Filling Stage

A complete mold-filling computer simulations requires the calculations of the velocity and temperature profiles throughout the flow region, including the position and shape of the advancing melt front in the cavity. 

Computer simulation packages for injection molding are now available commercially and have transformed the art of injection molding into a science-based process. 

The analysis of mold filling has been divided into the following three regions  

FIG U RE 14.25 Comparison between predicted melt fronts (dashed lines) and experimental short shots (solid lines) for the filling of a variable thickness rectangular cavity with a cylindrical insert. The polymer used was polypropylene, the injection temperature was 197°C, and the cavity wall temperature was 27°C. Predicted weld line is denoted by ++++. (Data from Hieber, C. A. et al., Polym. Eng. ScL, 23, 20,1983. Reprinted by permission of the Society of Plastics Engineers.) 

FIGURE 14.26 Tracer patterns near the advancing melt Iront showing the fountain effect for two different initial tracer locations. The rectangular element at the initial melt front gets sheared and extended and reverses direction as material on the flow front gets deposited near the wall. (Data from Coyle, D. J. et al., AIChE J., 33, 1168, 1987. Reprinted by permission of the American Institute of Chemical Engineers.) 

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For example for the preparation of a 15 cm long, 4.6 mm i.d. stainless tube column, 2.5 g of octadecyl-bonded silica gel was suspended in 25 ml of hexanol-methanol mixture, and kept in an ultrasonic bath for a few minutes to remove air. After the reservoir was filled with the slurry, methanol was pumped in at 10 ml min -1 under constant pressure, 45 MPa (450 bar). After the replacement of slurry solvent by methanol, the flow was stopped and the pressure allowed to drop. When 0 MPa was reached the reservoir was removed. Then, 20 ml of water was added and methanol was again pumped in under the same conditions as before. Again, the flow was stopped and the pressure allowed to drop until it reached 0 MPa. The pre-column was removed and the analytical column closed. The maximum pressure that can be applied in the filling stage is based on the pore size, particle shape, and purity of the silica gel. This reproducible packing procedure is performed at constant temperature by using a water bath (60-BO °C). 

The energy equation for the filling stage is for constant density and thermal conductivity as follows ... 

For the case of long cavities, B < H. In such a case, we may confine ourselves to the second, slowest filling stage, and complete information on the filling process is... 

The dimensionless parameters I and x in Eq. (6.6) are the measure of runner resistance and filling time for the initial ( semi-radial ) filling stage, respectively. Injection pressure P0, mould temperature T (and the respective viscosity r (T),... 

To analyze the temperature distribution in any real situation, it is necessary to consider mold filling and solidification simultaneously. An example illustrating temperature distributions at various times along the length of a polymeric layer at the surface of a solid wall is shown in Fig. 4.18. The initial temperature and conversion distributions are not constant but reflect mathematical simulations of various conditions at the mold filling stage. 

Tw) remains constant during the cure, and no reaction occurs during the mold-filling stage. Therefore, the following conditions are stated for T(t,z) and x(t,z) ... 

When the filling stage of the process is also relevant in the analysis, as in RIM, the momentum balance must be added to the analysis. This, in turn, requires the knowledge of constitutive equations describing the variation of... 

H.H. Chiang. Simulation and verification of filling and post-filling stages of the injection-molding process. Technical Report 62, Cornell University, Ithaca, 1989. 

S, -W. Kim. Three-Dimensional Simulation for the Filling Stage of the Polymer Injection Molding Process Using the Finite Element Method. PhD thesis, University of Wisconsin-Madison, 2005. 

L.-S. Turng and S.-W. Kim. Three-dimensional simulation for the filling stage of the polymer injection molding process using the finite element method. To be published, 2005. 

From a process simulation point of view, in addition to impingement mixing, there are two main problems (a) nonisothermal and transient flow with chemical reaction, prevalent during the filling stage of the process, and (b) conductive heat transfer with heat generation due to the polymerization reaction. We discuss these two problems next, using the case of... 

At the end of the filling stage, only heat transfer with chemical reaction occurs, which can be described by the following species and energy balance equations ... 

In earth fill dams, grout curtains placed for preventive purposes are completed before or during the very early fill stages. For remedial purposes, curtains can be placed from the crest of the dam, if it isn t too high, or from the downstream slope. 

Haagh et al. (1996) modelled the filling stage of a RIM process. They used the following equations to describe the cure kinetics and chemorheology ... 

The disease resistance of wheat was also enhanced by treatment with epibrassinolide, e.g.y in Henan Province. Leaf wilt of wheat is one of the most harmful effects induced by environmental stress during the period from the filling stage to the ripening stage. Epibrassinolide simultaneously reduced the incidence of this phenomenon and the accumulation of free ammonia and putrescine which are regarded as an indicator of this phenomenon as shown in Table IV. 

Fig. 1-7. A definition sketch for the proposed upscaling scheme depicting (a) gamma distribution of central pore lengths with % = 2, and hypothetical six bins (note the inverse relationships between 3 and 1.) (b) three different filling stages in the population of unit cells (represented by l. l.fl) defined at three chemical potential values to g (dry-wet) and (e) the rcNtdllng hypothetical characteristic curve.

Fig. 1-8. Limiting pore size values used for determining the expected pore filling stage at different potentials. These limits are expressed in terms ol pore length /. and vary with the chemical potential (see text lor details).

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