Shear stress apparent

Figure 4 Plots showing dependence of apparent viscosity (17) on apparent shear stress (t) [33].

Figure 9 shows the variation of apparent viscosity with apparent shear stress. It is evident that the mixes are pseudoplastic in nature. Furthermore, as expected, viscosity increases with an increasing filler loading. 

Velocity fluctuations can also cause extra apparent shear stress components. An element of fluid with a non-zero velocity component in the x-direction possesses an x-component of momentum. If this element of fluid also has a non-zero velocity component in the y-direction then as it moves in the y-direction it carries with it the x-component of momentum. The mass flow rate across a plane of area 8x8z normal to the y-coordinate direction is pvy8x8z and the x-component of momentum per unit mass is vx, so the rate of transfer of x-momentum in they-direction is given by the expression... 

In general, the time-averaged value of the product of the fluctuations is non-zero so there is an additional flux of x-momentum in the y-direction due to the velocity fluctuations v x and v y. This momentum flux is equivalent to an extra apparent shear stress acting in the x-direction on the plane normal to the y-coordinate direction. Consequently, the mean total shear stress for turbulent flow can be written as... 

Corporation film-grade Ziegler-Natta linear low density polyethylenes will be presented. They are Resin E, Nova FP-015-A, MFI = 0.55, p = 0.9175 g/cc, and Resin C, Nova PF-120-F, MFI = 1.00, p = 0.9170 g/cc. Their capillary-flow behavior in terms of apparent shear stress vs. apparent shear rate are shown on Fig. 12.24. The melt fracture onset is also noted in Figure 12.24 and the data presented in the table below, indicate that resin E undergoes both sharkskin and gross melt fracture at lower apparent shear rates and stresses. 

C (LLDPE FP-120-F) Apparent shear rate Apparent shear stress 100 0.24 1100 0.42... 

Equation (11-60) [cf. Eq. (3-60)] gives the relation between flow rate and viscosity for a fluid under pressure P in a tube with radius r and length /. In such a device the apparent shear stress, = Pr/2/ and the apparent shear rate, Xa =4(2/7rr, where Q, the volumetric flow rate, is simply the Qjt term of... 

The apparent shear stress at the wall Xa and the real shear stress at the wall tr are thus defined by ... 

This shearing in turn creates a hot melt deformation, or stress. The stress required to bring about a shearing type of a hot melt deformation (a required force divided by the area over which it works) is called shear stress (t, see below). In case of capillary flow, apparent shear stress is the measured resistance to the flow through a capillary die. 

In other words, apparent viscosity (as well as other apparent values in polymer rheology, snch as apparent shear rate and apparent shear stress) is a value calculated assuming Newtonian behavior and considering all pressure drops within the capillary (when using a capillary rheometer). A nonlinearity between shear rate and shear stress is typically observed for polymer melts. The fluid may behave like Newtonian at a very low shear rates to give a limiting viscosity iJq. 

In other words, the apparent shear stress is determined by the pressure drop along the length of the capillary (i.e., pressure at the entrance of the measuring capillary) and the radius and length of the capillary. 

Andersen Corporation, 79, 87-90 Angular rotation, 632 Anisotropic composites, 236 Annealing, 22, 24, 338 Antagonistic behavior of antioxidants, 529 Antibacterials, 415 Anti-microbial agents, 30, 210, 413 Antimony oxide, 471, 476 Antimony trioxide, 471, 476 Antioxidants, 28, 30, 37, 91, 133, 208, 429, 494, 495, 526, 605, 629 Apparent core density, 222 Apparent overall density, 222 Apparent shear rate, 619, 626, 627, 629 Apparent shear stress, 618, 619 Apparent viscosity, 618, 619 Arabinoxylans, 95 ARES, 640, 641 Arkema, 166, 168 Arrhenius equation, 633 Arrhenius plot, 513 Arsenic salt, 416 Asbestos, 80... 

The log-log plots of apparent shear stress versus apparent shear rate for STR5L/ EPDM and STR5L/BEPDM blends with various blend compositions are shown in Figs. 15.12 and 15.13, respectively (71). Flow curves of all the blends show reasonably straight hnes, whose intercept K and slope n correspond to the power law equation (the Ostwald-de Waele equation) (72). Table 15.4 shows the power law index and the consistency of flow of STR5L/EPDM and STR5L/BEPDM blends. The values of n n < 1) indicate the pseudoplastic nature of STR5L, EPDM, BEPDM, and their blends. 

Figure 15.12 Effect of apparent shear rate on the apparent shear stress of STR5L/EPDM blends at various blend compositions. (From Reference 71 with permission from John Wiley Sons.)...

Using the extrusion pressure (AP) measured in the barrel just above die entrance, the apparent shear stress is calculated according to the well-known equation. 

The measured values of polymer flow taken by capillary rheometers are often presented as plots of shear stress versus shear rate at certain temperatures. These values are called apparent shear stress and apparent shear rate at the tube wall. Corrections must be applied to these values in order to obtain true values. The corrected value of shear stress is determined by the Bagley correction [20]... 

It is appropriate to consider the multiphase systems as composed of a matrix and concentration-dependent dynamic clusters or aggregates characterized by specific strength, a, the aggregate relaxation time, Xy, and the cluster size polydispersity index, w w 0.2 — 1.0 [44]. Thus the apparent shear stress may he expressed as ... 

To capture the onset of extrudate distortions which can be associated with melt flow instabilities in the die, several modelling approaches have been followed [4]. Two common hypotheses are forwarded and centre around the so-called constitutive and slip instability issues. The constitutive approach starts with the premise that, on the basis of some viscoelastic theory, the shear stress becomes a many-valued function of shear rate. As a consequence of this noiunonotone function, a melt flow instability and the associated distorted extrudate will develop. For many commercial polymers, the nonmonotone function could be considered as the sum total of many nonmonotone functions, each associated with a specific molecular weight fraction. The associated experimental apparent shear stress-apparent-shear rate curve could then become monotone, i.e. as in Figure 1(b), as is the case for PP. It should be noted that for viscoelastic materials, no direct linear relation exists between a constitutive shear stress-shear rate function and the experimental pressure (apparent shear stress)-flow rate (apparent shear rate) curve. 

Figure 1 (opposite) Schematic representation of an experimental nonmonotone (a) and monotone (b) flow ciuvc with indications of the sequence of characteristic extrudate distortions, typical for linear polymers, e.g. HOPE and PP, respectively. The apparent shear stress and shear rate are directly related to the measured pressure and set flow rate in a capillary experiment and presented on logarithmic... 

Figure 18.25 Relationship between apparent shear stress and shear rate for simple blends of 60/40 MNR/PP with various quantities of PP- -MA.

The maximum apparent shear viscosity was observed at a loading level of 5% w/w for both compatibilizers used. This trend of apparent shear viscosity was found to be the same as the apparent shear stress. 

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