Getting the Complete Picture: How to Best Measure a Viscosity Flow Curve

The flow behavior, or rheology, of a product often defines its value and contributes to processability and ease of manufacture. Paints, coatings, foods, personal-care products and inks are examples of products with well-defined flow profiles that benefit from rheological characterization. Crucial to this process is flow-curve measurement—the generation of a plot of viscosity as a function of applied shear rate or shear stress.

What are flow curves?

This article focuses on the best way to measure flow curves to optimize value. A flow curve is a graphical representation of how the shear viscosity of a sample changes when it is subjected to different shear rates or shear stresses. Flow curves are often measured over a limited shear rate range, which can result in vital behaviors being overlooked as well as inadequate control of the product profile. Measurement across all relevant conditions is key to optimal use of this simple but effective rheology tool.

What is viscosity?

Viscosity quantifies a material’s resistance to flow. Fluids that move very easily, like water, have low viscosity, while thicker fluids such as paints with high solids content have much higher viscosity. Shear viscosity is a function of shear rate, pressure, time and temperature and is mathematically defined as shear stress divided by shear rate (see Figure 1):

 Figure 1 – Mathematical definitions associated with flow-curve generation.

Viscosity = shear stress/shear rate
Shear stress (σ) = force/area = F/A
Shear strain (γ) = deformation/height = x/h
Shear rate (γ) = change in strain/change in time = dγ/dt

Shear stress is a measure of the force acting on a cross-section of a material sample in a direction parallel to its plane. The application of shear stress induces deformation in a sample; shear strain quantifies the degree of deformation. Shear rate is the rate of strain change over time.

To generate a flow curve, a sample must be subjected to different shear stresses, and the resulting shear rate measured at each applied stress. Alternatively, the shear rate can be controlled and the stress measured. These measurements are usually made with a rotational viscometer or rheometer.

Why are flow curves useful?

A material that exhibits viscosity that is independent of shear rate is known as Newtonian, and a single viscosity measurement is needed to define its behavior. Newtonian behavior is common for pure, small-molecule fluids and very dilute dispersions. More complex materials— such as polymer solutions, suspensions and emulsions—tend to exhibit non-Newtonian behavior, that is, either viscosity decreases (shear thinning) or, less commonly, viscosity increases (shear thickening) with increasing shear rate (see Figure 2). This occurs as a result of the material’s complex microstructure and the way it rearranges under the applied stress, and can be beneficial for many products.

 Figure 2 – Flow curves for shear thinning and shear thickening.

During processing and use, the shear rate to which a product is subjected can vary significantly. The most informative viscosity value is that which corresponds to the conditions applied; a single-point measurement is only sufficient for non-Newtonian fluids if the shear rate applied at all points during product manufacture and use is constant. In the many instances in which this condition is not met, generation of a flow curve that spans the range of interest provides the information required to characterize and control product performance.

How can an optimum measurement range be determined for a flow curve?

Measuring a flow curve over an excessively wide range can be unnecessarily time-consuming, while limiting this measurement to too narrow a range risks missing important behavior that could impact product value. It is therefore important to identify the relevant shear rates and shear stresses for the range of applications or processes the product will encounter and measure across this range.

Consider paint, which is a complex suspension. Important attributes for paint include stability during storage and ease of application. Viscosity values at very low shear are critical for stability studies because, during storage, paint is subject to gravity, resulting in a relatively low applied force. Brushing applies shear rates of around 103 s-1, while a spray gun may apply shear rates as high as 106 s-1 to break up the paint into fine droplets. Figure 3 shows the shear rate associated with these and other processes.

 Figure 3 – Shear rates for various processes.

Viscosity data collected for two paint samples are shown in Figure 4. Based on the criteria given in Figure 3, these flow curves would indicate that paint A is more stable to sedimentation and less likely to drip due to its higher low-shear viscosity, while paint B will most likely result in a thicker paint layer upon brushing due to its greater high-shear viscosity. Single-point viscosity measurements or measurements made over a limited range of shear rates could not provide the information required to describe the complex rheological behavior of such non- Newtonian paints.

 Figure 4 – Viscosity versus shear rate for two paint samples, A (blue) and B (red).

How to choose an instrument for flow-curve measurement

Tools for viscosity flow-curve measurement range from simple rotational viscometers to highly specific rotational rheometers; these vary in terms of the tests and conditions that can be applied. In certain cases, a viscometer can provide the necessary information. For measurements across a much broader range of shear rates (see Figure 3), especially in the lower range, a rotational rheometer is more useful; a capillary rheometer is more suited for measurements at very high shear rates. The resulting rheometry data can be extremely valuable for stability studies and for quantifying performance in higher shear processes, such as brushing and roller-coating.

Design features of rotational rheometers that are critical to delivering this performance include:

  • Precise control of the gap between the instrument’s upper and lower measuring system, i.e., sample height or thickness
  • Accurate measurement and control of the rotational speed and torque applied during testing.

Sophisticated software simplifies and controls measurement, provides data analysis and streamlines data interpretation.

Looking beyond flow-curve generation

Many other rheological tests can be used to provide information about how a product will perform. At rest, some materials take on liquid-like qualities, while others become solid or gel-like (see Figure 5). For the latter, yield stress marks the point of transition from solid- to liquid-like behavior, and can be an important parameter with which to define product behavior. Solid-like behavior at rest can make a product appear thicker, which consumers may associate with higher quality. Quantifying and controlling yield stress can therefore be a useful strategy when designing a new product or benchmarking performance.1

 Figure 5 – A rotational rheometer provides an extended flow curve across a much wider shear rate range than can be measured with a viscometer.

Unlike viscometers, rotational rheometers also make it possible to quantify viscoelasticity by oscillatory testing. The sample is subjected to a small displacement applied in the form of a sinusoidal, bi-directional pattern. This type of testing permits nondestructive probing of a sample’s structure in terms of its stiffness and viscoelastic characteristics, with elasticity associated with solid-like behavior and viscosity with liquid-like behavior. This can help quantify features like spreadability, mouth feel, texture and gel strength.

In summary, rotational rheometers deliver high performance for a wide range of rheological tests alongside the ability to measure relevant flow curves easily, offering greater potential for product optimization.

Reference

  1. www.malvern.com/en/support/resource-center/Whitepapers/WP120416UnderstandYieldStressMeas.aspx

John Duffy is product marketing manager, Malvern Instruments, Enigma Business Park, Grovewood Rd., Malvern WR14 1XZ, U.K.; tel.: +44 (0) 1684 892456; e-mail: [email protected]www.malvern.com

Related Products

Comments