Shear rate solution

At a viscosity range exceeding 600 mN-sec-m-2 (cP) methylcellulose solutions are pseudoplastic which means that the apparent viscosity decreases with increasing shear rate. Solutions of low viscosities again tend to be thixotropic, resulting in a decreased viscosity with increasing shear times. 

Chemical modification of hydroxyethylcellulose or hydroxypropylcellulose with long-chain hydrocarbon alkylating reagents, such as C8-C24 epoxides or halides, has been reported to yield novel water-soluble compositions exhibiting enhanced low-shear-rate solution viscosities and polymeric surfactant properties [ 104,105]. Patents have also been issued for water-soluble phosphonomethylcellulose and phosphonomethylhydroxyethylcellulose [106,107]. 

From slow-shear-rate solutions of the Smoluchowski equation, Eq. (11-3), with the Onsager potential, Semenov (1987) and Kuzuu and Doi (1983, 1984) computed the theoretical Leslie-Ericksen viscosities. They predicted that ai/a2 < 0 (i.e., tumbling behavior) for all concentrations in the nematic state. The ratio jai is directly related to the tumbling parameter X by X = (1 -h a3/a2)/(l — aj/aa). Note the tumbling parameter X is not to be confused with the persistence length Xp.) Thus, X < I whenever ai/a2 < 0. As discussed in Section 10.2.4.1, an approximate solution of Eq. (11-3) predicts that for long, thin, stiff molecules, X is related to the second and fourth moments Sa and S4 of the molecular orientational distribution function (Stepanov 1983 Kroger and Sellers 1995 Archer and Larson 1995) ... 

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. 

Figure 18.8 Variation of shear viscosity with weight per cent of NR at different shear rates (solution cast and melt mixed).

Cone-and-plate viscometers of the type shown here are usually limited to fairly low shear rates. At higher shear rates, solutions tend to be flung from the gap by centrifugal force, and melts tend to ball up (like rubbing a finger over dry mbber cement). These problems can be overcome by enclosing the fluid around a biconical rotor, giving, in effect, two cone-and-plate viscometers back-to-back [6]. The flow curves earlier in this chapter were obtained with such a device. 

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. 

Solutions of methylceUuloses are pseudoplastic below the gel point and approach Newtonian flow behavior at low shear rates. Above the gel point, solutions are very thixotropic because of the formation of three-dimensional gel stmcture. Solutions are stable between pH 3 and 11 pH extremes wiU cause irreversible degradation. The high substitution levels of most methylceUuloses result in relatively good resistance to enzymatic degradation (16). 

Viscosity of Resin Solutions. The viscosity of coatings must be adjusted to the appHcation method to be used. It is usually between 50 and 1000 mPa-s(=cP), at the shear rate involved in the appHcation method used. The viscosity of the coating is controUed by the viscosity of the resin solution, which is in turn controUed mainly by the free volume (4). The factors controlling free volume are temperature, resin stmcture, solvent stmcture, concentration, and solvent-resin interactions. 

At low shear rates, aqueous solutions of polyacrylamide are pseudoplastic. With increasing shear rates and temperature the viscosity of the solutions decrease. At high shear rates during violent mixing and pumping operations the molecular weight of polyacrylamide decreases by destruction of macromolecules. 

Many microbial polysaccharides show pseudoplastic flow, also known as shear thinning. When solutions of these polysaccharides are sheared, the molecules align in the shear field and the effective viscosity is reduced. This reduction of viscosity is not a consequence of degradation (unless the shear rate exceeds 105 s 1) since the viscosity recovers immediately when die shear rate is decreased. This combination of viscous and elastic behaviour, known as viscoelasticity, distinguishes microbial viscosifiers from solutions of other thickeners. Examples of microbial viscosifiers are ... 

The viscosity of a solution of microbial exopolysaccharide must, therefore, be defined as a function of the shear rate (see Figure 7.7). 

In a number of works (e.g. [339-341]) the authors sought to superimpose graphically the flow curves of filled melts and polymer solutions with different filler concentrations however, it was only possible to do so at high shear stresses (rates). More often than not it was impossible to obtain a generalized viscosity characteristic at low shear rates, the obvious reason being the structurization of the system. 

Recently, patented ethoxylation catalysts have become available that can significantly narrow the ethylene oxide distribution of the alcohol ethoxylates used to obtain alcohol ether sulfates. These products are termed peaked alcohol ether sulfates whereas all others are termed conventional alcohol ether sulfates. Peaked alcohol ether sulfate solutions thicken more than those with a conventional ethylene oxide distribution [78]. Peaked alcohol ether sulfate solutions also exhibit behaviors different from those of conventional sulfates [79]. Smith [78] studied the viscosities of 15% sodium dodecyl ether sulfate solutions of both families with NaCl content between 2% and 10% at 25°C using a Brookfield model DVII viscometer at a shear rate of 2 s 1. The results are shown in Fig. 5 where the very different viscosities achieved are clearly observed. 

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