The range of shear rates

The approximate value of the shear rate encountered in a wide variety of circumstances found in everyday life or in industrial situations is shown in table 1. Readers may relate these numbers to their own field of interest by simply dividing a typical velocity in any flow of interest by a typical dimension. An example of this is the average velocity of a liquid flowing in a pipe divided by the pipe radius, or the velocity of a moving sphere divided by its radius. 

Sedimentation of fine powders in liquids 10-6 -10-3 Medicines, paints, salad dressing 

Levelling due to surface tension 10-2 -10-1 Paints, printing inks 

Draining off surfaces under gravity 10-1 -101 Toilet bleaches, paints, coatings 

Pipe flow 100.103 Pumping liquids, blood flow 

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When log (viscosity) is plotted against log (shear rate) or log (shear stress) for the range of shear rates encounterd in many polymer processing operations, the result is a straight line. This suggests a simple power law relation of the type... 

Polyethylene is injected into a mould at a temperature of 170°C and a pressure of 100 MN/m. If the mould cavity has the form of a long channel with a rectangular cross-section 6 mm X 1 mm deep, estimate the length of the flow path after 1 second. The flow may be assumed to be isothermal and over the range of shear rates experienced (10 -10 s ) the material may be considered to be a power law fluid. 

Because it is very difficult to measure the flow characteristics of a material at very low shear rates, behaviour at zero shear rate can often only be assessed by extrapolation of experimental data obtained over a limited range of shear rates. This extrapolation can be difficult, if not impossible. From Example 3.10 in Section 3.4.7, it can be seen that it is sometimes possible to approximate the behaviour of a fluid over the range of shear rates for which experimental results are available, either by a power-law or by a Bingham-plastic equation. 

Thermoplastic elastomeric compositions from reclaimed NR and scrap LDPE with 50 50 mbber/plastic ratio shows good processability, ultimate elongation, and set properties. Polymer blends of reclaimed mbber and LDPE exhibit higher viscosity over the range of shear rate at various temperatures compared to virgin NR-LDPE blends due to the influence of filler present in the reclaimed mbber (Eigure 38.7) [109]. 

Two of Miller s suspensions were slightly non-Newtonian in behavior (0.8 < n < 1.00). For these he determined the differential viscosities over the range of shear rates from 5.8 to 77 sec.-1 with a MacMichael viscometer. They were constant over about the upper 70% of this shear-rate range and were found to be equal to the experimentally determined turbulent-flow viscosities in the heat exchanger. 

For the investigation of thixotropy, it may be desirable that the range of shear rates in the viscometer be small (W4). This means that the... 

As a final remark it may be mentioned that the discussed polypropylene melts do not at all behave like second-order fluids in the range of shear rates and angular frequencies accessible to measurement. This is shown in Fig. 4.6. In this figure the doubled extinction angle 2 is plotted... 

It is important for the process engineer to know the rheological properties of a material since the properties dominate the flow of the material in extrusion processes and also dominates the physical and mechanical properties of the extrudates. Therefore, it is also important to measure the properties utilizing a similar miniaturized extruder in the laboratory so that a process engineer knows the flow properties in the system by simulating the production line. Also, it is desirable to know the flow properties of a material to be processed in the range of shear rates of equipments to be used. 

In the case of elastic fluids and for simple shear flow, the first normal stress difference is N[ =on — o22- When shearing a fluid between two plates (x, direction), the first normal stress difference N( forces the plates apart (x2 direction). The first normal stress difference N i is shown together with the measured shear stress x as a function of the shear rate in Fig. 3.9. In the range of shear rates investigated, the shear stress in the case of silicone oil is substantially greater than the normal stress difference and we see substantially greater normal stress differences for viscoelastic PEO solution than for viscous silicone oil. 

Rheological Behavior. Figure 4 shows the room-temperature steady-shear viscosity as a function of shear rate for PDM-PMAS polymers and their precursors. Polymers with Ciq, C12, and C14 side chains exhibit Newtonian behavior over the range of shear rates monitored. 

The rheological behavior of the flowing fluid is represented by a model that is valid in the range of shear rates to be encountered inside the porous medium. 

All of the emulsions appear to be Newtonian in the range of shear rates studied (Fig. 5). No significant change in the viscosity of the fresh emulsions was observed at NaOH concentrations above 6.0 x 10 moles NaOH/gram oil, but the viscosity did decrease as NaOH concentration decreased, particularly below 4 x 10 as shown in Table I and Fig. 5. 

The viscosity of microemulsions was measured with a Rheotest 2 (Medingen, Germany) instrument in the range of shear rates 5 - 1800 s. ... 

The zero-shear viscosity rip is defined as the melt viscosity in the limit of y=0, and is a function of T and Mw. It is important to keep in mind, however, that rp) is very often not measured directly, but extrapolated from measurements at low shear rates. Such extrapolations can introduce an error in the value of r o if the range of shear rates used in the extrapolation is sufficiently high for non-Newtonian effects to begin manifesting themselves. 

Polyacrylamides and xanthan gum show pseudoplasticity up to shear rates of about 300-500 sec l. Above this shear rate, a Newtonian zone appears. One would expect another Newtonian zone at very low shear rates (6). This was not observed over the range of shear rates considered in this study however, Mungan showed the existence of this zone for polyacrylamides (18). 

Ib/in ). The shear stress limits of the viscometer are represented by the two vertical lines. The two lines with a slope of unity represent the range of shear rates over which the instrument was operated. Within the operating limits of the instrument the viscosity of the liquid was constant t.e., the flow was Newtonian. 

The range of shear rates encountered in polymer processing varies approximately from y= 1 to 10 sec f For proper analysis of polymer processing operations, it is necessary to represent the behavior in each region with an appropriate model. The one most frequently used for non-Newtonian fluids is the power-law model ... 

Small amplitude dynamic viscoelastic properties of apple butter, mustard, table margarine, and mayonnaise were compared to their respective properties in steady shear flow in the range of shear rates and frequencies of 0.1 to 100 sec" (Bistany and Kokini, 1983). Comparisons of dynamic and steady viscosities showed that dynamic viscosities (tj ) are much greater than steady viscosities (17). Consequently, the Cox-Merz rule is not obeyed (Bistany and Kokini, 1983). This phenomenon can be explained by a signifi-... 

Commercial instruments are available the Brabender Plastograph, and Plasticorder, this latter allowing use of an extruder head the RAPRA variable torque rheometer [5]. The advantages of these instruments are based on the similarity of their action to full-scale extrusion equipment and on the fact that they can be operated at shear rates appropriate for factory equipment. But because of the difficulty of matching exactly the range of shear rates which exist in full-scale plant, successful scaling-up is difficult. Elongation flow measurements have been reported by several workers, in which a sample is stretched in uniaxial tension at a constant strain rate [6]. 

As just stated, the L3 phase resembles structurally a bicontinuous microemulsion, which makes it interesting to compare their rheological properties. Viscosity measurements on an L3 phase [in the system cetylpyridinium chloride-hexanol-brine (0.2 M NaCl)] showed Newtonian flow behavior for the range of shear rates of 0.1-100 s" [113]. The viscosity of this highly interconnected, spongelike system is always very low and close to the solvent viscosity, even for a volume fraction of 0.2 it is less than 10 mPa s. (Similar viscosity values have been observed in the L3 phase of the system tetradecyldimethylamine oxide-hexanol-water [114].) It increases linearly with the volume fraction of the amphiphilic material, where it is interesting to note that extrapolation to zero concentration does not yield the solvent viscosity but a value about three times as high. A similar value for the extrapolated viscosity was also reported more recently for another L3 phase (in the system SDS pentanol-dodecane-water [115]), and it seems that this enhanced viscosity is a universal property connected to the structure of the L3 phase. 

Over the range of shear rates over which m is approximately constant, one may write a power-law type equation for this segment as... 

The width of the region of negative is approximately one decade in shear rate, and the range of shear rates over which it occurs shifts with concentration to an extent that agrees with theory. 

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