Single-screw extruders Newtonian fluid

Karwe, M. V. and Jaluria, Y., Numerical Simulation of Fluid Flow and Heat Transfer in a Single-Screw Extruder for Non-Newtonian Fluids, Numer. Heat Transfer, Part A, 17, 167 (1990)... 

Chiruvella, R. V., Jaluria, Y., Sernas, V., and Esseghir, M., Extrusion of Non-Newtonian Fluids in a Single-Screw Extruder with Pressure Back Flow, Polym. Eng. Set, 36, 358 (1996)... 

Fig. 6.11 Vector field of the cross-channel flow of an incompressible isothermal Newtonian fluid in a channel with an aspect ratio of 5. [Reprinted by the permission from M. Kaufman, Advection and Mixing in Single Screw Extruder—An Analytic Model, The AIChE Annu. Tech. Conf. Meeting Proc., San Francisco (2003).]...

The two expressions above were derived for a Newtonian fluid using the flat plate approximation considering both down- and cross-channel velocity components. Figure 7.159 shows the RTD for a single screw extruder as well as for pressure flow of a Newtonian fluid between flat plates. 

The Pinto RTD for a single screw extruder is narrower than the RTD for pressure flow between a flat plate for a Newtonian fluid. The effect of shear thinning is to further narrow the RTD as discussed earlier. These two effects explain why hackmixing is such a critical issue in screw extruders. 

The simple extruder design analyzed here would not be implemented in practice because of obvious mechanical problems, but, as we shall see subsequently, it is sufficiently close to the description of a true single-screw extruder that the calculations done here are all relevant. There are three weaknesses in the analysis. First, we have considered only a Newtonian fluid, while most real polymers have highly shear-dependent viscosities. Second, our heat transfer analysis is inadequate, both because we have considered temperature- and pressure-independent physical properties and because we have been able to obtain explicit solutions only for certain limiting cases. Finally, we have not dealt with the flow in the neighborhood of the transition from the extruder channel to the die. All of these restrictions can be relaxed, as we shall see, but to do so for the latter two generally requires the use of numerical algorithms to solve the full equation set. We shall address this topic in Chapter 8. 

The basic principle of operation of the metering section of the single-screw extruder is illustrated by the simple plate model shown in Figure 8.16. The fluid between the two plates is considered to be Newtonian and under isothermal and steady flow conditions. Because of a restriction at the end of the channel (which is not shown) the pressure increases along the z direction, is assumed to depend only on y, since the aspect ratio of the plates is large (i.e., W/H > 10). The equation of motion becomes, after substituting in the expression for the shear stress for a Newtonian fluid. 

B.5 Maximum Shear Rate in the Metering Section. Obtain an expression for determining the maximum shear rate in the metering section of a single-screw extruder for the Newtonian fluid case. 

B.6 Pressure Profile in a Single-Screw Extruder. Show that the pressure profile along the barrel wall of a single-screw extruder for a Newtonian fluid is given by the following expression ... 

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