Shear-thinning exponent

The so-called shear-thinning exponent describes the steepness of the viscosity-shear rate curve... 

Table 9. Vassenden and Holt used a value of 1 for the shear thinning exponent ev for these experiments ev equal to 0.65 was more suitable.

The shear thinning exponents n) for the PEN/CNT nanoeomposites can be obtained fi om the relationship of rf of [89, 90], and their result are shown in Table 6. In this study, the shear thinning exponents of the PEN/CNT nanoeomposites were estimated by fitting a straight line to the data at low frequency, because some curvature was observed in the plot of log I I versus log co. 

Table 6. Variations of shear thinning exponent and activation energy of the PEN/CNT nanocomposites with the CNT content.

Materials Shear thinning exponent ( ) Activation energy, (kJ/mol)... 

Complex shear viscosity of carbon nanofibre reinforced PEEK composites as a function of frequency, at a temperature of 360°C, in the linear viscoelastic regime. The insert shows the resulting shear thinning exponent as a function of nanofibre content. 

K has units of Pa s" in the SI system and is termed the fluid consistency n is a dimensionless number related to the shear-thinning exponent introduced earlier and is termed the power-law index... 

Zero-shear viscosity Shear-thinning exponent Upper and lower Newtonian Random coil strnctnre Relaxation time End-to-end distance Deborah nnmber Weissenberg nnmber Constitntive eqnation Power-law llnid Ellis model Cross model... 

Table 3. Shear thinning exponent and relaxation exponent of the TLCP/MWCNT nanocomposites ...

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... 

Many materials are conveyed within a process facility by means of pumping and flow in a circular pipe. From a conceptual standpoint, such a flow offers an excellent opportunity for rheological measurement. In pipe flow, the velocity profile for a fluid that shows shear thinning behavior deviates dramatically from that found for a Newtonian fluid, which is characterized by a single shear viscosity. This is easily illustrated for a power-law fluid, which is a simple model for shear thinning [1]. The relationship between the shear stress, a, and the shear rate, y, of such a fluid is characterized by two parameters, a power-law exponent, n, and a constant, m, through... 

Figure 3.3 illustrates the special cases of Eq. 3.6 used to describe Herschel-Bulkley fluids and, depending on the flow exponent and yield stress values, Newtonian fluids, shear thinning, shear thickening, and Bingham fluids. The values for Eq. 3.6 are given in Table 3.1. 

If the material to be processed is subject to shear thinning, the linear relationships for the pressure and energy behavior illustrated above no longer apply. With shear thinning, there is a non-linear relationship between the shear rate and shear stress that is reflected in the flow curve (see Chapter 3). As a rule, the zero viscosity and one or two rheological time constants are enough to describe the flow curve with sufficient accuracy. The Carreau equation is often used it contains a dimensionless flow exponent in addition to the zero viscosity and a rheological time constant. 

The polymer melt used in this example has a density of 1000 kg/m3. The following initially assumes a Newtonian flow behavior with a viscosity of 1000 Pa-s. In later computations, a more realistic shear thinning flow behavior is assumed, which can be described using the power law equation. The flow exponent n ranges between 0.4 and 0.9 and the consistency... 

As the flow exponent becomes smaller, the polymer melt becomes increasingly shear thinning, and the pressure required to achieve a specific flow rate becomes even smaller (Fig. 8.10). We also note that the intersection of the curve with the x-axis is not dependent on the flow exponent. There is no axial pressure gradient at the intersection. A simple two-dimensional analogy model is the planar channel. If only the walls are moved and no pressure gradient is overlaid, the flow rate, according to an analytical solution, is not dependent on the flow exponents. 

The power characteristic is also strongly dependent on the flow exponents (Fig. 8.11). The more shear thinning the polymer, the less power is required to convey the polymer melt. Unlike the conveying characteristic, the intersections of the individual curves with the x-axis lie far apart and are located outside the figure. 

Suppose there is a single relaxation time, so that m(/ — t ) = (G/t) exp[—(t — r )l. and suppose that h(y) = exp(—y). Calculate a formula for the steady-state shear viscosity as a function of shear rate. At high shear rate, what is the shear-thinning power-exponent p, with rj [Pg.188]

Figure 18 shows some examples. The asymptotic formula also describes the neighborhood of the inflection point correcfly for sufficiently small , but does not represent a real power law. In the framework of asymptotic expansions, there is thus no real exponent p. The power-law shear thinning, often reported in the literature, in the ITT-flow curves is thus a trivial artifact of the double logarithmic plot. 

For a Newtonian fluid [ike. water the exponent ti is given by I independent of the rotation speed. This is indeed observed experimentally by an approximately linear dependence of the velocity on the radial position (Fig. 10.1.6, top right). For a shear-thinning fluid... 

It is seen to contain two parameters m referred to as the consistency index with units of Pa s" and the dimensionless power law exponent . If = 1, the fluid is Newtonian and m = fi. For < 1, the fluid is shear thinning and the shear stress—shear rate slope decreases monotonically with increasing shear rate for > 1, the fluid is shear thickening and the stress-shear rate slope increases with increasing shear rate. We have already indicated that most macromolecular non-Newtonian fluids are shear thinning, however, shear thickening behavior is also observed over some ranges of shear rate with a number of polymer solutions and concentrated particle suspensions (Barnes et al. 1989). 

The practical consequence is that a polymeric fluid will evidence a far stronger non-Newtonian shear thinning behavior than will a suspension. This can result in a fairly wide range in the power law exponent with the exponent n in Eq. (9.1.8) ranging between 0.1 and 0.6 for typical polymeric liquids (Bird et al. 1987), a behavior not found in suspension rheology. 

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