Shear thinning fluid power

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. 

Equation 5.2, with the modified parameter X used in place of X, may be used for laminar flow of shear-thinning fluids whose behaviour can be described by the power-taw model. 

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. 

The y-velocities are all set to zero the problem is numerically underconstrained otherwise. Figure 2 also shows the finite-element prediction of this velocity profile for two cases a Newtonian fluid (power-law exponent = 1) and a shear-thinning fluid (power-law... 

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). 

Figure 6.48 presents the reduction of the striation thickness as a function of number of revolutions, as well as ratio of inner to outer cylinder radius, k for a Newtonian fluid. If we were to plot the striation thickness for a shear thinning fluid, say a power law index n = 0.5, the naked eye would not be able to distinguish between the Newtonian and the shear thinning results. 

For a shear thinning fluid following a power law model, the residence time distribution becomes... 

Figure 6.50 presents the cumulative residence time distribution for a tube with a Newtonian model and for a shear thinning fluid with power law indices of 0.5 and 0.1. Plug flow, which represents the worst mixing scenario, is also presented in the graph. A Bingham fluid, with a power law index of 0, would result in plug flow. 

In Chapter 5 of this book we derived the equations that govern the pressure flow between two parallel discs for a Newtonian fluid. In a similar fashion, we can derive the equations that govern flow rate, gate pressure, and pressure distributions for disc-shaped cavities filling with a shear thinning fluid. For the equations presented in this section, we assumed a power law viscosity. For the velocity distribution we have... 

Figures 8.37 and 8.38 [9] present velocity and temperature fields across the thickness, respectively, for various values of Br, and forn = 1 and n = 0.6. Griffith calculated the screw characteristic curves for Newtonian and non-Newtonian shear thinning fluids using various power law indices. Figure 8.39 presents these results and compares them to experiments performed with a carboxyl vinyl polymer (n = 0.2) and corn starch (n = 1).

From numerical simulation of flow of power law fluids in a narrow-gap vane-in-cup geometry (r = 8.5 mm, r = 9.5 mm), Bames and Camali (1990) suggested that for shear-thinning fluids with the flow behavior index <0.5, the fluid within... 

Figure 7-13 Increasing the Power Law Consistency Coefficient of a Shear-Thinning Fluid Generally Increased the Swallowing Time.

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. 

Flow of Power Law Fluids in Smooth Pipes. Oil-in-water emulsions having oil volume fractions greater than 0.5 are often non-Newtonian shear-thinning fluids (3,10-13). For such fluids, the shear stress (t) and the shear rate (7) can be related by the power law model ... 

Soft glasses are known to exhibit remarkable nonlinear shear rheology. They are yield-stress fluids that respond either like an elastic solid when the applied stress is zero or below the yield stress, or a like a viscoelastic fluid when a stress greater than the yield value of the material is applied [185]. Above their yield stresses, soft glasses are shear thinning fluids and very often the shear stress increases with the shear rate raised to the one-half power. This is well documented for the case of concentrated emulsions [102, 182, 186], microgel suspensions [31], and multilamellar... 

In [682] the power consumption of a Rushton turbine in Newtonian and in shear-thinning fluids has been investigated by measurements and using a commercial software package FLUENT. A good agreement between both methods was found. 

COJ of 65 °Brix is a mildly shear-thinning fluid 160) with magnitudes of flow behavior index of the power law model (n) (Equation 2) of about 0.75 that is mildly temperature dependent. In contrast, the consistency index (K) is very sensitive to temperature for example, Vital and Rao (hi) found for a COJ sample magnitudes of 1.51 Pa sec11 at 20 °C and 27.63 Pa secn at -19 °C. Mizrahi and Firstenberg (hi) found that the modified Casson model (Equation 5) described the shear rate-shear stress data better than the Herschel-Bulkley model (Equation 4). 

In Figure 3.28, the shear stress is shown as a function of shear rate for a typical shear-thinning fluid, using logarithmic coordinates. Over the shear rate range (ca 10 to lO-" s the fluid behaviour is described by the power-law equation with an index n of 0.6, that is the line CD has a slope of 0.6. If the power-law were followed at all shear rates, the extrapolated line CCDD would be applicable. Figure 3,29 shows the corresponding values of apparent viscosity and the line CCDD has a slope of n — I = —0.4. It is seen that it extrapolates to jXa = oo at zero shear rate and to /Zq = 0 at infinite shear rate. 

At — 5 C (the temperature at which it normally leaves the factory freezer) ice cream is a viscoelastic, shear-thinning fluid. Like the mix, it obeys the power-law equation, but with different values of b and n. As its temperature is lowered, it becomes more solid-like. Below about — 12°C it displays a yield stress whose value increases as the temperature decreases further. 

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