is vital for ensuring consistent product quality, processing efficiency, and enhancing safety across various industrial processes.
By measuring properties beyond just viscosity, such as time-dependency and yield stress, rheometers provide insights into a material's microstructure and stability, which are crucial for ensuring product performance and quality. With the Discovery Core Rheometer, these insights, already widely used in R&D, can be made in QA/QC labs with the ease of use of a viscometer.
Experimental
RheoGuide Software, provided with the Core Rheometer, is shown in Figure 2 on the touchscreen of the rheometer. This software offers pre-defined methods, and on-screen illustrations. This workflow helps eliminate sources of operator error, such as using the incorrect geometry or missing a step. RheoGuide Software enables users to perform successful rheology measurements with minimal training, resulting in more consistent data. TechTips are also available to help users get acquainted with the innovative features of RheoGuide Software [5, 6].
RheoGuide Software methods are customizable, allowing users to incorporate steps of a designed operating procedure. Users may also specify Pass or Fail criteria which populate on the touchscreen at the end of tests for immediate feedback. When customizing the methods, it’s crucial to pay attention to specific details to get the best out of your rheometry measurements, especially when characterizing time-dependent materials. Materials exhibiting thixotropy or viscoelasticity may respond differently under prolonged stress or varying shear rates, impacting their functionality in coatings, pharmaceuticals, and food products. Understanding these properties helps ensure better material design, quality control, and application performance.
For this note, various rheology tests were run on the Core Rheometer using everyday materials such as ointment, after sun gel, hair gel, and shampoo. These tests include flow sweeps, flow ramps, oscillatory stress amplitudes, and time sweeps. They demonstrate the details that make a difference in characterizing time-dependent materials, specifically in obtaining reliable yieldstress values, considering the influence of wall slip and providing hints to optimize procedures from an industry perspective. All tests were conducted using 40 mm cross-hatched parallel plates (Figure 3), except for the tests shown in Figures 9 and 10, which used 40 mm smooth parallel plates.
Results and Discussion
Viscosity Profile & Time-Dependency
Time-dependent behavior of materials can lead to challenges in measurement and data reproducibility. When setting up a flow sweep test with steady-state sensing, a common question is how to determine the correct value for maximum equilibration time. Different periods may yield varying results, leading to data that lacks reproducibility. Parallelly, artifacts may be observed at lower shear rates when performing flow sweeps to measure viscosity profiles over different shear rates. These issues are related and stem from the time-dependency of materials.
Time-dependent materials require longer periods to reach steadystate at lower shear rates compared to higher shear rates. As a result, artifacts can appear in the data at lower shear rates. This issue becomes more pronounced as the material exhibits greater time-dependency. As shown in Figure 4, when the maximum equilibrium time is too short, the viscosity data deviates more from the true viscosity data points obtained at steady state.
To determine the proper maximum equilibration time, the best solution is to run a constant shear rate test (peak hold) at the lowest desired shear rate. Figure 5 illustrates that for = 1000 1/s, the topical ointment being measured needs only a few seconds to reach steady-state but for = 0.001 1/s, at least 10 minutes is required. Reaching steady state in a constant shear rate test means that the shear stress or viscosity of the non-Newtonian fluid has stabilized and is no longer changing with time. If the maximum equilibrium time is set based on the steady-state period for = 1000 1/s, the data points obtained at low shear rates will not be recorded at steady-state. However, if = 0.001 1/s steady-state period is used to set the maximum equilibrium time, all data points will be obtained at steady-state.
It is important to note that for every non-Newtonian fluid, the corresponding flow curve should be unique to that fluid. This can only be achieved if all data points are obtained at steady-state. Additionally, the fluid must be reversible. A unique flow curve is one of the best tools for quality assurance (QA) of a material, because when done correctly, it eliminates discrepancies between different instruments or operators in different labs.
Figure 5. Constant shear rate tests of the topical ointment at = 0.001 and 1000 1/s
Thixotropy
Thixotropy is a reversible time-dependent shear thinning behavior observed in various materials, including some types of paints, personal health products, and cosmetics. These materials become less viscous over time when subjected to shear and gradually return to their thicker state when allowed to rest [7, 8, 9]. A common test in the industry to assess the time-dependency of materials is a flow ramp loop, also known as a thixotropic loop, with a shear rate ramp from close to zero to = 100 1/s through a short period of time.
As an example, the thixotropic loop test was used to compare the time-dependency of two distinct paints, revealing a notable difference: as shown in Figure 6, one paint had a thixotropy measure a hundred times larger than the other.
If a material has low thixotropy, it regains its viscosity quickly. For paints, this can result in brush marks on the painted surface. If a material has high thixotropy, sagging may occur, and the paint will appear to have drips on the surface. Therefore, the correct thixotropic behavior for the application is required. These thixotropy values, and in general this test, are also useful tools to compare the material’s time-dependency, but not the best indicator to quantify it.
When running thixotropy experiments, it is important to remember that the shear history of the sample will impact the results of a thixotropic loop test. For example, after loading the sample, repeating the test multiple times changes the shear history, altering the initial conditions and resulting in different thixotropy values each time. Shear history is also impacted by sample loading, which can vary from operator to operator. To improve repeatability and user variability, it is best to establish a constant initial condition for these tests.
One way to establish a constant initial condition is to observe a sufficient rest period after loading the sample, allowing the material to recover to a fully structured state. This approach also eliminates the influence of various operators. To quantify the minimum recovery period required to achieve a fully structured state, run a constant relatively high shear rate test to completely destroy the material’s microstructure. Then, immediately perform a time-sweep test at a stress or strain below the yield value, allowing the material to rebuild itself. The material has recovered when the moduli values reach a plateau. The period to reach a moduli plateau can be used to achieve a constant initial condition.
In Figure 7, the topical ointment was subjected to a shear rate of 100 s-1 long enough to reach a steady state, i.e., a fully destructed state. Immediately afterward, a time-sweep test was conducted at an oscillation stress of 10 Pa, well below the yield stress value. It was observed that after approximately 200 seconds, the storage modulus (G’) was higher than the loss modulus (G’’) and both became parallel, indicating that the material’s microstructure had fully recovered. This method ensures that, even with different sample loading styles by various operators, a constant initial condition can be expected after performing a pre-shear and observing a sufficient recovery period.
Thixotropy three-step oscillation tests can be used to compare and quantify the degree of time dependency of materials. These tests inherently include the constant initial condition step. Figure 8 shows the results of the thixotropy three-step tests conducted for two topical ointments [10].
In the first step, after loading the sample, a stress of 10 Pa (below the yield stress of both samples) is applied. In the second step, a stress of 300 Pa, well above the yield stress, is applied to fully destroy the microstructure. In the third step, a stress of 10 Pa is applied again to allow the microstructure to rebuild over time. It is important that the duration of each step is sufficient to approach a steady state, and the evolution of G’ and G” is monitored. To ensure the comparison of their time-dependency was valid, both samples were tested after experiencing the same initial conditions of microstructure destruction above their yield stresses and recovery periods well below their yield stresses.
It was observed that in the third step, for topical ointment #1, G’ started larger than G” and then the two moduli became parallel within a few seconds. For topical ointment #2, G’ started below G”, indicating the sample was not in a gel state. Over time, G’ exceeded G” and they became parallel. Ointment #2 took longer to rebuild its microstructure, indicating that it is more thixotropic than topical Ointment #1. Thus, the time required for thixotropic rebuild can be quantified for both.
In step 2, it was observed that topical ointment #1 achieved parallel G’ and G” faster, emphasizing its lower degree of timedependency. Again, the periods to reach parallel G’ and G” can be quantified in these materials.
To wrap up this section, it is important to note that not all shearthinning materials are thixotropic, but all thixotropic materials exhibit shear-thinning behavior. When a time-dependent material is shear thinning and reversible, it is called a thixotropic material. However, if it is time-dependent and shear thinning but irreversible, like gelled waxy crude oils, it cannot be classified as thixotropic [7, 9].
Yield Stress & Wall Slip
When constructing a flow curve for complex fluids like high molecular weight polymer dispersions, suspensions of large or flocculated particles, and emulsions with large droplet sizes, wall slip is a common issue. It is typically caused by large velocity gradients in a thin region adjacent to the wall. When slip occurs, the measured viscosity and shear stress can be significantly lower than the actual values of the sample [11, 12].
In flow sweeps (flow curves), wall slip is often observed at low shear rates, which is the most important region for identifying yield stress. The yield stress can be extrapolated from the linear portion of the flow curve to zero shear rate, with the intercept on the shear stress axis representing the yield stress.
In Figure 9, flow sweeps were conducted to build the flow curve of an after-sun gel using smooth. and crosshatched parallel plates. It can be observed that below = 1 1/s, the shear stress values obtained with smooth parallel plates start to deviate from those obtained with crosshatched parallel plates, indicating the presence of wall slip. The yield stress extrapolated from the flow curve obtained with smooth parallel plates (≈ 25 Pa) would be significantly lower than the value obtained with crosshatched parallel plates (≈ 75 Pa), resulting in an almost 100% error in your measurement!
A common question is how to identify if your data is affected by wall slip. For parallel plates, the best practice is to change the gap. When there is no wall slip present, altering the gap should not significantly influence your data. In Figure 10, it can be observed that using smooth parallel plates, as the gap increases, the yield stress values obtained also increase. This is an obvious sign of wall slip presence. The effect of wall slip can be reduced by increasing the gap, which reduces the contribution of the slip layer to the measurement. However, there are two important points to consider. As seen in Figure 10, you may never fully mitigate the influence of wall slip by only increasing the gap for many materials. Also, in many circumstances, it is not feasible to increase the gap, as it makes it harder to hold the sample between parallel plates. However, when possible, it is a useful test to check for the presence of wall slip.
Another method to check for wall slip is to use different geometries. For example, building a flow curve using smooth and crosshatched parallel plates should give very similar curves if no wall slip exists. If discrepancies are observed at low shear rates, it could be a sign of wall slip.
Optimized (Streamlined) Core Rheometry
Time is crucial in industry, so a major concern in rheometric studies is how to conduct the shortest analysis possible without compromising data integrity. Some steps may be taken to improve efficiency while maintaining data integrity.
When running flow sweeps to obtain a viscosity profile over a range of shear rates or to discover the yield stress, it is faster to construct your flow curve by starting from higher shear rates. Higher shear rates break the material’s microstructure faster, allowing it to achieve steady state more quickly when transitioning to lower shear rates. Starting at the lowest shear rate will prolong the testing as it will take longer to break the sample’s microstructure. Ensure the highest shear rate feasible for your material to stay between the parallel plates. You can adjust the gap within the recommended range to identify the highest feasible shear rate for your material. Be aware of viscous heating at high shear rates; typically, gaps smaller than 500 μm are not recommended unless you are familiar with your material and conditions. Furthermore, when adjusting the geometry gap for parallel plates, it’s crucial to consider the particle sizes within your sample. The gap should be at least 10 times larger than the biggest particle to avoid interference and ensure accurate measurements.
Another recommendation to shorten a flow sweep test is to reduce the number of points per decade. For example, the flow curves for a hair gel in Figure 11; one flow curve was built using four points per decade and another using one point per decade. The Herschel-Bulkley model fitting to both curves yields almost the same value of yield stress, but the flow curve built with one point per decade takes 70% less time.
It is recommended to use enough data points when initiating a rheometric study of an unknown batch of samples. However, once the behavior of the materials is known, fewer data points can be used for QA data to accelerate testing.
The same strategy applies for creating a viscosity profile over shear rates (see Figure 12). Seven points are sufficient to compare different batches or formulations. However, you could use even fewer points — three points at lower, medium, and higher shear rates for comparison and QA/QC purposes.
Three points would be the minimum number suggested to ensure a fair and reliable comparison between different samples. Tests can also be performed using constant shear rate (Peak hold), but note that steady-state sensing is not available in this case. Instead, the steady-state viscosity must be identified manually.
With RheoGuide Software, results are immediately available on the touchscreen, allowing users to take swift action, ideal for fastpaced environments. For instance, three viscosity points can be displayed on the monitor (see Figure 14), chosen based on your process and objectives. By running just one test (flow sweep), different formulations can be compared at relatively low, medium, and high shear rates, rather than a single condition typically provided by viscometers.
Another test to determine yield stress in QA/QC is the oscillatory stress amplitude test. During this test, the amplitude of applied stress is gradually increased, helping to assess the material’s behavior under different stress levels and identify its yield stress. For time-dependent materials, yield stress is also a time-dependent property. In an oscillatory stress amplitude test, the yield stress depends on the frequency. As shown in Figure 14, the crossover point, where G’ transitions to lower than G’’, is often associated with yield stress. This crossover indicates the transition from predominantly elastic behavior to predominantly viscous behavior, signifying the onset of flow. At higher frequencies, the crossover stress is higher, while at lower frequencies, this transition occurs at lower stress amplitudes.
These crossover values can be displayed on the RheoGuide Software screen with a pass/fail indicator, making it easy to instantly recognize whether these values fall within the desired range. For example, in Figure 15, an unknown hair gel was tested in the lab to check if it had the same yield stress as the hair gel shown in Figure 14. A quick oscillatory stress amplitude test was conducted at a frequency of 0.1 Hz, with the crossover range set between 90 and 100 Pa based on Figure 14. The fail status was indicated on the RheoGuide Software screen, showing that the crossover value of the unknown hair gel did not match, confirming that they are different materials.
The crossover value can be used in industry for QA to compare the yield stress of samples. However, there are a few points to consider before proceeding. The crossover point, where already viscous behavior becomes dominant over elastic behavior, corresponds to a stress slightly above the yield stress. To get a value closer to the true yield stress from this test, identify the onset of flow when G’ starts to drop [13].
When analyzing the onset of flow using TRIOS™ Software, ensure that the same group of data points are used for comparison and QA. As shown in Figure 16, for two tests at the same frequency for the same hair gel, almost the same crossover value was obtained. However, since different data points were chosen for the flow onset analysis, the onset values differed by close to 10%. Therefore, for comparison of flow onset using this test, always use the same set of data points.
TRIOS Software contains a variety of analysis functions specific to the selected data. To utilize these functions, open the desired data file you wish to analyze. Display the graph for the desired step and configure the graph variables as needed. Click on the desired curve you wish to analyze or highlight a section of data on the curve. Then, click the Analysis tab to display the toolbars. From the Function toolbar, select the desired analysis/model from the drop-down menu. Click Analyze to execute the analysis.
Conclusions
Viscometers can be efficient instruments for measuring viscosity, but their limited range of testing parameters may exclude valuable material insights. Rheometers, on the other hand, allow for a wider range of loads, speeds, and geometries to characterize complex fluids. However, rheometers are typically not as simple to use as viscometers, which can be off putting for users. The Discovery Core Rheometer with RheoGuide Software aims to bridge this gap for users. This note outlines how to conduct essential investigations on yield-stress and time-dependency of materials using the Core Rheometer.
- RheoGuide Software methods are customizable to incorporate every step of your standard operating procedure. Once the methods are established, tests can be performed directly from the instrument touchscreen, from start to finish, without the need to interact with a PC.
- Many materials have some degree of time-dependency. Overlooking this behavior severely impacts data quality and diminishes the power of rheology in solving issues.
- Rheometric studies may take longer than single-point viscometer measurements, but the cost-benefit is incomparable. Also as shown, there are ways to accelerate rheometric measurements, and the RheoGuide Software can help even more to improve time efficiency.
- For measuring each rheological parameter, there are different methods. Ensure you study and choose the proper method for your process.
- Using a rheometer without selecting the right geometry is like trying to run your car without gasoline. Pay absolute attention to this.
- Wall slip is a common challenge with structured fluids. It is essential to identify if wall slip is affecting your measurements and switch to geometries with roughened surface if it is detected. In rheology, it is easy to generate a curve, but ensuring the integrity of the data and obtaining curves free of artifacts is crucial. Pay attention to details and refer to the numbered sources of artifacts in this note.
Future application notes will expand upon this one, covering more advanced topics related to yield stress time-dependent materials, including dynamic and static yield stress, yield stress and longterm stability, and further discussion on wall slip.
References
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Acknowledgement
For more information or to request a product quote, please visit www.tainstruments.com to locate your local sales office information.
This paper was written by Behbood Abedi, PhD.
TA Instruments, Discovery, RheoGuide and TRIOS are trademarks of Waters Technologies Corporation.
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