Screw surfaces

Molar flux of volatile component in wiped film on screw surface... 

As discussed previously in Section 5.2.4, screw rotation physics need to be used in order to calculate the sliding velocity of the solid bed relative to the barrel and screw surfaces. For barrel rotation physics, the sliding velocities at the barrel and screw surfaces are considerably different than that for screw rotation. At the barrel wall, the z component of motion must be corrected for the moving velocity of the barrel wall, as provided in Eq. 5.38. For the example above, V(,s= 12.5 cm/s. Because the screw is stationary for barrel rotation physics, = 0, and the sliding velocity at screw surface using Eq. 5.39 sets = 4.4 cm/s. At a pressure of 0.7 MPa... 

The X- and z-component velocities of the screw are calculated as follows, and they are used as the boundary conditions at the screw surface ... 

The results presented here are encouraging but only qualitative and have been produced using this first-order model. Current limitations of the model are the use of a constant-viscosity function independent of temperature and shear rate. Also, the dynamic local temperature of the barrel and screw (Section fO.lO) must be incorporated into the model they are currently set as constants. An enhanced model for the film thickness at both the barrel and screw surfaces should be added to the current model along with flows induced by pressure gradients. 

The double integral represents the nonzero terms of the dissipation rate tensor as adapted by Middleman [61] and Bernhardt and McKelvey for adiabatic extrusion [62]. The nontensorial approach was adopted by Tadmor and Klein in their classical text on extrusion [9]. In essence these are the nonzero terms of the dissipation rate tensor when it is applied to the boundary of the fluid at the solid-fluid interface. In the following development this historic analysis was adopted for energy dissipation for a rotating screw. In this case the velocities Ui are evaluated at the screw surface s and calculated in relation to screw rotation theory. The work in the flight clearance was previously described in the literature [9]. The shear... 

If n = 1 then this is a Newtonian fluid and K is the Newtonian viscosity. The shear stress, T, is the viscosity times the shear rate. The reader is encouraged to go to references [4-6, 45] to become familiar with the literature development of the screw surface velocities. 

The heat transferred through the barrel wall over the channel, Ej, is given by Eq. 7.83. A heat transfer expression could also be written for energy transferred from the molten polymer to the barrel over the flight iand and also from the melt to the screw surface. 

Dynamic mixers are a class of secondary mixers where part of the mixing device is aiiowed to move reiative to the barrei and screw surfaces or has an active channei positioned in the barrei waii. In generai, these mixers provide improved mixing over traditionai secondary mixers, but they are more compiicated and costiy to produce, require higher maintenance ieveis, and tend to have higher ieveis of wear. 

Transport of energy in the screws was modeled previously for single-screw extruders [30-32] and for twin-screw extruders [33]. In order to predict the axial screw temperature in a single-screw extruder, heat conduction along the screw has to be modeled. The model developed by Derezinski [32] included heat conduction from the barrel through the screw flights to the screw surface, heat conduction from the polymer to the screw root, and heat conduction in the axial direction. The model showed that the screw does not behave adiabatically and that the steady-state heat conduction in the screw depends greatly on the size of the extruder. 

The stress at the interface was measured as a function of temperature and sliding velocity for the resin using the equipment shown in Fig. 4.11, and the data are shown in Fig. 12.33. The stress curve had two maximums the first peak was at the Tg of the resin at 150 °C, and the second peak occurred at a temperature of about 240 °C. In order to maximize solids conveying while maintaining a viable process, the optimal forwarding forces would occur at a barrel surface temperature near 240 °C, and the retarding forces at the screw surfaces would be minimized at temperatures less than about 120 °C. In order to maintain the high rate of this line and the inside barrel wall at a temperature near 240 °C, the first zone of the extruder needed to be maintained at a temperature of 310 °C. 

The viscous energy dissipation is caicuiated by muitipiying the normai shear stress for the screw surface by the veiocity of the screw surface integrated over the screw surface area. The method for caicuiation of dissipation for screw rotation is as foiiows ... 

The solids conveying zone. The task of the solids conveying zone is to move the polymer pellets or powders from the hopper to the screw channel. Once the material is in the screw channel, it is compacted and transported down the channel. The process to compact the pellets and to move them can only be accomplished if the friction at the barrel surface exceeds the friction at the screw surface. This can be visualized if one assumes the material inside the screw channel to be a nut sitting on a screw. As we rotate the screw without applying outside friction, the nut (polymer pellets) rotates with the screw without moving in the axial direction. As we apply outside forces (barrel friction), the rotational speed of the nut is less than the speed of the screw, causing it to slide in the axial direction. Virtually, the solid polymer is then "unscrewed" from the screw. To maintain a... 

Figure 10.39 Pressure distribution on the screw surfaces of a co-rotating double flighted twin screw extruder.

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