Fluid 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 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. 

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 ... 

Fluids with shear stresses that at any point depend on the shear rates only and are independent of time. These include (a) what are known as Bingham plastics, materials that require a minimum amount of stress known as yield stress before deformation, (b) pseudoplastic (or shear-thinning) fluids, namely, those in which the shear stress decreases with the shear rate (these are usually described by power-law expressions for the shear stress i.e., the rate of strain on the right-hand-side of Equation (1) is raised to a suitable power), and (c) dilatant (or shear-thickening) fluids, in which the stress increases with the shear rate (see Fig. 4.2). 

The experimental and theoretical literature on instabilities in fiber spinning has been reviewed in detail by Jung and Hyun (28). The theoretical analysis began with the work of Pearson et al. (29-32), who examined the behavior of inelastic fluids under a variety of conditions using linear stability analysis for the governing equations. For Newtonian fluids, they found a critical draw ratio of 20.2. Shear thinning and shear thickening fluids... 

Rheopectic (antithixotropic) fluids are shear-thickening fluids whose r a increases with time under constant or low y. Rheopexy is a property of linear... 

Equation 3.5 contains a constant factor K and a varying factor n, which specifies the slope of the viscosity function. For Newtonian fluids, K corresponds to the shear viscosity r) and n=l. For 0 < n < 1, the fluid is a shear thinning fluid. For shear-thickening fluids, i.e. liquids, whose viscosity increases with shearing, 1 < n < °°. 

Table 3.2 Summary of the relations for Newtonian and shear thinning/shear thickening fluids in the case of a simple fully developed pipe flow (isothermal) [61, [14]...

Figure 3.18 Radial profile of shear stress, shear rate, and speed through the cross-section for an isothermal pipe flow with Newtonian, shear thinning, and shear thickening fluids...

With respect to the shear stress distribution, shear thinning fluids (0 < n < 1) generally lead to lower shear stresses than shear-thickening fluids (n > 1), because the viscosities of shear thinning fluids in a stationary state are lower than in the case of Newtonian or shear thickening fluids at the same shear rate. 

Shear-Thinning and Shear-Thickening Fluids Viscoelastic Fluids... 

Shape-memory polymers, 207 Shear, 124, 261 Shear-thickening fluids, 125 Shear-thinning fluids, 124-125 Shirakawa, Hideki, 74 Shivers, Joseph, 149 Shrink-wrap film, 207 Siemans, 72... 

Shear stress-shear rate plots of many fluids become linear when plotted on double logarithmic coordinates and the power law model describes the data of shear-thinning and shear thickening fluids ... 

Resolution of the velocity data and removal of data points near the center of the tube which are distorted by noise aid robustness of the curve fit the polynomial curve fit introduced a systematic error when plug-like flow existed at radial positions smaller than 4 mm in a tube of 22 mm diameter. The curve fit method correctly fit the velocity data of Newtonian and shear-thinning behaviors but was unable to produce accurate results for shear-thickening fluids (Arola et ah, 1999). 

Griskey, R. G. and Green, R. G. 1971, Flow ofdilatant shear-thickening fluids, jfnt. Inst. Chem. Engrs.J. 17 725-728. 

Dilatant Fluids. Dilatant fluids or shear-thickening fluids are less commonly encountered than pseudoplastic (shear-thinning) fluids. Rheological dilatancy refers to an increase in the apparent viscosity with increasing shear rate (3). In many cases, viscometric data for a shear-thickening fluid can be fit by using the power law model with n > 1. Examples of fluids that are shear-thickening are concentrated solids suspensions. 

Measurements of power consumption of a I ARAVISC stirrer (combination of anchor and helical ribbon stiners) in dilatant (shear-thickening) fluids are presented in [708]. 

In Equation (2), n is the flow behavior index (-),K is the consistency index (Pa secn), and the other terms have been defined before. For shear-thinning fluids, the magnitude of nl, and for Newtonian fluids n=l. For PFDs that exhibit yield stresses, models that contain either (Jo or a term related to it have been defined. These models include, the Bingham Plastic model (Equation 3), the Herschel-Bulkley model (Equation 4), the Casson model (Equation 5), and the Mizrahi-Berk model (Equation 6). 

Newtonian fluids are a subclass of purely viscous fluids. Purely viscous nonnewtonian fluids can be divided into two categories (1) shear-thinning fluids, and (2) shear-thickening fluids. Such fluids can be described by a constitutive equation of the general form... 

W. H. Suckow, P. Hrycak, and R. G. Griskey, Heat Transfer to Non-Newtonian Dilatant (Shear-Thickening) Fluids Flowing Between Parallel Plates, AIChE Symp. Ser. (199/76) 257,1980. 

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