Measuring Flow CUrve

1. Getting the Complete Picture: How to Best Measure a
Viscosity Flow Curve
Wednesday, July 13, 2016
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John Duffy
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):
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2. 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
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3. (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
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4. 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.
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5. 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.
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6. 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
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7. 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
www.malvern.com/en/support/resource-center/Whitepapers/WP120416UnderstandYieldStressMeas.aspx
1.
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: salesinfo@malvern.com; www.malvern.com
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