Pure shear flow

Using this concept, Erwin [9] demonstrated that the upper bound for the ideal mixer is found in a mixer that applies a plane strain extensional flow or pure shear flow to the fluid and where the surfaces are maintained ideally oriented during the whole process this occurs when N = 00 and each time an infinitesimal amount of shear is applied. In such a system the growth of the interfacial areas follows the relation given by... 

If an extensional force is also applied in addition to the pure shear force (for types of flow, see Fig. 9.2), the critical value of the Weber number is considerably lower. It is possible to break up droplets in an extensional flow even when the viscosity ratios are very high. Thus, extensional flow is significantly more effective than pure shear flow when attempting to disperse droplets and break up high-viscosity gels or polymer particles. 

Figure 9.13 Critical Weber number for breaking up droplets as a function of the viscosity ratio, in pure shear flow and in extensional flow...

Qearly, only slight deformation of the droplet takes place in pure shear flow. The droplet is not drawn out into a filament, and the droplet does not break up. Starting at a value of a=0.2, the droplet is drawn out into a filament and when the duration of deformation is... 

Figure 9.14 Droplet deformation as a function of the duration of deformation for different flow fields (ratio of shear and extensional flow) for a viscosity ratio of X = 3 the larger a, the larger the ratio of extensional flow a=0 corresponds to pure shear flow...

To break up agglomerates or disperse liquid droplets, flow forces that exceed a certain minimum value are required. In addition, the type of flow is crucial for the dispersion result, namely, the respective ratio of shear and extension. The shear and extension rates are not constant over the cross-section in an extruder. There are zones with more or less loading. In addition, there are zones with almost pure shear flow and zones where extensional flow dominates. The different zones in the cross-section of a twin screw extruder are shown in Fig. 9.15. 

Other forms of extensional flow are biaxial extensional flow and planar extensional flow or pure shear flow. 

Planar extensional flow or pure shear flow is extensional flow with the same but opposite rates of strain in two directions in the third direction, there is no flow ... 

Pulsed Fourier Transform NMR, 361 Pulsed NMR, 365 Pure shear flow, 533 Pyrolysis, 765... 

An arbitrary shear Stokes flow past a fixed cylinder is described by the stream function (2.7.9). We restrict our discussion to the case 0 2 fi < 1, in which there are four stagnation points on the surface of the cylinder. Qualitative streamline patterns for a purely straining flow (at CIe 0) and a purely shear flow (at CIe = 1) are shown in Figure 2.10. 

Note that in shear for A, = 1, the critical capillary number = 1, whereas for A, > 1, increases with X and becomes infinite for X > 3.8. This means that the breakup of the dispersed phase in pure shear flow becomes impossible for X > 3.8. This limitation does not exist in extensional flows. 

In contrast to the extrusion of plastics, we do not postulate wall adhesion and pure shear flow. As known from practice [1], the extrusion of ceramic bodies involves pronounced wall slippage, even in sharply conical dies. That being so, oixr main problem is friction. 

The extrusion body used in the production of continuous-column ceramic products is, by nature, highly kneadable and workable. Permanent deformation takes place due to the effects of external forces that induce states of stress within the material as soon as a certain boundary stress is exceeded. This kind of behaviour is summarized under the heading plasticity . The body s intrinsic dimensional stability, i.e. its resistance to creep induced by its own weight, stems from the presence of the aforementioned boundary (or minimum) stress, which in the case of pure shear flow is termed yield point or flow limit . The flow limit indicates at which applied pressure the body begins to flow. 

Presstu e-driven flows in straight microchannels with uniform cross section are purely shearing flows (useful information about molecular conformation (through [ 7]) and shear flow behavior, they cannot yield information about a liquid s response to any flow... 

The intrinsic viscosity of the polymers attained a value two orders of magnitude greater than that measured in pure shear flow. After an abrupt onset the intrinsic viscosity increased rapidly with increasing strain rate to a peak value, whereafter it decreased. The increase in intrinsic viscosity correlates with a permanent lowering of the apparent molecular weight, i.e. a polymer degradation. 

Cone and plate systems (Fig. 3.5) allow the build up of a defined constant shear field with only a very small amount of polymer liquid. Because they require high precision motor drives and sensors and because of the high error when wrong distance alignments are used, cone and plate systems are mostly found in expensive rheometers that are capable of more sophisticated kinds of stress fields than the pure shear flow. Nevertheless, they can be used for pure viscosity measurements. 

Figure 8.8 Oscillation-induced stationary flow of liquid around a bubble. See the main text for the geometry. Acoustic streaming is absent in pure shear flow because the flow direction and the gradient direction are perpendicular. However, the bubble deviates the flow, which creates a time-averaged net force. The stationary flow increases the rate of dissolution of the bubble in the liquid phase, which presumably is part of the reason why nanobubbles are less often observed in EQCM experiments than expected. We believe that shear-induced acoustic streaming is a second reason— in addition to Lapiace pressure and apparently "solid nanobubbles—why nanobubbles are less commonly observed in EQCM experiments than one might think.

For K90 by 4 wt% at shear rates up to 1000 s a mean shear viscosity of 0.025 Pa s is found. The rheological response in pure shear flows is similar than for K30 solutions with 20 % polymer mass fraction. However, the atomization experiments show that the fragmentation process for K90 solutions is fundamentally different from those of low concentrated K30 solutions. 

From this equation, it follows that in pure shear flow, droplets with a viscosity ratio above 4 cannot be broken (infinite value of Beyond p = 4 the droplet contin-... 

Viscosity coefficients measured in these geometries when n is immobilised by boMiesowicz viscosities. (Note, that in the literature a variety of alternative notations are common in particular the definitions of r i and r 2 are frequently interchanged.) If the orientation of n is fixed in an arbitrary direction with respect to v and Vv, then the effective viscosity coefficient is given by a linear combination of the Miesowicz viscosities, and another viscosity constant Tju, which cannot be visualised in a pure shear-flow ... 

Finally, we consider the uniaxial elongational flow. This flow is more frequently encountered in practice than pure shear flow. Material flowing in a conical die experiences this type of flow. Van der Reijden-Stolk and Sara (1986) studied this flow and found that the deformation grows as... 

So far, the discussion in this chapter focuses on shear flow. However, the elon-gational flow of polymers also is important for fiber formation. In a pure shear flow, the velocity gradient is normal to the flow direction. On the other hand, the... 

The polymer in the zone were the side test specimens are cut, is the material that freezes immediately when it is in contact with the cavity walls, so it slows down the next material layer and advances with a very high friction generating pure shear flow. The difference in the flow pattern generates variations on the adhesion resistance. It is possible to observe that the adhesion resistance of the test specimens cut from the center of the plates is slightly differences that the ones from the sides. 

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