Polymeric flow model

Example.s of polymeric flow models where the above simplifications have been successfully used are presented in Chapter 5. 

PCM (polymeric core model), PFM (polymeric flow model), and MGM (multigrain model). 

In the Multigrain model, fractured catalyst microparticles are produced during the polymerization and uniformly dispersed in the polymer each of these particles behaves as a micro Solid core and diffusion within them, as well as in the interstices between them, can take place. In the Polymeric flow model the catalyst microparticles are dispersed in a polymer continuum and move outward in proportion to the volumetric expansion due to polymerization only one value of diffusivity is considered. Both these models predict significant MWD broadening due to mass transfer limitations (Q , 9 for polypropylene in the Polymeric flow model) on the basis of mathematical calculations carried out assuming reasonable values of the kinetic and physical parameters. 

Later the growth model developed for a neodymium catalyst system was applied for the butadiene polymerization in gas phase. The ideas concerning the initial polymerization stages are in agreement with a core—shell model .The subsequent polymerization stages correspond to the polymeric flow model . 

Another common single-particle model is the polymeric flow model (PFM), in which a pseudohomogenous hypothesis is made for the macroparticle [127-129]. Instead of being located at the center of microparticles, as in the MGM, active sites are considered to be dispersed in a pseudohomogenous medium with varying radial concentrations. The PFM is somewhat easier to implement than the MGM and leads to similar prediction trends. Several models that combine features of the MGM and PGM have also been developed over the years [114, 130]. 

PFM polymeric flow model PLTA Plastics Lumber Trade Association... 

Finite Element Modelling of Polymeric Flow Processes... 

FINITE ELEMENT MODELLING OF POLYMERIC FLOW PROCESSES 3.1.1 The U-V-P scheme... 

FINITE FXEMENT MODELLING OF POLYMERIC FLOW PROCESSES... 

The majority of polymer flow processes are characterized as low Reynolds number Stokes (i.e. creeping) flow regimes. Therefore in the formulation of finite element models for polymeric flow systems the inertia terms in the equation of motion are usually neglected. In addition, highly viscous polymer flow systems are, in general, dominated by stress and pressure variations and in comparison the body forces acting upon them are small and can be safely ignored. 

The majority of polymer flow processes involve significant heat dissipation and should be regarded as nou-isothermal regimes. Therefore in the finite element modelling of polymeric flow, in conjunction with the equations of continuity... 

For the bulk polymerization of styrene using thermal initiation, the kinetic model of Hui and Hamielec (13) was used. The flow model (Harkness (1)) takes radial variations in temperature and concentration into account and the velocity profile was calculated at every axial point based on the radial viscosity at that point. The system equations were solved using the method of lines with a Gear routine for solving the resulting set of ordinary differential equations. 

Polymer growth models which are more sophisticated and adhere more closely to reality have recently been reproposed These are the Polymeric flow ... 

---