Several complex fluids such as network forming polymers, surfactant mesophases, emulsions etc do not flow till the applied stress exceeds a specific critical value known as the yield stress.
Materials showing this behavior are said to be exhibiting yield flow behavior. The yield stress is defined as the stress that must be applied to the sample before it starts to flow. Below the yield stress the sample will deform elastically (like stretching a spring), above the yield stress the sample will flow like a liquid.
Most fluids showing a yield stress can be thought of as having a structural skeleton extending throughout the entire volume of the system. The skeleton strength is governed by the dispersed phase and its interactions. The continuous phase has a low viscosity, however high volume fractions of a dispersed phase and/or strong interactions between components can increase the viscosity by a thousand times or more and induce solid like behavior at rest.
The stress at which this catastrophic breakdown of the structural skeleton occurs is the yield stress and the associated strain the yield strain. This process can be shown using mechanical analogues as in Figure 1 using a spring in parallel with a dashpot (or damper) for a viscoelastic solid, and a spring and dashpot in the case of a gel. In both cases it is not possible for the material to deform plastically or flow since it is restricted by the spring which must initially be broken.
In case of a viscoelastic solid, the yielded material will behave similar to a Newtonian liquid, while for the gel, yielding will result in a viscoelastic liquid showing shear thinning behavior.
Figure 1. Illustration showing mechanical analogues and associated yielding for a viscoelastic solid and a gel.
In the case of emulsions and foams, this solid-like behavior results from tight or ordered packing of the dispersed phase, while in polymer gels, for example, molecular association or interaction is largely responsible. A glassy liquid and an entangled polymer system will behave like a solid when deformed rapidly. At longer deformation times these materials show liquid properties and hence do not possess a true yield stress.
Figure 2 shows a material having a true yield stress, showing an infinite viscosity approaching zero shear rate and a material with an apparent yield stress showing a zero shear viscosity plateau.
Figure 2. Illustration showing an expected flow curve for a material with a true yield stress.
Determining Yield Stress
Determining a yield stress as a true material constant can be difficult, as the measured value can be can be very much dependent on the measurement technique employed and the conditions of the test. There is no universal method for determining yield stress and there are a number of approaches that find favor across a range of establishments and industries. Time is one such variable that can affect the measured yield stress value.
A number of complex fluids are thixotropic in nature and can change structurally with time of applied shear and/or take a finite time to recover after yielding. This can be especially important while loading samples before measurement as thus process requires yielding the material first. Some typical frequency spectrums and their mechanical analogs are shown in Figure 3.
Since G’ is the modulus related to elasticity (and association) then when this value exceeds the viscous modulus (G”), which is related to flow, the material can be considered to have an associated structure and hence a yield stress. For a material to have a true yield stress then G’ must exceed G” at infinitely low frequencies, which would be the case for a viscoelastic solid and an ideal gel. For a viscoelastic liquid the material will only appear to yield in the frequency range where G’ exceeds G” and thus these materials can be considered to have an apparent yield stress or critical stress.
Figure 3. Illustration showing some typical frequency profiles for materials with a yield stress/critical stress and their mechanical analogs.
Temperature is another important factor. At higher temperatures, material components have more thermal energy and hence a lower stress input is required to initiate flow. Yield stress decreases with increasing temperatures to the extent that there is no thermally induced structural enhancement at high temperatures.
There are a number of methods for determining the yield stress of a material ranging from accurate rheometric techniques to some cruder non-absolute techniques.
This information has been sourced, reviewed and adapted from materials provided by Malvern Panalytical.
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