Shear thinning, polymers

Thus, the pipe friction chart for a Newtonian fluid (Figure 3.3) may be used for shearthinning power-law fluids if Remit is used in place of Re. In the turbulent region, the ordinate is equal to (R/pu2)n 0 fn5. For the streamline region the ordinate remains simply R/pu2, because Reme has been defined so that it shall be so (see equation 3.140). More recently, Irvine(25j has proposed an improved form of the modified Blasius equation which predicts the friction factor for inelastic shear-thinning polymer-solutions to within 7 per cent. 

Figure 6.36 presents a plot of final sheet thickness as a function of fed sheet thickness for a Newtonian polymer and a shear thinning polymer with a power law index of 0.25. 

Sample balancing problem. Let us consider the multi-cavity injection molding process shown in Fig. 6.54. To achieve equal part quality, the filling time for all cavities must be balanced. For the case in question, we need to balance the cavities by solving for the runner radius R2. For a balanced runner system, the flow rates into all cavities must match. For a given flow rate Q, length L, and radius R, solve for the pressures at the runner system junctures. Assume an isothermal flow of a non-Newtonian shear thinning polymer. Compute the radius R2 for a part molded of polystyrene with a consistency index (m) of 2.8 x 104 Pa-s" and a power law index (n) of 0.28. Use values of L = 10 cm, R = 3 mm, and Q = 20 cm3/s. 

Predicting pressure profiles in a disc-shaped mold using a shear thinning power law model [1]. We can solve the problem presented in example 5.3 for a shear thinning polymer with power law viscosity model. We will choose the same viscosity used in the previous example as the consistency index, m = 6,400 Pa-sn, in the power law model, with a power law index n = 0.39. With a constant volumetric flow rate, Q, we get the same flow front location in time as in the previous problem, and we can use eqns. (6.239) to (6.241) to predict the required gate pressure and pressure profile throughout the disc. 

Using the geometry and notation given in Fig. 6.14, relate the die land length ratio, L1/L2 for a die land thickness h //i2 = 2 to the power law index of a shear thinning polymer. 

For the slit-shaped cavity with a unidirectional flow, presented in Fig. 6.79, derive an expression for the pressure at the gate during mold Ailing for a constant injection speed. Assume a volumetric flow rate Q and an isothermal flow of a shear thinning polymer with a power law model. 

Modeling the calendering process for Newtonian and shear thinning polymer melts. Using the RF method, Lopez and Osswald [5] modeled the calendering process for Newtonian and non-Newtonian polymer melts. They used the same dimensions and process conditions used by Agassant et al. [1], schematically depicted in Fig. 11.17. 

Wide-disc kneading blocks achieve the most effective dispersion because they generate the greatest shear stresses. This also leads to high energy input, however, which increases the melt temperature and reduces the viscosity of the predominantly shear-thinning polymer melts, which in turn leads to a reduction of shear stress. Therefore, dispersive mixing is an optimization problem. 

Rofe, C. J., Lambert, R. K., and Callaghan, P. T. (1994). Nuclear magnetic resonance imaging of flow for a shear-thinning polymer in cylindrical Couette geometry. J. Rheology 38, 875-887. 

This model also gives a good account of the shear rate dependence of the viscosity for shear thinning polymers. It slightly overpredicts the value of t o and it also predicts longer transitions from the zero shear rate to the shear thinning behavior. 

The most common type of time-independent non-Newtonian fluid behavioiu observed is pseudoplasticity or shear-thinning, characterised by an apparent viscosity which decreases with increasing shear rate. Both at very low and at very high shear rates, most shear-thinning polymer solutions and melts exhibit Newtonian behaviour, i.e. shear stress-shear rate plots become straight lines. 

Figure 1.6 Demonstration of zero shear and infinite shear viscosities for a shear-thinning polymer solution [Roger, 1977]...

Where a fluid is not spinnable the various orifice flow techniques, which involve pressure drop measinements across a contraction [Binding, 1988, 1993], can provide a means of estimating the extensional-viscosity behaviour of shear-thinning polymer solutions. 

Wen and Yim [1971] reported a few results on axial dispersion coefficients (Dl) for the flow of two weakly shear-thinning polymer (PEO) solutions (n = 0.81 and 0.9) through a bed packed with glass spheres (d = 4.76 and 14.3 mm) of voidages 0.4 and 0.5. Over the range (7 < Rei < 800), then-results did not deviate substantially from the correlation developed by these authors previously for Newtonian fluids ... 

Figure 5.14 Typical bed expansion data for 3.57 mm glass spheres fluidised by shear-thinning polymer solutions [Srinivas and Chhabra, 1991]...

Fig. 5.10. Intrinsic viscosity [q] determined at high shear rates Y with a capillary viscosimeter and at lower shear rates with a Zimm-Crothers viscosimeter for different xanthan gums in 0.1 mol/l sodium chloride (NaCI) solution at 25 C. Data from [93]. For strongly shear thinning polymer solutions, only low shear viscosimeters reach the shear rate independent viscosity region...

It is interesting to see that the isothermal viscous temperature rise increases with clearance while the adiabatic temperature rise decreases with clearance. For both thermal boundary conditions, the temperature rise increases strongly with the power law index of the polymer melt. This indicates that highly shear thinning polymers (low power law index) will have much lower melt temperature rise in the flight clearance than weakly shear thinning polymers. 

Figure 6 Regions of a typical flow curve for a shear-thinning polymer.

In the case of polymers like nylon, polyethylene terephthalate (PET) and polycarbonate (PC), the steady shear viscosity is near Newtonian up to even a shear rate of a little over 100 s as can be seen from Figures 6.23-6.25. As an example of a moderately shear-thinning polymer, polyetherimide (PEI) could be considered [136] as shown in Figure 6.26 while, for a predominantly shear-tiunning pol3mier, polypropylene (PP) is a reasonable example as shown in Figure 6.27. Note that in Figures 6.24 and 6.27, the plots are shown as shear stress vs. shear rate which is, of course, another method of representation of the same information. 

Figure 5.6.3 compares vane-in-cup to bob-in-cup measurements for a very shear thinning polymer solution. The bob-in-cup data indicate that there is yield stress, but this is actually due to wall slip. 

Figure 4.33 Simulated flow patterns of (a) Newtonian and (b) shear-thinning polymer melts (LDPE) in a wire-coating die. The Newtonian fluid exhibits a big vortex, while in the same geometry the LDPE melt flows without recirculation [88].

Example. 1-D laminar flow of a shear-thinning polymer melt... 

FIGURE 7.3 Flow curve for a shear-thinning polymer solntion. t and y are both plotted on logarithmic scales for clarity. The cartoon provides a simplified view of how polymer structure evolves in flow. Dots in the figure represent the surronnding molecules. 

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