The Rheology Handbook. Thomas Mezger
Figure 3.13: Structural changes of dispersions showing shear-thinning behavior
b) Shear range 2 at medium shear rates: the “flow range”
At increased shear rates, the number of disentanglements is more and more exceeding the number of the re-entanglements. As a consequence, the polymer shows shear-thinning behavior, and therefore, the curve of the viscosity function η( γ ̇ ) is decreasing now continuously (see Figure 3.10, range 2).
c) Shear range 3 at high-shear conditions: the “high-shear range”
For polymer solutions the high-shear range may begin at around γ ̇ = 1000 s-1, however, for some of them γ ̇ = 10,000 s-1 has to be exceeded. Finally, all macromolecules are almost fully oriented and disentangled. Flow resistance is reduced to a minimum value now and cannot be decreased any further, corresponding to the friction between the individual disentangled molecules gliding off each other. Viscosity is measured then as a constant value which is referred to as the infinite-shear viscosity η∞.
Infinite-shear viscosity is occurring as a constant limiting value of the viscosity function towards sufficiently high shear rates which are “close to an infinitely high shear rate”. Sometimes here, rheologists are speaking of the plateau value of the limiting high-shear viscosity.
Infinite-shear viscosity in mathematical notation
Equation 3.4
η∞ = lim γ ̇ →∞ η( γ ̇ )
Infinite-shear viscosity is the limiting value of the shear rate-dependent viscosity function at an “infinitely high” shear rate.
Note: Degradation of polymer molecules
At these extreme shear conditions, there is always the risk of degradation of macromolecules. The polymer chains may be torn and divided into pieces, a process which might destroy their original chemical structure. However, this should be avoided when performing rheological tests. Using the previously highly sheared sample again, it is easy to check if degradation has really taken place by carrying out a second measurement at the same low-shear conditions of shear range 1 (see Figure 3.10). If the η0-value remains still unchanged, no effective degradation has taken place. If the occurring η0-value is significantly lower then, polymer molecules have been destroyed under the previously applied high shear load, thus, the value of the average molar mass is significantly lower now.
3.3.2.2Structures of dispersions showing shear-thinning behavior
Besides polymers, also other materials may show shear-thinning behavior. For dispersions, a shear process may cause orientation of particles into flow direction. Shearing may also cause disintegration of agglomerates or a change in the shape of particles (see Figure 3.13). Usually then, the effectivity of interactive forces between the particles is more and more reduced, which results in a decreasing flow resistance.
Note 1: Observation and visualization of flowing emulsions using a rheo-microscope
Deformation and flow behavior of droplets in flowing emulsions at defined shear conditions can be observed when using a rheo-microscope or other rheo-optical devices (like SALS; see Chapter 10.8.2.5). Corresponding photographic images are shown e. g. in [3.13] [3.15] [3.85].
Note 2: Visualization of flowing suspensions using polarized light imaging
Shear-induced particle orientation and alignment of particles can be tracked during flow by color changes resulting from the varying angle between the particle axis and the orientation of the polarizer/analyzer (see Chapter 10.8.2.1d; e. g. cellulose nanocrystals; between 100 nm and 200 nm long and around 10 nm thick).
3.3.3Shear-thickening flow behavior
Experiment 3.1: Shear-thickening of a plastisol dispersion (see Figure 3.14)
1 Placed in a beaker, a wooden rod inclines very slowly under its own weight through the dispersion.
2 Pulling the rod very quickly, causes the sample to solidify immediately.
3 Therefore then, the rod, the plastisol mass, and even the beaker are lifted all together now.
Viscosity of a shear-thickening material is dependent on the degree of the shear load. The flow curve shows an increasing curve slope (see Figure 3.15), i. e., viscosity increases with increasing load (see Figure 3.16).
Figure 3.14: Testing shear-thickening behavior of a plastisol dispersion
Figure 3.15: Flow curve of a shear-thickening liquid
Figure 3.16: Viscosity curve of a shear-thickening liquid
Examples of shear-thickening materials
Dispersions showing a high concentration of solid matter or gel-like particles; ceramic suspensions, starch dispersions, paper coatings, plastisol pastes (containing not enough plasticizer), natural rubber (NR), highly filled elastomers (such as polybutadiene or butyl rubber BR), dental composites, shock-resistant “smart fluids”
The terms shear-thickening and dilatant are identical in their meaning; sometimes the terms shear-hardening, shear-stiffening or solidifying can be heard. The Note on the term “apparent viscosity” of Chapter 3.3.2 also applies here.
Problems with flow processes should always be taken into account when working with shear-thickening materials. Flow should be observed carefully for the occurrence of wall-slip effects and separation of the material, e. g. on surfaces of measuring geometries, along pipeline walls or between individual layers of the sample. This can be investigated by repeating the test several times under identical measuring conditions, comparing the results with regards to reproducibility.
For dispersions, shear-thickening flow behavior should be taken into account
at a high particle concentration
at a high shear rate
Figure 3.17 presents the dependence of viscosity on the particle concentration (here with the volume fraction solid Φ). For Φ = 0 (i. e. pure fluid without any particle), the liquid shows ideal- viscous flow behavior. For 0.2 ≤ Φ ≤ 0.4, the suspension displays shear-thinning, particularly in the low-shear range. For Φ > 0.4, on the one hand there is shear-thinning in the low-shear range, but on the other hand occurs shear-thickening in the medium and high-shear range. At higher concentrations, the range of shear-thickening behavior is beginning at lower shear rate values already.
Shear-thickening materials are much less common in industrial practice compared to shear-
thinning materials. Nevertheless, shear-thickening behavior is desirable for special applications and is therefore encouraged in these cases (example: dental composites). Usually, however, this behavior is undesirable and should never be ignored since it may lead to enormous technical problems and in some