Viscosity Versus Shear Rate

It is possible for two materials with the same MFR to behave completely differently during moulding, as shear stresses are different from those used in MFR determination where low shear rates are used. Owing to the higher shear rates encountered in injection moulding, MFR is not a reliable measurement for the mouldability. 

Redr aunt from Handbook of Polyolefins Synthesis and Properties, 1st Edition, Eds., C. Vasile and R.B. Seymour, Marcel Dekker, New York, NY, USA, 1993. Copyright Marcel Dekker, 1993. 

The final choice of the grades for injection moulding from different equivalent grades available may be made from the injection pressure versus injection time curve for different grades. The material that offers the lowest injection time at minimum injection pressure would be a candidate for the final choice. In blown film applications, screw speed, power required, and head pressure estimation based on rheological characterisation may be useful. 

Redrawn from Handbook of Polyolefins Synthesis and Properties, 1st Edition, Eds., C. Vasile and R.B. 

Shot volume is limited by the residence time. PP has a tendency to oxidise and is routinely protected by the inclusion of antioxidants in the polymer production process. Hence, PP cannot be exposed to very high residence times. Allowable residence time depends on the material temperature and the nature of heat stabilisation. Longer residence time is possible at lower temperature. The shot volume may be up to 85% of the machine maximum shot volume. The minimum shot volume depends on the residence time and can be as low as 15% of the maximum shot volume of the machine. 

PP normally requires no predrying before injection moulding. Exceptions can arise after storage under unfavourable conditions or when processing filled grades. In the case of filled plastics or daik coloured plastics, additional enhancement of the surface quality could be achieved by predrying the compounds at 120 for 3 hours in a dried air circulating oven. 

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The shear rate calculated from impeller rotational speed is used to identify a viscosity from a plot of viscosity versus shear rate determined with a capillaiy or rotational viscometer. Next Nr is calculated, and Np is read from a plot like Fig. 18-17. 

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

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... 

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. 

FIGURE 38.7 Viscosity versus shear rate plots of virgin natural mbber-low-density polyethylene (NR-LDPE) blends (N2) and reclaimed rubber (RR)-LDPE blends (A2). (Reprinted from Nevatia, P., Baneijee, T.S., Dutta, B., Jha, A., Naskar, A.K., and Bhowmick, A.K., J. Appl. Polym. Sci., 83, 2035, 2002. With permission from Wiley InterScience.)... 

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.

Fig. 4.2.9 Viscosity versus shear rate obtained using a cone and plate viscometer (a) and MRI ( ) 13 mLs"1, ( ) 22 mL s-. ...

Figure 3-3 Examples of (a) cup-and-bob viscosity (torque vs. speed) and (b) viscosity versus shear rate. (Lines are least-mean-square fit.)...

The plot of viscosity versus shear rate is shown in Fig. 3-3b, in which the line represents Eq. (3-24), with n = 0.77 and m = 1.01 dyn s /cm2 (or poise ). In this case the power law model represents the data quite well over the entire range of shear rate, so that n = n is the same for each data point. If this were not the case, the local slope of log T versus log rpm would determine a different value of n for each data point, and the power law model would not give the best fit over the entire range of shear rate. The shear rate and viscosity would still be determined as above (using the local value of n for each data point), but the viscosity curve could probably be best fit by some other model, depending upon the trend of the data (see Section III). 

Figure 3-6 Viscosity versus shear rate for fluids in Fig. 3-5.

Figure 3.10 displays some examples of viscosity versus shear rate for two different grades of polypropylene at 190°C and 250°C. 

Basic Protocol 2 is for time-dependent non-Newtonian fluids. This type of test is typically only compatible with rheometers that have steady-state conditions built into the control software. This test is known as an equilibrium flow test and may be performed as a function of shear rate or shear stress. If controlled shear stress is used, the zero-shear viscosity may be seen as a clear plateau in the data. If controlled shear rate is used, this zone may not be clearly delineated. Logarithmic plots of viscosity versus shear rate are typically presented, and the Cross or Carreau-Yasuda models are used to fit the data. If a partial flow curve is generated, then subset models such as the Williamson, Sisko, or Power Law models are used (unithi.i). 

Plot the data as viscosity versus shear rate on logarithmic axes. 

If a logarithmic ramp is performed, then the data should not be fit with linear models (unit m.i). These data should be plotted as viscosity versus shear rate on logarithmic axes and the Carreau-Yasuda or Cross models (or subsets) should be used instead. It is unlikely that the zero-shear plateau will be seen in these types of tests. For a complete flow curve, the equilibrium tests described in Basic Protocol 2 should be used. 

Figure 6.11 Typical curves of viscosity versus shear rate.

If this question can be answered in the affirmative, then dimensionless relationships where Q is used as the key parameter for the MMD (e.g. in rheological master graphs) will have a general validity. If not - one can hardly expect any generally valid set of master curves (e.g. viscosity versus shear rate) even for one polymer ... 

Steady State Measurements Fig. 1 shows the shear rate-shear stress curves at various bentonite concentrations (calculated on the basis of the continuous phase) Hysteresis in the shear rate-shear stress curves was insignificant and the correlation between the ascending and descending curves was within experimental error. The results shown in Fig. 1 were therefore, the mean value of the ascending and descending curves. In the absence of any bentonite the suspension was Newtonian, whereas all suspensions containing bentonite at concentrations > 30 g dm were all pseudoplastic. This is illustrated from a plot of viscosity versus shear rate (Figure 2) which shows an exponential reduction of h with increase in shear rate. 

At certain shear rates, one finds a sudden increase in viscosity, related to a structural transition from a continuous lamellar phase to a phase consisting of onions embedded in a continuous lamellar phase. The sudden increase in viscosity amounts to a factor 100 or so. After the transition, the power law for viscosity versus shear rate remains q y however, the zero shear viscosity is found to be two orders of magnitude higher than that of the initial continuous lamellar phase. This implies that the structural transition indeed relates to a functional property such as suspendability of the system. 

Figure 4, Steady-shear viscosity versus shear rate for PDM-PMAS. Key O, precursor A, Nc = 10 O, = 12 , Nc = 14 A, Nc = 16 and 9, Nc = 18. Nc is the number of side-chain carbon atoms.

The viscosity obtained from the above equation in the linear region of a creep experiment can be used to extend the low-shear rate region of apparent viscosity versus shear rate data obtained in a flow experiment by about two decades (Giboreau et al., 1994 Rayment et al., 1998). The low shear rate region of about 10 -10 is often used for the characterization and differentiation of structures in polysaccharide systems through the use of stress controlled creep and non destructive oscillatory tests. The values of strain (y) from the creep experiment can be converted to shear rate from the expression y t) = y t)/t. 

Figure 1-7 shows schematic curves of the steady-state shear stress and shear viscosity versus shear rate for solid-like and liquid-like complex fluids. For a solid-like complex fluid, the steady-state shear stress is independent of shear rate (Fig. l-7a), and so the shear viscosity decreases with increasing shear rate asA ()>) oc y K A decreasing shear viscosity with inrreasing shear rate, is referred to as shear thinning. For the liqiiid-... 

A plot of viscosity versus shear rate for a model HUER polymer is shown in Fig. 5-20, and compared to the dynamic viscosity versus frequency. Note that the Cox-Merz rule (see Section 1.3.1.5) fails in that at the frequency (o> 1 sec ) where the dynamic viscosity-... 

Figure5.21 Viscosity versus shear rate for 1.0 wt% HEUR =51,000Mt /M — 1.7) telechelic polymers with hexadecanol end caps at 22°C. The illustrations show the structural transitions that are thought to occur as the shear rate is increased. First, the bridging chains are stretched, producing shear thickening. Then, many bridging chains are pulled out at one end from the micelles to which they were attached, and shear thinning occurs. (Reprinted with permission from Yekta et al.. Macromolecules 28 956. Copyright 1995 American Chemical Society.)...

Figure 6.39 Hysteresis loops of viscosity versus shear rate of a 3% by weight suspension of fumed silica (surface area = 325 m /g) in poly(dimethyl-siloxane), (PDMS molecular weight = 67,000, ris 125 P) at 30°C. In each run, the shear rate was first increased up to a maximum shear rate /max located at the arrow, and then decreased. After a rest of 23 hours, another run was made, with a different /max, thus producing the series of curves shown. (Reprinted from J Non-Newt Fluid Mech 17 45, Ziegelbaur and Caruthers (1985), with kind permission from Elsevier Science NL, Sara Burgerhartstraat 25,1055 KV Amsterdam, The Netherlands.)...

Figure 10.26 Viscosity versus shear rate of cholesteryl myristate in a cone-and-plate rheometer as a function of shear rate. At high temperatures, T > 83 C, the sample is a low-viscosity, Newtonian isotropic liquid. At intermediate temperatures, 83 > T > 78°C, the sample is a shear-thinning cholesteric. At low temperatures the sample is a shear-thinning smectic. (From Sakamoto et al., reprinted with permission from Mol. Cryst. Liq. Cryst. 8 443, Copyright 1969, Gordon and reach Publishers.)...

Figure 11.7 Viscosity versus shear-rate curve for 60% hydroxypropylcellulose (HPC) in water, made from two different batches of of Klucel E. The power-law slopes at low shear rate are —0.51 for Lot 8195 and —0.56 for Lot 7590. (From Walker and Wagner 1994, with permission from the Journal...

Steady-state shear viscosity versus shear rate for PBLG solutions (molecular weight = 238,000) in m-cresol for several concentrations. The 38 wt% and 40 wt% samples show Region I behavior. (From Walker et al. 1995, with permission of the Journal of Rheology.)... 

Region I can be hysteretic. Figure 11 -28 shows the shear viscosity versus shear rate for... 

In this relation, M is the torque, K is the familiar consistency index from viscosity versus shear rate relationships, S is the rotor speed, and n is the power-law index, also familiar from viscosity versus shear rate plots. It can be seen from Equation 1 that a log-log plot of torque versus rotor speed should yield a straight line with intercept given by log (K C(n)) and slope given by n, the power-law index. 

Figure 15. Collapse of simulation data for the effective viscosity versus shear rate as a glass transition is approached by decreasing temperature (circles), increasing normal pressure at fixed number of fluid layers (triangles), or decreasing film thickness at fixed pressure with two different sets of interaction potentials (squares and crosses). The dashed fine has a slope of 0.69. With permission from Ref. 212. Microstructure and Microtribiology of Polymer Surfaces, American Chemical Society, 2000.

Figure 20.3 Viscosity versus shear rate for a shear thinning system.

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