Viscosity shear thickening

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 ... 

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. 

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. 

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. 

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]. 

Clearly, shear thinning behaviour corresponds to nshear thickening behaviour 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. 

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... 

There is an expression that does not truly fit either class of behaviour, for power law fluids which can be expressed in terms of stress, rate or apparent viscosity with relative ease. They can describe shear thickening or thinning depending upon the sign of the power law index n ... 

In wet grinding the power consumption is generally about 30 per cent lower than that for dry grinding and, additionally, the continuous removal of product as it is formed is facilitated. The rheological properties of the slurry are important and the performance tends to improve as the apparent viscosity increases, reaching an optimum at about 0.2 Pa.s. At very high volumetric concentrations (ca. 50 volume per cent), the fluid may exhibit shear-thickening behaviour or have a yield stress, and the behaviour may then be adversely affected. 

Bingham fluids that are either shear-thinning or shear-thickening above their yield stresses have corresponding power-law expressions incorporated into their viscosity models. 

Apparent Viscosity and Shear Thinning Versus Shear Thickening HI. 1.1... 

APPARENT VISCOSITY AND SHEAR THINNING VERSUS SHEAR THICKENING... 

Some materials will increase in viscosity as the flow rate increases, and, although this is relatively rare, it is crucial to be aware of this if processi ng is to be effective. Shear thickening occurs as a result of one or more of the following situations ... 

Shear-thickening is characterised by an increase in apparent viscosity with increasing rate of deformation. 

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