Rheology toolkit #2: The importance of yield stress

Product manager at Malvern Instruments Steve Carrington offers an introduction to the importance of yield stress and explores how rotational rheometers can be used to measure it.

The importance of yield stress

Toothpaste is a useful product with which to illustrate the concept and value of yield stress.

To perform effectively, a toothpaste formulation must flow from a tube under minimal force, like a viscous liquid, but sit securely on the toothbrush, exhibiting gel or solid-like behaviour.

This behavioural duality, which determines both functionality and perceived product quality, can be attained by achieving a defined value of yield stress during the formulation process.

Yield stress marks the point at which fluids that are solid- or gel-like when at rest become liquid-like in their behaviour: it is the shear stress threshold above which a material flows.

So what is yield stress?

Complex fluids have a figurative ’skeleton’, a microstructure that extends throughout the system.

The strength of this skeleton is governed by the structure of the dispersed phase and by the interactions between dispersed particles. At low stress, the structure has elastic properties, but as the applied stress increases and moves closer to the yield stress value it begins to break down and liquid like flow is established. This process is typically reversible so when the stress is lifted the internal structure rebuilds quite quickly.

The structural breakdown associated with the transition from solid- to liquid- like behaviour can be induced over a brief period of time by applying a high stress, or in some cases, through exposure to a lower stress for longer periods.

Many materials flow or creep if the measurement timescale is sufficiently long, so defining whether or not a material has a true yield stress can be problematical. This raises the question of whether it is necessary to establish true yield stress values, or whether measuring ’apparent’ yield stress is adequate (see Fig.1).

Choosing a technique for yield stress measurement

Characterising yield stress in a relevant way relies on adopting test conditions that reflect those that will apply during use of the product, most especially with respect to timescales, stress and environmental factors such as temperature.

No universal test method exists and different techniques have relative strengths and weaknesses.

Rotational rheometers and viscometers can both be used to measure yield stress, however rotational rheometers offer greater functionality for the adoption of multiple methods, including the unique facility for oscillatory testing.

In a rotational rheometer, the sample is held between two plates, or some similar geometry, such as a cone and plate.

Rotating the upper plate, relative to the lower stationary plate, applies a controlled stress to the sample.

The resulting strain or shear rate is then measured. Modern systems can be programmed to run a variety stress profiles and yield stress methodologies, depending on the nature of the sample being tested.

Testing with different methods and then selecting a preferred option on the basis of either relevance or practicality is a useful approach. Understanding the different methods available helps with making an informed choice.

Model fitting

Model fitting is a traditional method for yield stress measurement. Models are fitted to plots of shear stress versus shear rate, with the appropriate model depending on: the behaviour of the system under test, the goodness of fit, and the conditions of interest for the product.

The model fitting method determines dynamic yield stress, the minimum stress required for maintaining flow, as distinct from static yield stress, the stress required to initiate flow.

These two measurements are complementary and often used in tandem to give an overall view of how easily a material flows and the impact of stoppages after yielding.

Stress ramp and stress growth

Stress ramps are used to quickly, easily and directly measure yield stress. The technique involves ramping up shear, and determining viscosity, until a peak viscosity is observed (see Fig.2).

Peak viscosity correlates with the point at which the internal structure has completely broken down and the material begins to flow.

As yield stress behaviour is time dependent the rate at which the stress is ramped up is a critical factor.

Stress growth is an alternative but similar ramping method wherein the sample is subjected to a steadily increasing strain through application of a constant strain rate (shear rate).

As the material undergoes elastic deformation the stress build up is monitored as a function of time until a critical strain is reached and the structure breaks down (see Fig.3).

Again, the speed at which strain is ramped up is determined by the conditions of interest. Slower ramping is more reflective of behaviour over long periods, while steeper ramping generates data of more relevance to processes, such as dispensing.

Oscillatory testing

Oscillatory testing offers a more consistent approach for static yield stress determination than is provided by steady shear methods, particularly for systems with low yield stress. In oscillatory testing, as the name suggests, shear is applied in a sinusoidal pattern.

Yield stress marks the transition between solid- and liquid-like behaviour, a transition that with oscillatory testing can be determined from the relative magnitude of the elastic modulus (G’), which describes solid like behaviour, and the viscous modulus (G”), which relates to liquid-like characteristics (see Fig.4).

Yield stress is derived in oscillatory testing by applying an increasing oscillatory stress or strain to the sample and monitoring the change in the viscoelastic moduli with increasing amplitude.

Yield stress has been identified either from a sharp drop in elasticity, G’, or in some cases from the point where G” becomes larger than G’. The ’yield zone’ is the range spanned by the two values produced by these alternative methods.

Multiple creep

Multiple creep testing is one of the most accurate ways of determining yield stress. It involves applying a defined stress to a material to produce a compliance versus time curve.

Testing at different values of stress produces a series of compliance curves. These curves overlie one another at stresses below the yield stress, but deviate above the yield stress as liquid-like behaviour begins to dominate.

Measuring differences in the gradient of these curves highlights the point at which the deviation begins to occur, giving an extremely accurate measurement of yield stress.

Although accurate, this method can be extremely time-consuming, in some cases to the point of being industrially impractical (see Fig.5).

In order to find out more about methods for yield stress measurement, including more information on the techniques outlined here, please refer to Malvern Instruments’ whitepaper ’Understanding yield stress’ at: http://www.malvern.com/yield-stress

To read the first part of Malvern Instruments’ ’Rheology Toolkit’ series, click here.