Viscosity measurements shear

Figure 2.5 shows some actual experimental data for versus 7, measured on a sample of polyethylene at 126°C. Note that the data are plotted on log-log coordinates. In spite of the different coordinates. Fig. 2.5 is clearly an example of pseudoplastic behavior as defined in Fig. 2.2. In this and the next several sections, we discuss shear-dependent viscosity. In this section the approach is strictly empirical, and its main application is in correcting viscosities measured...

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. 

Effect of Temperature. In addition to being often dependent on parameters such as shear stress, shear rate, and time, viscosity is highly sensitive to changes in temperature. Most materials decrease in viscosity as temperature increases. The dependence is logarithmic and can be substantial, up to 10% change/°C. This has important implications for processing and handling of materials and for viscosity measurement. 

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). 

Controlled Stress Viscometer. Most rotational viscometers operate by controlling the rotational speed and, therefore, the shear rate. The shear stress varies uncontrollably as the viscosity changes. Often, before the stmcture is determined by viscosity measurement, it is destroyed by the shearing action. Yield behavior is difficult to measure. In addition, many flow processes, such as flow under gravity, settling, and film leveling, are stress-driven rather than rate-driven. 

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. 

The results of viscosity versus shear rate are reported in Fig. 11 for the two pure components and their blend, respectively. The temperatures were the same for the viscosity measurements and for the injection molding. At temperatures of 280°C and 320°C, the viscosities of the blend are found to be values between the limits of the two pure components. In both cases, the TLCP still... 

At least, in absolute majority of cases, where the concentration dependence of viscosity is discussed, the case at hand is a shear flow. At the same time, it is by no means obvious (to be more exact the reverse is valid) that the values of the viscosity of dispersions determined during shear, will correlate with the values of the viscosity measured at other types of stressed state, for example at extension. Then a concept on the viscosity of suspensions (except ultimately diluted) loses its unambiguousness, and correspondingly the coefficients cn cease to be characteristics of the system, because they become dependent on the type of flow. 

Linear novolac resins prepared by reacting para-alkylphenols with paraformaldehyde are of interest for adhesive tackifiers. As expected for step-growth polymerization, the molecular weights and viscosities of such oligomers prepared in one exemplary study increased as the ratio of formaldehyde to para-nonylphenol was increased from 0.32 to 1.00.21 As is usually the case, however, these reactions were not carried out to full conversion, and the measured Mn of an oligomer prepared with an equimolar phenol-to-formaldehyde ratio was 1400 g/mol. Plots of apparent shear viscosity versus shear rate of these p-nonylphenol novolac resins showed non-Newtonian rheological behavior. 

The zero-shear viscosities measured in toluene solution are listed in Table 1 together with the values of r 0(theor) calculated from Eq. (14). The percentage deviation of the theoretical from the measured viscosities is given in column 8. 

Fig. 4.2.8 Shear viscosity versus shear rate data for a 0.6% by weight aqueous carboxymethylcellulose solution. Data from MRI were obtained from one combined measurement of a velocity profile and a pressure drop, (a) Cone and plate ( ) MRI.

Utilization of a microfabricated rf coil and gradient set for viscosity measurements has recently been demonstrated [49]. Shown in Figure 4.7.9 is the apparent viscosity of aqueous CMC (carboxymethyl cellulose, sodium salt) solutions with different concentrations and polymer molecular weights as a function of shear rate. These viscosity measurements were made using a microfabricated rf coil and a tube with id = 1.02 mm. The shear stress gradient, established with the flow rate of 1.99 0.03 pL s-1 was sufficient to observe shear thinning behavior of the fluids. 

A plot of Tvs. G yields a rheogram or a flow curve. Flow curves are usually plotted on a log-log scale to include the many decades of shear rate and the measured shear stress or viscosity. The higher the viscosity of a liquid, the greater the shearing stress required to produce a certain rate of shear. Dividing the shear stress by the shear rate at each point results in a viscosity curve (or a viscosity profile), which describes the relationship between the viscosity and shear rate. The... 

Viscosity measurements were carried out using Cannon-Fenske viscometers of appropriate capillary diameter so as to keep the efflux time between 200-300 seconds. Approximate shear rate at the wall was calculated using the equation... 

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. 

As the name implies, the cup-and-bob viscometer consists of two concentric cylinders, the outer cup and the inner bob, with the test fluid in the annular gap (see Fig. 3-2). One cylinder (preferably the cup) is rotated at a fixed angular velocity ( 2). The force is transmitted to the sample, causing it to deform, and is then transferred by the fluid to the other cylinder (i.e., the bob). This force results in a torque (I) that can be measured by a torsion spring, for example. Thus, the known quantities are the radii of the inner bob (R ) and the outer cup (Ra), the length of surface in contact with the sample (L), and the measured angular velocity ( 2) and torque (I). From these quantities, we must determine the corresponding shear stress and shear rate to find the fluid viscosity. The shear stress is determined by a balance of moments on a cylindrical surface within the sample (at a distance r from the center), and the torsion spring ... 

Like the von Karman equation, this equation is implicit in/. Equation (6-46) can be applied to any non-Newtonian fluid if the parameter n is interpreted to be the point slope of the shear stress versus shear rate plot from (laminar) viscosity measurements, at the wall shear stress (or shear rate) corresponding to the conditions of interest in turbulent flow. However, it is not a simple matter to acquire the needed data over the appropriate range or to solve the equation for / for a given flow rate and pipe diameter, in turbulent flow. 

Common geometries used to make viscosity measurements over a range of shear rates are Couette, concentric cylinder, or cup and bob systems. The gap between the two cylinders is usually small so that a constant shear rate can be assumed at all points in the gap. When the liquid is in laminar flow, any small element of the liquid moves along lines of constant velocity known as streamlines. The translational velocity of the element is the same as that of the streamline at its centre. There is of course a velocity difference across the element equal to the shear rate and this shearing action means that there is a rotational or vorticity component to the flow field which is numerically equal to the shear rate/2. The geometry is shown in Figure 1.7. 

The phase angle changes with frequency and this is shown in Figure 4.7. As the frequency increases the sample becomes more elastic. Thus the phase difference between the stress and the strain reduces. There is an important feature that we can obtain from the dynamic response of a viscoelastic model and that is the dynamic viscosity. In oscillatory flow there is an analogue to the viscosity measured in continuous shear flow. We can illustrate this by considering the relationship between the stress and the strain. This defines the complex modulus ... 

Capillary rheometers are used extensively to measure viscosity in the intermediate to high shear rate range. The rheometer has for all practical purposes a lower limit in viscosity measurement because of the plunger seals. These seals are shown on the bottom of the plunger in Fig. 3.16, and they induce a frictional resistance when they are pushed through the rheometer barrel. The piston force can be evaluated without polymer in the barrel, but it is always a source of error at low viscosities because of experimental variability. Moreover, barrel friction is one of the critical corrections that must be made when evaluating viscosity measurements... 

Viscosity Measurements. A Zimm-Couette type low shear viscometer was used. The intrinsic viscosities were estimated from single concentration viscosity measurements using the equations for the concentration dependence of the specific viscosity (5,6). The Mark-Houwink equation was used to determine My (5,6). 

Steady state shear viscosity measurements indicate a power-law type relation for the variation of the shear viscosity with shear rate even in the lower shear rate range between 10"1 to 1 sec"l. The results at higher shear rates were questionable due to the slip between the sample and cone and plate fixtures. 

Low shear viscosity measurements for both heated and unheated oils should be similar. 

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