Thickening, shear

The increase in viscosity follows on from the normal decrease of viscosity with increasing shear rate seen with all suspensions. The increase then seen becomes more and more abrupt as the concentration is increased. Since the viscosity is double-valued with respect to shear stress, strange things can happen when stress-controlled rheometers are used to measure this phenomena. For instance, if a stress-sweep programme is used, the shear rate will increase, but eventually decrease. 

The overall situation with respect to the effect of particle size is shown in figure 15, where particle sizes from very small to quite large are responsible for the onset of shear thickening moving from very high to very low shear rates. In fact, the critical shear rate is approximately proportional to the inverse of the particle size squared. More details on this interesting but troublesome phenomenon may be found in a review written by the author [12]. 

In Brownian suspensions, as (p increases, the slope of the viscosity-shear rate curve in the shear-thickening regime typically increases, and for electrostatically stabilized suspensions at high-volume fractions, it can even become a discontinuous jump. At shear rates above the shear-thickening regime, there is typically a second shear-thinning regime (see 

Dimensional analysis implies that for a given value of / , all monodisperse hard-sphere suspensions ought to show an onset of shear thickening at a universal value of the Peclet number Pe, or reduced stress Or. Thus, the critical shear rate Yc foi shear thickening ought 

A shift factor/7j- fnrthp solvent is used tn rnllapgp data gathprpH at Hiffprpnt tpmper- 

The shape of these G ((o) and G ((o) curves look similar for all concentrations in the range 0.30 0 0.55 however, the curves shift toward lower frequencies and higher 

At high frequencies, the viscoelastic behavior of suspensions is primarily dissipative, as the particles are forced to move through the solvent much faster than they can relax by Brownian motion. The high-frequency behavior is characterized by a constant high-frequency viscosity = lim oo G jay, which has been subtracted from the data plotted in Fig. 

---

Dilatant fluids (also known as shear thickening fluids) show an increase in viscosity with an increase in shear rate. Such an increase in viscosity may, or may not, be accompanied by a measurable change in the volume of the fluid (Metzener and Whitlock, 1958). Power law-type rheologicaJ equations with n > 1 are usually used to model this type of fluids. 

For a Hquid under shear the rate of deformation or shear rate is a function of the shearing stress. The original exposition of this relationship is Newton s law, which states that the ratio of the stress to the shear rate is a constant, ie, the viscosity. Under Newton s law, viscosity is independent of shear rate. This is tme for ideal or Newtonian Hquids, but the viscosities of many Hquids, particularly a number of those of interest to industry, are not independent of shear rate. These non-Newtonian Hquids may be classified according to their viscosity behavior as a function of shear rate. Many exhibit shear thinning, whereas others give shear thickening. Some Hquids at rest appear to behave like soHds until the shear stress exceeds a certain value, called the yield stress, after which they flow readily. 

The fluid may be either shear-thinning or, less often, shear-thickening, and in either case the shear- stress and the apparent viscosity fia are functions of shear rate, or ... 

From equation 3.123 when n > 1. pa increases with increase of shear rate, and shear-thickening behaviour is described ... 

Thus, by selecting an appropriate value of n, both shear-thinning and shear-thickening behaviour can be represented, with n = 1 representing Newtonian behaviour which essentially marks the transition from shear-thinning to shear-thickening characteristics. 

For a shear-thickening fluid the same arguments can be applied, with the apparent viscosity rising from zero at zero shear rate to infinity at infinite shear rate, on application of the power law model. However, shear-thickening is generally observed over very much narrower ranges of shear rate and it is difficult to generalise on the type of curve which will be obtained in practice. 

In general, for shear-thinning pseudoplastic fluids the apparent viscosity will gradually decrease with time if there is a step increase in its rate of shear. This phenomenon is known as thixotropy. Similarly, with a shear-thickening fluid the apparent viscosity increases under these circumstances and the fluid exhibits rheopexy or negative-thixotropy. 

Non-llocculated suspensions can exist at very much higher concentrations and, at all but file highest volumetric concentrations, are often Newtonian. When such suspensions are sheared, some dilation occurs as a result of particles trying to "climb over each other . If the amount of liquid present is then insufficient fully to till the void spaces, particle-particle solid friction can come into play and the resistance to shear increases. This is just one way in which shear-thickening can occur. 

When the fluid behaviour can be described by a power-law, the apparent viscosity for a shear-thinning fluid will be a minimum at the wall where the shear stress is a maximum, and will rise to a theoretical value of infinity at the pipe axis where the shear stress is zero. On the other hand, for a shear-thickening fluid the apparent viscosity will fall to zero at the pipe axis. It is apparent, therefore, that there will be some error in applying the power-law near the pipe axis since all real fluids have a limiting viscosity po at zero shear stress. The procedure is exactly analogous to that used for the Newtonian fluid, except that the power-law relation is used to relate shear stress to shear rate, as opposed to the simple Newtonian equation. 

Compared with the parabolic profile for a Newtonian fluid (n = 1), the profile is flatter for a shear-thinning fluid ( < 1) and sharper for a shear-thickening fluid (n > l). The ratio of the centre line (uCl) to mean (k) velocity, calculated from equation 3.133, is ... 

Show how. by suitable selection of the index n, the power law may be used to describe the behaviour of both shear-thinning and shear-thickening non-Newtonian fluids over a limited range of shear rates. What are the main objections to the use of the power law Give some examples of different types of shear-thinning fluids. 

Shearing stress velocity 704, 715 Shear-thickening 106, 111, 121 Shear-thinning 106, 196... 

Certain polymeric systems can become more viscous on shearing ( shear thickening ) due to shear-introduced organization. These systems become more resistant to flow as the crystals form so that the introduction of the shear increases their viscosity. Figure 6.5 shows the viscosity versus strain rate relationship for Newtonian and non-Newtonian fluids, highlighting the differences in their behaviors. 

Swanson, B.L. "Oil Displacement Method Using Shear Thickening Compositions," US Patent 4,289,203(1981). 

Oscillatory shear experiments are the preferred method to study the rheological behavior due to particle interactions because they directly probe these interactions without the influence of the external flow field as encountered in steady shear experiments. However, phenomena that arise due to the external flow, such as shear thickening, can only be investigated in steady shear experiments. Additionally, the analysis is complicated by the different response of the material to shear and extensional flow. For example, very strong deviations from Trouton s ratio (extensional viscosity is three times the shear viscosity) were found for suspensions [113]. 

Some very concentrated suspensions are dilatant. If, in such a suspension, the particles are closely packed, then when the suspension is sheared the particles have to adopt a greater spacing in order to move past neighbouring particles and as a result the suspension expands, ie it dilates. Dilatant materials tend to be shear thickening but it does not follow that shear thickening behaviour is necessarily due to dilatancy. Consequently, dilatancy should not be used as a synonym for shear thickening behaviour. 

It should be noted that for shear thinning and shear thickening behaviour the shear stress-shear rate curve passes through the origin. This type of behaviour is often approximated by the power law and such materials are called power law fluids . Using the negative sign convention for stress components, the power law is usually written as... 

Clearly, shear thinning behaviour corresponds to n 1. The special case, n = 1, is that of Newtonian behaviour and in this case the consistency coefficient K is identical to the viscosity fx. Values of n for shear thinning fluids often extend to 0.5 but less commonly can be as low as 0.3 or even 0.2, while values of n for shear thickening behaviour usually extend to 1.2 or 1.3. 

Equation 3.29 is helpful in showing how the value of the correction factor in the Rabinowitsch-Mooney equation corresponds to different types of flow behaviour. For a Newtonian fluid, n = 1 and therefore the correction factor has the value unity. Shear thinning behaviour corresponds to < 1 and consequently the correction factor has values greater than unity, showing that the wall shear rate yw is of greater magnitude than the value for Newtonian flow. Similarly, for shear thickening behaviour, yw is of a... 

Nienow and Elson (1988) have reviewed work done mainly by them and their co-workers on the mixing of non-Newtonian liquids in tanks. The above approach for inelastic, shearing thinning liquids has been largely substantiated but considerable doubt has been cast over using this method for dilatant, shear thickening materials. 

The flow behaviour of aqueous coating dispersions, because of their high pigment and binder content, is often complex. They have viscosities which are not independent of the shear rate and are therefore non-Newtonian. Shear thickening (when the viscosity of the dispersion increases with shear rate) and shear thinning or pseudoplastic behaviour (when the viscosity decreases with shear rate), may... 

---