First critical shear rate

Theoretically, a polymer solution viscosity at different shear rates could have three regimes, as shown schematically in Figure 6.6. At very low shear rates that are below the first critical shear rate, the polymer solution behaves like a Newtonian fluid. The viscosity is independent of shear rate. At intermediate shear rates that are above the first critical shear rate and below the second critical shear rate, the polymer solution behaves like a pseudoplastic fluid. Here, the viscosity decreases with shear rate. At high shear rates that are above the... 

The second critical shear rate is much higher (i.e., 100 times Chauveteau, 1981) than the first one. The first critical shear rate is equal to the inverse of the longest rotational relaxation time k in the solution. Dilatancy starts as soon as the product of Rouse relaxation time and the maximum stretch rate, e, is greater than 4 (Chauveteau, 1981). The Rouse relaxation time demarcates the onset of entanglement effects (Roland et al., 2004). Chauveteau reported that the ratio of shear rate y to the maximum stretch rate e at the contraction was about 2.5 by laser anemometry for similar polymer solutions and flow geometries. Therefore, the second stretch rate (elongation rate) corresponds to the product of shear rate and Rouse relaxation time equal to 10. 

Russian researchers [70] have found that in glass tubes the same Ku value is obtained at Bd > 6. This discrepancy caused Eichhom [71] to carry out a detailed dimensional-analytical examination. He first discovered that the lower critical vG corresponded to a critical film thickness and to a critical shear rate in the phase boundary G/L. Therefore, there are three parameters independent of each other, which could be regarded as target quantities. However, vG can be measured more accurately and more easily than the others, therefore, it is accepted as the target quantity. 

Rheology is a powerful method for the characterization of HA properties. In particular, rotational rheometers are particularly suitable in studying the rheological properties of HA. In such rheometers, different geometries (cone/plate, plate/plate, and concentric cylinders) are applied to concentrated, semi-diluted, and diluted solutions. A typical rheometric test performed on a HA solution is the so-called "flow curve". In such a test, the dynamic viscosity (q) is measured as a function of the shear rate (7) at constant strain (shear rate or stress sweep). From the flow curve, the Newtonian dynamic viscosity (qo), first plateau, and the critical shear rate ( 7 c), onset of non-Newtonian flow, could be determined. 

It has often been stated that DR of surfactant solutions is related to their rheological properties. A rise in shear viscosity at a critical shear rate, caused by a shear-induced structure (SIS), viscoelasticity (nonzero first normal stress difference, quick recoil, and stress overshoot), and high extensional viscosity/shear viscosity ratios ( 100) are rheological properties found in many DR surfactant solutions. After reviewing the rheological behavior of many DR surfactant solutions, Qi and Zakin concluded that SIS and viscoelasticity are not always observed in DR surfactant solutions while high extensional/shear viscosity ratios may be a requirement for surfactant solutions to be DR. ... 

Table 17.29 shows that critical share rate is the best in identifying problem HDPE materials. For plastics resulted in a good run and good extruded profiles, critical shear rate was close to 500 and above it, up to 750 (the first four HDPE... 

One can see that the first four HDPE samples that ran well in the extrusion of the GeoDeck composition have a higher critical shear stress and higher critical shear rate. Their critical shear rate was in the range of 500-600 s . The extrusion window for them was wider in terms of extrusion speed, stress, and temperature. 

The critical shear rate, above which equation (11.31) leads to the first physically useful dispersion degree (>0.1%), is in the neighbourhood of what is known to cause melt fracture ( r > 1000 s , T > lO Nm). This leads to the hypothesis that dispersion can only occur and be observed under melt fracture conditions, a widely known rheological instability [122]. ... 

In order to study the onset of the Saffman-Taylor instability for the PPG-silica suspensions, we estimated the imposed shear rate 2v/b at which the unstable finger for the first time appears. The 2v/b values are obtained as 72, 30, 17, and 11 s for the 2.5, 5.0, 7.5, and 10.0 wt% PPG-silica suspensions, respectively and they are independent of the injection pressure. Moreover, these values are close to the critical shear rates of the corresponding PPG-silica... 

Moat lubricants which contain polymers will show a constant viscosity Newtonian behavior up to a critical shear rate. Above that shear rate, the viscosity of these polymer solutions decreases with increasing shear rate and as the first approximation this Shear-thinning region can be represented by a power-law rheological model. At very high shear rates, polymer solutions will also characteristically approach an upper Newtonian limit. 

Electron micrographs for such systems that have been produced without shear show that the first phase after the hydrolysis of the ester is a lamellar phase with flat stacked bilayers. This phase is transformed into a phase of polydisperse multilamellar vesicles after shearing the sample by shaking it for a short time. These vesicles loose their outer shells more and more with increasing shear rate, until above a critical shear rate rather monodisperse unilamellar vesicles are present in the solutions. In addition, in this case no transition back to flat bilayers can be observed, even at the highest available shear rates. 

The first theory for the mechanical degradation of polymers was developed by Frenkel [1]. A related concept was also espoused by Kauzman and Eyring [2]. Frenkel considered that sheared polymer molecules are extended in the flow direction. The bonds in the middle are the most extended while the chain ends retain more or less their coiled shape. The forces of viscous drag thus put a strain on the central bonds with a force that increases as the square of molecular length. Above a critical shear rate, the central bonds of the macromolecules are expected to be broken preferentially. Molecules with less than a critical molecular weight are considered to be stable under fixed shear conditions. For a DP (degree of polymerization) of 10, a critical shear rate, y, of 10 sec was given [1]. In retrospect, however, the results should also depend on the viscosity of the medium, which, with shear rate, controls the stress. 

Figure 9.19 Correlation between the critical shear rate at which roughness on e tnided sample first occurs versus the melt flow index recovery. (Prom Ref. 22.)...

Critical shear rate (yg) First normal stress... 

Figure 5.7, the CP first decreases, indicating demrxing and, above a critical shear rate, it increases, suggesting shear-induced mixing, a behavior that was later confirmed for other blend systems. 

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