Viscosity shear thinning systems

So far the results have been shown in which the metal alkoxide solutions are reacted in the open system. It has been shown that the metal alkoxide solutions reacted in the closed container never show the spinnability even when the starting solutions are characterized by the low acid content and low water content (4). It has been also shown from the measurements of viscosity behavior that the solution remains Newtonian in the open system, while the solution exhibits structural viscosity (shear-thinning) in the closed system. 

Figure 20.3 Viscosity versus shear rate for a shear thinning system.

Simple classifications of fluids can be made on the basis of their rheological profiles. Figure 3.78 shows the (a) shear stress and (b) viscosity profiles for various systems. From Figure 3.78 one may define the following systems. Newtonian systems have a constant viscosity with respect to shear rate. Dilatant (or shear-thickening) systems have a viscosity that increases with respect to shear rate. Pseudo-plastic (or shear-thinning) systems have a viscosity that decreases with respect to shear rate. Yield-stress materials are materials that have an initial structure that requires a finite stress before deformation can occur. The stress that initiates deformation is defined as the yield stress. 

This chapter is an in-depth review on rheology of suspensions. The area covered includes steady shear viscosity, apparent yield stress, viscoelastic behavior, and compression yield stress. The suspensions have been classified by groups hard sphere, soft sphere, monodis-perse, poly disperse, flocculated, and stable systems. The particle shape effects are also discussed. The steady shear rheological behaviors discussed include low- and high-shear limit viscosity, shear thinning, shear thickening, and discontinuity. The steady shear rheology of ternary systems (i.e., oil-water-solid) is also discussed. 

For most practical suspensions (with > 0.1 and containing thickeners to reduce sedimentation) a plot of viscosity depends on the applied shear rate). The most common flow curve is shown in Figure 7.42 (usually described as a pseudo-plastic or shear thinning system). In this case, the viscosity decreases with increasing shear rate, reaching a Newtonian value above a critical shear rate. 

There are usually oil-in-water (0/W) emulsions that are formulated in such a way (see section on cosmetic emulsions) to give a shear thinning system. The emulsion will have a high viscosity at low shear rates (0.1 s ) in the region of few hundred Pa s, but the viscosity decreases very rapidly with increasing shear rate, reaching values of few Pa s at shear rates greater than 1 s h... 

Dispersion of a soHd or Hquid in a Hquid affects the viscosity. In many cases Newtonian flow behavior is transformed into non-Newtonian flow behavior. Shear thinning results from the abiHty of the soHd particles or Hquid droplets to come together to form network stmctures when at rest or under low shear. With increasing shear the interlinked stmcture gradually breaks down, and the resistance to flow decreases. The viscosity of a dispersed system depends on hydrodynamic interactions between particles or droplets and the Hquid, particle—particle interactions (bumping), and interparticle attractions that promote the formation of aggregates, floes, and networks. 

If there is particle—particle interaction, as is the case for flocculated systems, the viscosity is higher than in the absence of flocculation. Furthermore, a flocculated dispersion is shear thinning and possibly thixotropic because the floccules break down to the individual particles when shear stress is appHed. Considered in terms of the Mooney equation, at low shear rates in a flocculated system some continuous phase is trapped between the particles in the floccules. This effectively increases the internal phase volume and hence the viscosity of the system. Under sufficiently high stress, the floccules break up, reducing the effective internal phase volume and the viscosity. If, as is commonly the case, the extent of floccule separation increases with shearing time, the system is thixotropic as well as shear thinning. 

Calculate the theoretical power in watts for a 0.25 m diameter, six-blade flat blade turbine agitator rotating at N = 4 rev/s in a tank system with a power curve given in Figure 5.10. The liquid in the tank is shear thinning with an apparent dynamic viscosity dependent on the impeller speed N and given by the equation fia = 25(N)n 1 Pa s where the power law index n = and the liquid density p = 1000 kg/m3. 

The results of Equation (3.56) are plotted in Figure 3.14. It can be seen that shear thinning will become apparent experimentally at (p > 0.3 and that at values of q> > 0.5 no zero shear viscosity will be accessible. This means that solid-like behaviour should be observed with shear melting of the structure once the yield stress has been exceeded with a stress controlled instrument, or a critical strain if the instrumentation is a controlled strain rheometer. The most recent data24,25 on model systems of nearly hard spheres gives values of maximum packing close to those used in Equation (3.56). 

The term a controls the critical strain where the system shear thins and n controls the rate of thinning. The low and high shear viscosity are given by... 

A numerical implementation of this approach can be generalised to include the polydispersity of the polymer. As polydispersity is increased the power law of — 0.8181... reduces. The onset of shear thinning, where Tn y 1 — 1, results in a slightly lower viscosity for polydisperse systems at this rate. So far we have neglected the origin of the characteristic time for the system which we would like to describe in terms of the chemical... 

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