Fluid, shear-thinning results

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. 

Characteristics of Emulsified Acid. Al-Anazi et al. [14] measured the apparent viscosity of the acid-in-diesel emulsion as a function of shear rate at various temperatures by using a Brookfield viscometer Model DV-II. Figure 3 shows that the apparent viseosity decreased as the shear rate was increased. This result indieates that the aeid-in-diesel emulsion is a non-Newtonian fluid (shear-thinning behavior). Crowe and Miller [45] and Krawietz and Rael [53] reported a similar behavior. The apparent viscosity ( /) can be predieted over the shear rate (y) examined using the power-law model given by the following equation ... 

Many fluids show a decrease in viscosity with increasing shear rate. This behavior is referred to as shear thinning, which means that the resistance of the material to flow decreases and the energy required to sustain flow at high shear rates is reduced. These materials are called pseudoplastic (Fig. 3a and b, curves B). At rest the material forms a network structure, which may be an agglomerate of many molecules attracted to each other or an entangled network of polymer chains. Under shear this structure is broken down, resulting in a shear... 

The typical viscous behavior for many non-Newtonian fluids (e.g., polymeric fluids, flocculated suspensions, colloids, foams, gels) is illustrated by the curves labeled structural in Figs. 3-5 and 3-6. These fluids exhibit Newtonian behavior at very low and very high shear rates, with shear thinning or pseudoplastic behavior at intermediate shear rates. In some materials this can be attributed to a reversible structure or network that forms in the rest or equilibrium state. When the material is sheared, the structure breaks down, resulting in a shear-dependent (shear thinning) behavior. Some real examples of this type of behavior are shown in Fig. 3-7. These show that structural viscosity behavior is exhibited by fluids as diverse as polymer solutions, blood, latex emulsions, and mud (sediment). Equations (i.e., models) that represent this type of behavior are described below. 

A stability analysis made by Ryan and Johnson (1959) suggests that the transition from laminar to turbulent flow for inelastic non-Newtonian fluids occurs at a critical value of the generalized Reynolds number that depends on the value of The results of this analysis are shown in Figure 3.7. This relationship has been tested for shear thinning and for Bingham... 

Experimental results for the Fanning friction factor for turbulent flow of shear thinning fluids in smooth pipes have been correlated by Dodge and Metzner (1959) as a generalized form of the von Karman equation ... 

Because most shear-thinning fluids, particularly polymer solutions and flocculated suspensions, have high apparent viscosities, even relatively coarse particles may have velocities in the creeping-flow of Stokes law regime. Chhabra(35,36) has proposed that both theoretical and experimental results for the drag force F on an isolated spherical particle of diameter d moving at a velocity u may be expressed as a modified form of Stokes law ... 

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. 

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).

Figure 6.16 shows an example of a computational field. It is the viscosity distribution for a shear thinning fluid. It is yet to be determined whether such results can be achieved by measurement. Further examples can be found in Chapter 8. 

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). 

These data suggest that perhaps one reason shear-thinning non-Newtonian liquids are safer to swallow than thin Newtonian liquids is due to the reduced fluid flow during the second half of the swallowing process. The reduced flow in turn allows more time for air passages (e.g., entry to the trachea or the nasopharynx) to completely shut off prior to the arrival of food. Asa result, the dysphagic patient does not aspirate as he or she would with a Newtonian bolus. 

In the MEB equation, kinetic energy losses can be calculated easily provided that the kinetic energy correction factor a can be determined. In turbulent flow, often, the value of a = 2 is used in the MEB equation. When the flow is laminar and the fluid is Newtonian, the value of a = 1 is used. Osorio and Steffe (1984) showed that for fluids that follow the Herschel-Bulkley model, the value of a in laminar flow depends on both the flow behavior index ( ) and the dimensionless yield stress ( o) defined above. They developed an analytical expression and also presented their results in graphical form for a as a function of the flow behavior index ( ) and the dimensionless yield stress ( o)- When possible, the values presented by Osorio and Steffe (1984) should be used. For FCOJ samples that do not exhibit yield stress and are mildly shear-thinning, it seems reasonable to use a value of a = 1. 

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