Newtonian fluid compression molding

Hele-Shaw model for compression molding of a Newtonian fluid. A special case, where the z-velocity component plays a significant role and must be included, is the compression molding process. The process is schematically depicted in Fig. 5.21. 

For compression molding inside the disc-shaped cavity shown in Fig. 6.81, derive an expression for the flow field and pressure distribution inside the mold during filling for an arbitrary flow front location Rf. Assume a Newtonian fluid and the notation found in the figure. 

Figure 18.3. Orientation function vs. volume loading of talc in compression molded polystyrene. [Data from Kim K J, White J L. J. of Non-Newtonian Fluid Mechanics, 66, Nos.2/3, 1996, 257-70.]...

Squeeze flow between parallel plates was analyzed in Section 6.3 as an elementary model of compression molding. In that treatment we were able to obtain an analytical solution to the creeping flow equations for isothermal Newtonian fluids by making the kinematical assumption that the axial velocity is independent of radial position (or, equivalently, that material surfaces that are initially parallel to the plates remain parallel). In this section we show a finite element solution for non-isothermal squeeze flow of a Newtonian hquid. The geometry is shown schematically in Figure 8.16. We retain the inertial terms in the Navier-Stokes equations, thus including the velocity transient, and we solve the full transient equation for the temperature, including the viscous dissipation terms. The computational details. 

Determine the velocity field and the pressure distribution for the flow of an incompressible Newtonian fluid between two disks as shown in Figure 2.13. Flows similar to this occur in several polymer processes including injection molding in a center-gated disk mold or compression molding. 

B.2 Lubricated Compression Molding. For the compression molding process shown in Figure 10.11 the plates are lubricated either with mold-release agent or by using Teflon sheets. Calculate an expression for the force required to close the plates similar to Eq. 10.50 when the polymer is assumed to exhibit complete slip. Do this first for a Newtonian fluid and then a polymer melt with rheological properties described by the PTT model. 

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