Solution viscosity, shear rate

Fig. 2.51 The shear viscosity of 530 ppm Habon G solution vs. shear rate. Reprinted from Hetsroni et al. (2001b) with permission...

Fig. 8.10. Viscosity-shear rate master curve for concentrated polystyrene-n-butyl benzene solutions. The data were obtained for molecular weights ranging from 160000 to 2400000 concentrations from 0.255 to 0.55 gm/ml, and temperatures from 30° C to 60° C (155)...

Low-shear-rate solution viscosity was measured on a Couette-type rheometer (Contraves LS 30) with a No. 1 bob and cup. The viscosity-shear rate profile was determined fi om 10" to 10 s" at 25 BC. The system was allowed to reach steady state at each shear rate before the measured viscosity was recorded. 

Numerous microscale devices and techniques have been developed to characterize the flow behavior of polymer solutions. The principal motivation for this broad class of techniques is to enable characterization of tiny liquid volumes for which samples are costly or difficult to obtain in large quantities. These microfluidic rheometers fall into three categories, organized in order of increasing De devices to measure intrinsic viscosity, shear-rate-dependent viscosity, and non-Newtonian behavior for a range of flow types. 

Lot to lot variations in polymer properties were observed. Because of this, there were differences in rheological properties between fluids which had the same nominal concentration. It was necessary to determine viscosity-shear rate curves for several concentrations in order to match polymer solution characteristics of previous runs. 

Typical experimental results at two temperatures from the high-shear capillary viscometer technique are shown in Figure 4. These results show that the addition of polymer Increases the viscosity of the oil and that the resulting viscosity decreases with increasing shear rate. This plot indicates that the viscosity-shear rate behavior is approximated by the power-law model. The viscosity behavior over a complete range of shear rate can be determined by coupling these results with measurements of polymer-solution viscosities at low-shear rates in the region where Newtonian behavior is exhibited. The extension of the... 

Figure 2 Viscosity/shear-rate curve for a dilute solution of polyacrylamide in glucose syrup.

Figure 4 Viscosity/shear-rate curves for 1% aqueous solutions of two natural polymeric thickeners.

Figure 11 Viscosity/shear-rate curves for aqueous solutions of locust bean gum.

Figure 14 Viscosity/shear-rate curves for 0.35% aqueous Carbopol solution.

Figure 19 Viscosity/shear-rate curves for blood, liquid crystalline polymer, shampoo, yoghurt and an aqueous xanthan gum solution.

Figure 6.5. Influence of pore size on apparent viscosity/shear rate curves for the flow of xanthan solutions through glass beads (from Chauveteau and Zaitoun, 1981).

This unusual effect is a property of only a few select water-soluble polymers, among which are the extensive family of acrylamide polymers and copofymers. The exact flow mechanism which causes this resistance factor has not been established but it does appear to be a complex combination of several factors. Although polymer solutions are generally highly non-Newtonian, this is not the only factor. The resistance factor is substantially constant over normal field fluid advance rates as shown in Fig. 2, which also shows the slope line and range of the viscosity-shear rate data from 4.8 to 960 sec determined with a Fann viscometer. Since the shear... 

In packed beds of particles possessing small pores, dilute aqueous solutions of hydroly2ed polyacrylamide will sometimes exhibit dilatant behavior iastead of the usual shear thinning behavior seen ia simple shear or Couette flow. In elongational flow, such as flow through porous sandstone, flow resistance can iacrease with flow rate due to iacreases ia elongational viscosity and normal stress differences. The iacrease ia normal stress differences with shear rate is typical of isotropic polymer solutions. Normal stress differences of anisotropic polymers, such as xanthan ia water, are shear rate iadependent (25,26). 

The flow properties of sodium alginate solutions depend on concentration. A 2.5% medium viscosity sodium alginate solution is pseudoplastic, especially at the higher shear rates in the range of 10—10,000/s. 

Properties. Xanthan gum is a cream-colored powder that dissolves in either hot or cold water to produce solutions with high viscosity at low concentration. These solutions exhibit pseudoplasticity, ie, the viscosity decreases as the shear rate increases. This decrease is instantaneous and reversible. Solutions, particularly in the presence of small amounts of electrolyte, have exceUent thermal stabiHty, and their viscosity is essentially constant over the range 0 to 80°C. They are not affected by changes in pH ranging from 2 to 10. 

Solutions of rhamsan have high viscosity at low shear rates and low gum concentrations (90). The rheological properties and suspension capabiUty combined with excellent salt compatibihty, make it useful for several industrial apphcations including agricultural fertilizer suspensions, pigment suspensions, cleaners, and paints and coatings. 

Heat Exchangers Using Non-Newtonian Fluids. Most fluids used in the chemical, pharmaceutical, food, and biomedical industries can be classified as non-Newtonian, ie, the viscosity varies with shear rate at a given temperature. In contrast, Newtonian fluids such as water, air, and glycerin have constant viscosities at a given temperature. Examples of non-Newtonian fluids include molten polymer, aqueous polymer solutions, slurries, coal—water mixture, tomato ketchup, soup, mayonnaise, purees, suspension of small particles, blood, etc. Because non-Newtonian fluids ate nonlinear in nature, these ate seldom amenable to analysis by classical mathematical techniques. 

Because of the rotation of the N—N bond, X-500 is considerably more flexible than the polyamides discussed above. A higher polymer volume fraction is required for an anisotropic phase to appear. In solution, the X-500 polymer is not anisotropic at rest but becomes so when sheared. The characteristic viscosity anomaly which occurs at the onset of Hquid crystal formation appears only at higher shear rates for X-500. The critical volume fraction ( ) shifts to lower polymer concentrations under conditions of greater shear (32). The mechanical orientation that is necessary for Hquid crystal formation must occur during the spinning process which enhances the alignment of the macromolecules. 

Concentration and Molecular Weight Effects. The viscosity of aqueous solutions of poly(ethylene oxide) depends on the concentration of the polymer solute, the molecular weight, the solution temperature, concentration of dissolved inorganic salts, and the shear rate. Viscosity increases with concentration and this dependence becomes more pronounced with increasing molecular weight. This combined effect is shown in Figure 3, in which solution viscosity is presented as a function of concentration for various molecular weight polymers. 

Effect of Shear. Concentrated aqueous solutions of poly(ethylene oxide) are pseudoplastic. The degree of pseudoplasticity increases as the molecular weight increases. Therefore, the viscosity of a given aqueous solution is a function of the shear rate used for the measurement. This relationship between viscosity and shear rate for solutions of various molecular weight poly(ethylene oxide) resins is presented in Figure 8. 

Of the models Hsted in Table 1, the Newtonian is the simplest. It fits water, solvents, and many polymer solutions over a wide strain rate range. The plastic or Bingham body model predicts constant plastic viscosity above a yield stress. This model works for a number of dispersions, including some pigment pastes. Yield stress, Tq, and plastic (Bingham) viscosity, = (t — Tq )/7, may be determined from the intercept and the slope beyond the intercept, respectively, of a shear stress vs shear rate plot. 

The other models can be appHed to non-Newtonian materials where time-dependent effects are absent. This situation encompasses many technically important materials from polymer solutions to latices, pigment slurries, and polymer melts. At high shear rates most of these materials tend to a Newtonian viscosity limit. At low shear rates they tend either to a yield point or to a low shear Newtonian limiting viscosity. At intermediate shear rates, the power law or the Casson model is a useful approximation. 

Depending on the concentration, the solvent, and the shear rate of measurement, concentrated polymer solutions may give wide ranges of viscosity and appear to be Newtonian or non-Newtonian. This is illustrated in Eigure 10, where solutions of a styrene—butadiene—styrene block copolymer are Newtonian and viscous at low shear rates, but become shear thinning at high shear rates, dropping to relatively low viscosities beyond 10 (42). The... 

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.

Capillary viscometers are useful for measuring precise viscosities of a large number of fluids, ranging from dilute polymer solutions to polymer melts. Shear rates vary widely and depend on the instmments and the Hquid being studied. The shear rate at the capillary wall for a Newtonian fluid may be calculated from equation 18, where Q is the volumetric flow rate and r the radius of the capillary the shear stress at the wall is = r Ap/2L. 

Controlled stress viscometers are useful for determining the presence and the value of a yield stress. The stmcture can be estabUshed from creep measurements, and the elasticity from the amount of recovery after creep. The viscosity can be determined at very low shear rates, often ia a Newtonian region. This 2ero-shear viscosity, T q, is related directly to the molecular weight of polymer melts and concentrated polymer solutions. 

The Hercules viscometer was originally designed for paper and paperboard coatings, but its use has been extended to paints, adhesives, mineral slurries, emulsions, and starch solutions. The iastmment, noted for being robust and rehable, is particularly well suited for quaUty control and product formulation. It is capable of measuting viscosity over a moderate range 1-10 mPa-s) up to high shear rates (115,000 ). A more recent model is the... 

As substituent uniformity is increased, either by choosing appropriate reaction conditions or by reaction to high degrees of substitution, thixotropic behavior decreases. CMCs of DS >1.0 generally exhibit pseudoplastic rather than thixotropic rheology. Pseudoplastic solutions also decrease in viscosity under shear but recover instantaneously after the shear stress is removed. A plot of shear rate versus shear stress does not show a hysteresis loop. 

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