The first part of the Malvern Instruments rheology toolkit series, designed to explore some fundamental rheological tests that can be used to generate valuable information for formulation, product development, QC, and process troubleshooting, has been released.
The toolkit series from Malvern Instruments is introduced by Steve Carrington, product marketing manager for rheology at Malvern Instruments.
Generate a flow curve
Viscosity is a measure of a fluid’s resistance to flow and is one of the most widely engineered rheological properties.
Lowering viscosity makes liquids easier to pump and spread, while increasing it reduces dripping, potentially an advantage for products such as paint and ink.
High viscosity can also provide the structure needed to suspend particles, in medicines, personal care products and drinks. Making sure that the viscosity of a product is closely matched to end-use requirements is a valuable strategy for building product value.
Getting product viscosity ’right’ is complicated by the fact that relatively few complex fluids exhibit a viscosity that is independent of the shear force applied to them.
Most industrially interesting fluids are non-Newtonian, meaning that their viscosity varies depending on shear rate; shear rate being the rate at which a shearing force is applied.
The majority of complex fluids are shear thinning i.e. their viscosity decreases with shear rate, although certain systems such as concentrated suspensions can exhibit shear thickening, an increase in viscosity at high shear rates.
This means we can only successfully match the viscosity of a formulation to performance requirements if we measure it under the conditions applied during product use.
An equilibrium flow curve (generated using a table of shear rates) is a plot of viscosity as function of shear rate and is a primary tool for achieving this goal.
Defining a measurement range
As discussed above, the viscosity value of interest for any given application is the one that corresponds to the conditions applied.
If these are constant then a single value of viscosity is sufficient but for the majority of products more information is required, creating the need to generate an equilibrium flow curve, under an appropriate set of conditions.
Consider a paint destined for spray application. Performance goals here might include good stability during storage and effective application with moderate levels of force during spraying.
For stability studies it is viscosity values at very low shear that are critical because in storage the paint is simply subject to gravity.
On the other hand, since the spray gun is designed to apply considerable levels of shear, high shear viscosity will define performance at this point.
To fully scope and control the behaviour of the paint it is necessary to measure viscosity as a function of shear rate, over the extremes of conditions that the product will be subjected to. This will generate a relevant equilibrium flow curve.
The practicalities of testing
At this point it is probably helpful to briefly discuss the instrument options for viscosity measurement.
In many industries viscometers provide all the data needed. These tend to measure at a single shear rate or over a fairly limited range but can be sufficient for QC and certain aspects of formulation, as long as the range of the instrument covers the area of interest for the application.
A rotational rheometer, in contrast, enables measurement across a very broad range of shear rates and the generation of a more complete flow curve.
As we have seen, this may be essential to fully scope product performance under all applicable conditions.
Furthermore, rotational rheometers offer a whole host of alternative rheological characterisation methods that can be used to explore in more detail and refine product performance. We’ll be discussing these in subsequent articles. (See figure 1 image above).
Figure 1 (i) Table of shear rates (solid line) and sample viscosity response (dashed line). The ’Sampling interval’ is set to allow the material to get to equilibrium (time a), followed by an integration period (time b) over which data is averaged to generate a final viscosity value. (ii) Equilibrium flow curve (plot of final viscosity value against shear rate) showing responses for a shear thinning material with a zero shear viscosity (dashed line) and with a yield stress (solid line).
Figure 1 (i) above illustrates the practicalities of generating an equilibrium flow curve. Equilibrium viscosity, the viscosity value established as a steady state is reached, is measured at a series of shear rate values.
Each shear rate is applied for a defined sampling time to allow the sample to equilibrate under these conditions (a) and to produce a robust, averaged value of equilibrium or ’steady state’ viscosity (b).
Note that modern rheometers report ’Live’ (or instantaneous) data that allows the approach to equilibrium to be followed, as well as a ’Steady State’ parameter - the use of which enables an optimum sampling interval to be set up for a particular sample.
Plotting each final value of viscosity against the shear rate at which it was measured results in the equilibrium flow curve (see Figure 1 (ii)).
This test is applicable to all materials types - including synthetic and bio-polymer solutions, surfactant systems, suspensions, emulsions and foams, pastes, gels and polymer melts.
Note that as with any rheology measurement, it is essential to select an appropriate measuring system (or geometry) based on consideration of particular sample and test attributes.
Sample attributes that impact on geometry choice include viscosity e.g. is it high (treacle-like) or low (water-like), whether it contains particulates (and the size of these if it does), which may also increase the possibility of wall slip (against the measuring system surface), and the likelihood of solvent evaporation during the measurement.
Ideally, a cone and plate geometry, where the shear rate is constant across the entire shear gap would be preferred for measurement of a flow curve for a non-Newtonian complex fluid.
However, some dispersed systems may have particulates that prevent the use of a narrow-gap cone and plate geometry, or require roughened (sandblasted) or even serrated measurement surfaces to minimise wall slip, in which case alternative geometries such as parallel plate should be considered.
For dispersions with a microstructure that may be susceptible to ’damage’ by sample loading e.g. foams and some high particle-loaded pastes or muds, then a vane tool and cylindrical cup may actually be the optimum measurement set-up.
Interpreting the data
The flow curves displayed above (in Figure 1(ii)) are typical of shear thinning fluids where viscosity decreases with increasing shear rate.
However, the samples are markedly different in terms of their behaviour at very low shear rates or at rest.
One exhibits a yield stress (solid line on graph), meaning it becomes solid or gel-like at rest (with the viscosity values tending to infinity), while the other (dashed line on graph) behaves as a relatively viscous liquid, and exhibits a plateau in viscosity as shear rate goes to zero i.e. it has a Zero Shear Viscosity (n0).
Examples of every day products engineered to have a yield stress include toothpaste, tomato ketchup and mayonnaise.
Paint is a good example of a product that may have a high but measurable viscosity even at very low shear rates.
At high shear rates, the flow curve may show another plateau that represents the Infinite Shear Viscosity (n00), although for many samples the ability to generate sufficiently high shear rates to access this regime may not be achievable due to experimental or material constraints.
When plotted on log-log axes, the flow curve of a typical shear thinning material (with a zero shear viscosity) will show the two limiting Newtonian plateaus (n0 and n00) separated by a (linear) power law region.
Many mathematical models have been proposed and used to fit flow curve data using a small number of fitting parameters e.g. Power Law or Ostwald, Cross and Sisko.
Such model fits enabled the use of a few model parameters to compare materials against (providing the data fit was good), rather than assessing complete curves, and this approach can still be beneficial for some QC applications, or for use in process simulations.
However, the powerful capabilities and ease with which modern rheometers and associated data analysis software can make measurements and report data to specific user requirements (including some automatic model fitting if required) makes direct use of measured rheological data fully accessible.
Top tips for successful equilibrium flow curve measurement
- Think of all the conditions that the product will be subjected to and measure over a shear rate range that fully covers the operating window of interest.
- Make sure that the measuring system (or geometry) used is suitable for the material type under test.
- Choose a sampling interval that measurably allows for sample equilibrium (or steady state) followed by an integration period for robust final viscosity data.
Part 2 of the series: Evaluating Yield Stress.
