Injection Molding - Isothermal Flow Problems

At some point in time, which we will call t = 0, we mark a portion of the secondary component entering the tank (Fig. 6.5 lb), say with a pigment, so we can distinguish it from the material that was in the tank before t = 0 (Fig. 6.51a), as well as the material that enters the tank after (Fig. 6.51c) the marked material is inserted. We now call F(t) the fraction of the material that was in the tank the instant the marked material is added, and has left the tank at time t. Hence, the volumetric output of the marked secondary component is F(t)C0Q. The concentration of the marked secondary component in the output is C(t). We can now write the balance 

If we assume a perfectly homogeneous stirring tank, a balance of the marked material inside the tank will give 

Injection molding is a rather complex process during which non-Newtonian as well as non-isothermal effects play significant roles. Here, we present a couple of problems that are relatively simple to allow an analytical solution. Injection molding is discussed further in the next chapters. 

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Sample balancing problem. Let us consider the multi-cavity injection molding process shown in Fig. 6.54. To achieve equal part quality, the filling time for all cavities must be balanced. For the case in question, we need to balance the cavities by solving for the runner radius R2. For a balanced runner system, the flow rates into all cavities must match. For a given flow rate Q, length L, and radius R, solve for the pressures at the runner system junctures. Assume an isothermal flow of a non-Newtonian shear thinning polymer. Compute the radius R2 for a part molded of polystyrene with a consistency index (m) of 2.8 x 104 Pa-s" and a power law index (n) of 0.28. Use values of L = 10 cm, R = 3 mm, and Q = 20 cm3/s. 

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