Screw Shear flow

Illustration Optimum strain per period in shear flows with periodic reorientation. Many practical mixing flows (e.g., single screw extruder with mixing... 

This can be easily checked by assuming that the flow inside this section of the screw can be modeled using a simple shear flow, and that most of the conduction occurs through the channel thickness direction. For such a case, the energy equation in that direction, say the -direction, reduces to... 

The cross channel flow is derived in a similar fashion as the down channel flow. This flow is driven by the x-component of the velocity, which creates a shear flow in that direction. However, since the shear flow pumps the material against the trailing flight of the screw channel, it results in a pressure increase that creates a counteracting pressure flow which leads to a net flow of zero1. The flow rate per unit depth at any arbitrary position along the 2-axis can be defined by... 

Erwin [8] developed the theoretical background to assess the effect orientation has on the distributive mixing in single screw extruders. His starting point was the equation that relates the growth of an interface between fluids undergoing shear flow (Fig. 6.43), and described... 

Summarizing, the model of the screw channel flow is governed by eqns. (8.99), (8.105) and (8.106) with boundary conditions eqns. (8.100), (8.101) and (8.104). The constitutive equation that was used by Griffith is a temperature dependent shear thinning fluid described by... 

Also noteworthy is the appreciable coalescence caused by the shear flows in the single screws, of the rheology section of the TSMEE following the mixing element section. Flow of dispersed immiscible blends involves continuous breakdown and coalescence of the dispersed domains (122). Shear flows, where droplet-to-droplet collisions are frequent—in contrast to extensional flows—favor coalescence over dispersion. The presence of compatibilizers shifts the balance toward reduced coalescence rate. Macosko et al. (123) attribute this to the entropic repulsion of the compatibilizer molecules located at the interface as they balance the van der Waals forces and reduce coalescence, as shown on Fig. 11.36. 

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. 

Figure 1 Typical stages in thermoplastics processing. (1) Solids flow (2) screw filling and solids conveying (3) melting (4) polymer melt shearing/pumping (5) shear flow in channels (6) die swell (7) elongational flow (8) volume change under pressure (9) thermal conduction and (10) shrinkage.

Fillers are mainly used for reasons of economy, but in many cases they also improve some properties of the polymer. The most important fillers for polymers are minerals such as talc, chalk and china clay. Filler content generally used with plastics is up to 60 wt%. The most common practice is to feed the filler downstream into the melt by means of a twin-screw side feeder (Figure 6.3). It is well-known that thermoplastic melts with high loadings of small particles such as calcium carbonate, carbon black and titanium dioxide give both yield values in shear flow [58, 59], and uniaxial extension [60, 61]. 

Couette flow n. Shear flow in the annulus between two concentric cylinders, one of which is usually stationary while the other turns. By measuring the relative rotational velocity and the torque required to maintain steady flow, one can infer the viscosity of the liquid. Flow in the metering section of a single-screw extruder resembles Couette flow, modified by the presence of the flight and, normally, by the pressure rise along the screw. 

Shear flow n. The flow caused by the relative parallel or concentric motion of the surfaces confining a liquid, as in an extruder screw or caused by a pressure drop, in the direction of flow, from the entrance of a flow passage to its exit, as in a die. Sometimes the two basic driving modes coexist, as in the metering sections of most extrusion screws and in wire-covering dies. In the direction crosswise to any laminar flow, successive layers slide past each other in shear. 

The barrier screw geometry is shown in Fig. 8.108. The Maddock screw has a fluted mixing element similar to the one shown in the bottom of Fig. 8.108. The CRD screw is a screw with a distributive mixing element that is based on elongational flow rather than shear flow [128-131]. 

Recall from Section 12.3.1 that a flow number of 0.5 indicates shear flow while a flow number of 1.0 indicates pure elongational flow. For mixing purposes, a flow number near 1.0 is preferred. Figures 12.10(a-c) illustrate that the co-rotating, double-flighted twin screw produces a flow that is mainly shear to elongation. 

Figures 12.10(a-c) shows that the flow number distribution for the single- and double-flighted screws are nearly identical, whereas, the triple-flighted screw produces mainly shear flow due to the small gaps that are present with this geometry. Interestingly, the geometry that created the highest volumetric strain rate was the double-flighted screw, which is the most commonly used screw geometry for twin screw extruders.

Evolution of the average drop diameter along the screw was computed from the microrheological rules supplemented by the coalescence kinetics, see Eqs 19-21. The model assumed steady state shear flow, viscosity dependent on shear stress and temperature, and interfacial tension coefficient dependent on temperature. The... 

In considering the laminar shear flow due to screw rotation, we can simplify the mechanism by considering a cross section as follows (Figure 2.12). 

Laminar shear flow in the melt zones of the screw may be inadequate to prevent striations... 

However, as much of the fundamental work, which dates back to the 1930s uses simple laminar shear flow models and Couette flow, it is apparent that there should be a niche for single screw extruders. This raises the question of how large is this niche ... 

This also applies to the break-up of droplets. According to Taylor, the breaking up of a single drop requires the viscous forces acting on the droplet to exceed the interfacial forces for a sufficient amount of time. This also indicates that a limit may exist in single screw extruders whereby under certain conditions, laminar shear flow fails to achieve a critical level of stress needed to break up the droplet. 

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