Viscosity for shear

Where G represents the shear modulus, and Gq and Goo are the minimum and maximum values of the shear modulus during cure, respectively. The induction time, tQ, has been mentioned previously [11]. This induction time is defined as the time needed for polymer systems to reach the temperature necessary for cure onset. (This is why the cure curve decreases to a minimum value before it increases.) For predicting viscosity during cure, one only needs to substitute viscosity for shear modulus in Eq. (3). 

Figure 2-3 Plot of Shear Rate versus Apparent Viscosity for Shear Thinning Foods Identifying Three Separate Regions A Zero-Shear Viscosity at Low Shear Rates, a Power Law Region at Intermediate Shear Rates, and an Infinite-Shear Viscosity at High Shear Rates. Often, only data in the power law region are obtained.

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. 

Irregular and chaotic behavior. The shear stress and the viscosity, for shear rates between 3.5 and 4.1 are displayed in Fig. 13. A rather irregular behavior, i.e., a sensitive dependence on the value of the imposed shear rate is seen. This is indicative of a chaotic behavior. Indeed, the computation of Lyapunov exponents revealed that the largest one is positive for shear rates in intervals which have a are rather fractal character [8]. 

The normal stress functions corresponding to the apparent viscosity for shear stress are called the first (ij/i) and second (i i2) normal stress coefficients. As shown,... 

Fig. 7.19. Time dependent viscosities for shear and extensional flow, and as predicted by Lodge s equation of state. Calculations are performed for different Hencky strain rates en, assuming a single exponential relaxation modulus G(t) exp — t/r...

Fig. 21.2 Shear viscosity for shear rates up to 5 X 10 s for aqueous PVP K30 solutions (20-50 wt%), according to [2]...

A common choice of functional relationship between shear viscosity and shear rate, that u.sually gives a good prediction for the shear thinning region in pseudoplastic fluids, is the power law model proposed by de Waele (1923) and Ostwald (1925). This model is written as the following equation... 

By analogy with Eq. (3.1), we seek a description for the relationship between stress and strain. The former is the shearing force per unit area, which we symbolize as as in Chap. 2. For shear strain we use the symbol y it is the rate of change of 7 that is involved in the definition of viscosity in Eq. (2.2). As in the analysis of tensile deformation, we write the strain AL/L, but this time AL is in the direction of the force, while L is at right angles to it. These quantities are shown in Fig. 3.6. It is convenient to describe the sample deformation in terms of the angle 6, also shown in Fig. 3.6. For distortion which is independent of time we continue to consider only the equilibrium behavior-stress and strain are proportional with proportionality constant G ... 

Melt Viscosity. As shown in Tables 2 and 3, the melt viscosity of an acid copolymer increases dramatically as the fraction of neutralization is increased. The relationship for sodium ionomers is shown in Figure 4 (6). Melt viscosities for a series of sodium ionomers derived from an ethylene—3.5 mol % methacrylic acid polymer show that the increase is most pronounced at low shear rates and that the ionomers become increasingly non-Newtonian with increasing neutralization (9). The activation energy for viscous flow has been reported to be somewhat higher in ionomers than in related acidic... 

For non-Newtonian fluids the correlations in Figure 35 can be used with generally acceptable accuracy when the process fluid viscosity is replaced by the apparent viscosity. For non-Newtonian fluids having power law behavior, the apparent viscosity can be obtained from shear rate estimated by... 

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. 

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.

Rotational viscometers often were not considered for highly accurate measurements because of problems with gap and end effects. However, corrections can be made, and very accurate measurements are possible. Operating under steady-state conditions, they can closely approximate industrial process conditions such as stirring, dispersing, pumping, and metering. They are widely used for routine evaluations and quahty control measurements. The commercial instmments are effective over a wide range of viscosities and shear rates (Table 7). 

With appropriate caUbration the complex characteristic impedance at each resonance frequency can be calculated and related to the complex shear modulus, G, of the solution. Extrapolations to 2ero concentration yield the intrinsic storage and loss moduH [G ] and [G"], respectively, which are molecular properties. In the viscosity range of 0.5-50 mPa-s, the instmment provides valuable experimental data on dilute solutions of random coil (291), branched (292), and rod-like (293) polymers. The upper limit for shearing frequency for the MLR is 800 H2. High frequency (20 to 500 K H2) viscoelastic properties can be measured with another instmment, the high frequency torsional rod apparatus (HFTRA) (294). 

Fig. 5. Shear rate vs viscosity for PDMS. Numbers on curves indicate molecular weights. To convert Pa-s to poise, multiply by 10.

The uncured property most often used for CSM in dry appHcations is Mooney viscosity, alow shear bulk viscosity (ca 1.6 ) determined at 100°C. 

Mewtonian andMon-Mewtonian Materials. A Newtonian material s viscosity is shear-independent, whereas non-Newtonian materials are shear-dependent (Eig. 7). Eor most potting materials, a Newtonian material is preferred because the material is required to flow under all electronic components, but not be susceptible to shear. However, when flowable material is used for conformal coating appHcations, a non-Newtonian material with thixotropy agent added is desired since the material should flow on the electronic substrate but stop at the edge without creeping or mnover at the circuitry. 

The Prandtl mixing length concept is useful for shear flows parallel to walls, but is inadequate for more general three-dimensional flows. A more complicated semiempirical model commonly used in numerical computations, and found in most commercial software for computational fluid dynamics (CFD see the following subsection), is the A — model described by Launder and Spaulding (Lectures in Mathematical Models of Turbulence, Academic, London, 1972). In this model the eddy viscosity is assumed proportional to the ratio /cVe. 

The factor 3 appears because the viscosity is defined for shear deformation - as is the shear modulus G. For tensile deformation we want the viscous equivalent of Young s modulus . The answer is 3ri, for much the same reason that = (8/3)G 3G - see Chapter 3.) Data giving C and Q for polymers are available from suppliers. Then... 

For non-New tonian fluids, viscosity data are very important. Every impeller has an average fluid shear rate related to speed. For example, foi a flat blade turbine impeller, the average impeller zone fluid shear rate is 11 times the operating speed. The most exact method to obtain the viscosity is by using a standard mixing tank and impeller as a viscosimeter. By measuring the pow er response on a small scale mixer, the viscosity at shear rates similar to that in the full scale unit is obtained. 

Figure 8.6. Relationship between molecular weight and zero shear rate viscosity for melts of linear...

A plot of apparent viscosity against shear rate produces a unique flow curve for the melt is shown in Fig. 5.3. Occasionally this information may be based on the true shear rate. As shown in Section 5.4(a) this is given by... 

Figure 4 shows the plots of apparent viscosity versus shear stress at 170°C for different mixes. It is evident that the materials behave as pseudoplastic fluids, and the viscosity decreases with increasing zinc stearate... 

The mechanism of droplet deformation can be briefly summarized as follows. The factors affecting the droplet deformation are the viscosity ratio, shear stress, interfacial tension, and droplet particle size. Although elasticity takes an important role for general thermoplastics droplet deformation behavior, it is not known yet how it affects the deformation of TLCP droplet and its relationship with the processing condition. Some of... 

Variation of melt viscosity for both the preblends and preheated blends with the blend ratio are shown in Fig. 19. There are two distinct regions in viscosity change with the addition of polyacrylic rubber (ACM) in the blends. First, in the higher shear rate region, the viscosity increases with the addition of the ACM (up to 40% ACM) in the blend and then it decreases. In the lower... 

Figure 4 shows viscosity versus shear rate results for the two original components and their blends, re-... 

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