Contracting geometry

Figure 6.24 Flow through contracting geometries and contracting flow fields...

Observation, discussion and understanding of recirculating vortices in flows of polymer solutions and melts through abrupt contraction geometries have been the subject of many papers over the last 30 years, (e.g. review papers by Boger [1], White et al. [2], McKinley et al. [3])... 

This paper reports experiments and numerical simulations related to a linear low-density polye ylene (LLDPE) and a low-density polyethylene (LDPE), in a significant number of axisymmetric and planar mixed flows. Converging and abrupt contraction geometries involving short and long dies were considered as well as extrudate swell flows occurring at the exit of the ducts under investigation. 

The decomposition curves which result from such a reaction show either (a) an initial rapid decomposition followed by a more gradual decomposition rate, or (b) an initial lag period, giving a sigmoidal appearance. The shape produced by (a) can usually be accounted for by topochemical (or contracting geometry) reactions and that produced in (b) by nucleation theories. 

The contracting geometry equation expressed in its most general form is ... 

Fig. 1 Flow regimes in De-Re space for dilute aqueous PEO solutions through microlength-scale contraction geometries [4]...

Figure 7 shows this effect for three particles close to the reentrant corner in the contraction geometry for P -C quadrilaterals. The closer the initial position of the particle to the separation line, the more difficult it is to turn around the corner. Low-order algorithms lead to particle trajectories that intersect impenetrable boundaries. 

To get more information on the kinetics, isothermal runs were made using a Cahn balance with a controlled furnace and otherwise similar reaction conditions. Isothermal data were collected between 1 and 32 mg and temperatures between 600 and 700 K. Using 18 different functions to represent the data, it was found that Eq. (7) in Fig. 7.18 gives the best fit. This equation can be justified if one assumes that the mass loss is governed by the contracting geometry of the particles. 

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