Viscosity vs. shear rate

Fig. 3. Examples of Casson plots (viscosity) vs (shear rate). The Casson equation is 77 = 77), + Tq 7...

Fig. 4. Graphic representations (viscosity vs shear rate) of Cross model with different values for d.

Fig. 10. Viscosity vs shear rate for solutions of a styrene—butadiene—styrene block copolymer (42). A represents cyclohexanone, where c = 0.248 g/cm (9-xylene, where c = 0.246 g/cm C, toluene, where c = 0.248 g/cm. Courtesy of the Society of Plastics Engineers, Inc.

Fig. 23. Viscosity vs shear rate curves for two fluids showing the fallacy of a single point measurement. Fluid Vl would appear to be more viscous than fluid B if measured only at point X, of the same viscosity if measured at point V, and less viscous if measured only at point Z.

Fig. 10. Viscosity vs. shear rate for polystyrene samples of various molar masses in toluene at 25 °C...

The viscosity vs. shear rate data for PTF and BTF (Figure 9) were obtained in n-heptane solution at 25°C using a Contraves low shear rate instrument. n-Heptane was used as a nonpolar solvent, as it has a high enough boiling point to avoid losses due to evaporation during the measurement period. The curves presented here are reproducible in both directions of shear and are thus t ime-independent. 

Fig. 8.15. Viscosity vs shear rate in concentrated solutions of narrow distribution polystyrene The solvent in n-butyl benzene, the concentration is 0.300 gm/ml and the temperature is 30° C. The symbols are O for M = 860000 and for M = 411000 at low shear rates (155) and at high shear rates (346). The solid line for M= 860000 is the master curve for monodisperse systems from Graessley (227). The solid line for M=411000 is the master curve from Ree-Eyring (341). Either master curve fits data for both molecular weights...

The apparent viscosity is determined from Eq. 4. The value of shear rate that corresponds to this viscosity is obtained from the known viscosity vs shear rate rheogram for the non-Newtonian fluids generated using the cone-and-plate method. The value of k is determined from Eq. 5. 

Fig. 2. Viscosity vs shear rate for corn stover suspensions between 5 and 30 wt%.

Newtonian and non-Newtonian calibration fluids were used to determine the necessary calibration constants for the impeller method. It has been previously determined that the impeller method is only valid for a Reynolds number (Re) <10. Impeller rotational speed and torque data from Newtonian calibration fluids of known viscosity were employed to determine the Newtonian calibration constant, c. Cone-and plate-viscometer data from non-Newtonian calibration fluids were used to determine a viscosity vs shear rate relationship. Impeller rotational speed and torque data of the non-Newtonian calibration fluids combined with a determined viscosity vs shear rate correlation were utilized to calculate the shear rate constant, k. The impeller method calibration constants allow the calculation of viscosity, shear rate, and shear stress data of non-Newtonian suspensions. Metz et al. (2) have thoroughly discussed the equations utilized in the impeller method. 

Holden et al. (47) first noted the peculiar characteristics in the steady shear behavior of the SBS block copolymer melts. For a certain composition of styrene and butadiene, no limiting Newtonian viscosity was found at low shear rates. For some of the others, there exist two distinct viscosity vs. shear rate relationships (Figure 10). Arnold and Meier (73) carried out the experiments in oscillatory shear and found the same... 

Figure 3. Short term steady flow viscosity vs shear rate for two samples of BK-62 X and two samples of BK-60 +.

FIGURE 11.12 Viscous behavior of complex fluids (i) shear stress vs. shear rate and (ii) viscosity vs. shear rate. The notation for the curves is (a) Newtonian, (b) shear thinning, (c) shear thickening, (d) Bingham plastic, and (e) pseudoplastic. 

Figure 7. Apparent viscosity vs. shear rate at various emulsion qualities (Fj. (Reproduced with permission from reference 26. Copyright 1970 Society of Petroleum Engineers.)...

Figure 11. Plot of viscosity vs. shear rate for spring relaxation experiment. Job 5374. Key , fit curve Q, actual data.

Fig. 6.19. Typical viscosity vs shear rate curve for a concentrated suspension.

The 17, 170, A, and n are all parameters that are used to fit data, taken here as 17 = 0.05, 170 = 0.492, A = 0.1, and n = 0.4. A plot of the viscosity vs shear rate is given in Figure 10.8. For small shear rates, the viscosity is essentially constant, as it is for a Newtonian fluid. For extremely large shear rates, the same is true. For moderate shear rates, though, the viscosity changes with shear rate. In pipe flow, or channel flow, the shear rate is zero at the centerline and reaches a maximum at the wall. Thus, the viscosity varies greatly from the centerline to the wall. This complication is easily handled in FEMLAB. 

FIG. 9.7 Generic examples of viscosity vs. shear rate plots for different rheological systems. (Reproduced from Laba, D., Ed., Cosmetic Science and Technology Series, Vol. 13, Marcel Dekker, New York, 1993. With permission.)... 

Figure 1. Apparent viscosity vs. shear rate of resins TV and V at...

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