Polymer processing problems

As mentioned in Chapter 2, the numerical solution of the systems of algebraic equations is based on the general categories of direct or iterative procedures. In the finite element modelling of polymer processing problems the most frequently used methods are the direet methods. 

The examples outlined above are intended to show the utility of a generalized computer model for polymer processing problems. Such a model is able to adapt itself to a wide variety of situations simply by adjustments to the input dataset, rather than requiring alterations to the code itself. This flexibility makes the code somewhat more difficult to learn initially, but this might be minimized by embedding the finite-element code itself in a more "user-friendly" graphics-oriented shell. 

There are many numerical issues that we must discuss before proceeding to applications of FDM when solving polymer processing problems. The most important are,... 

In the meantime, we will solve a number of flow problems that are highly relevant to polymer processing problems, which demonstrate the rather straightforward use of the equation of motion and continuity. 

There is a multitude of constitutive equations proposed for polymer melts. However, only a few have been used to solve actual polymer processing problems. Nevertheless, we feel, as we did in the first edition of this book, that it is instructive to trace their origin and to indicate the interrelationship among them. We will do this quantitatively, but without dealing in detail with the mathematical complexities of the subject. The following three families of empirical equations will be discussed ... 

The solution of any polymer processing problem reqnires it to be defined both qualitatively and quantitatively. It is important with polymer compounding to use the polymeric material in an expert way based on knowledge of how to deal with such materials with equipment, especially for practical applications. Polymer compounding is used to develop new products tailored to a particular end use. The effort is mutually profitable to both the supplier and consumer of the polymeric materials, bringing together both technical and economic competence. 

With these more general expressions (Eqs. 6.28-6.30), more complicated flow situations can be described, i.e., flow with velocity components in two or three directions. It should be remembered that the power law description is an approximation it is not accurate over the entire range of shear rate. However, in most practical polymer processing problems, the use of the power law equation yields sufficiently accurate results. The major advantage of the power law equation is its simplicity, despite the appearance of Eqs. 6.28-6.30. The relationship between stress and rate of deformation can be described with only two fluid properties, the consistency index m and power law index n. A drawback of the power law is that it does not allow construction of a time constant from the constants m and n. This is a problem in the analysis of transient flow phenomena where a characteristic time constant is necessary to describe the flow situation. 

Other applications to fluid mechanics and polymer processing problems can be found on a regular basis in pubhcations such as the Journal of Fluid Mechanics, the Journal of Non-Newtonian Fluid Mechanics, International Polymer Processing, and so forth. We address polymer processing flows in which polymer viscoelasticity is important in Chapter 10. 

Beloborodova T.G., Panov A.K. Effective constructions of reducers for soft polymers processing. Problems of machine - conducting and critical technology in machine -building complex of the Republic of Bashkortostan Collection of scientific works. -Ufa Gilem , 2005.-p.300. 

As there is no intention in this book to use the nonUnear constitutive equations in conjunction with the equations of motion to solve polymer processing problems, we at least show in the next several examples how one determines the predictions of a nonlinear model for flows in which the kinematics are known. In particular, we consider shear and shear-free flows. Furthermore, we show how one goes about finding the material parameters in a constitutive equation from rheological data for a polymer melt. 

The method of simulation selected is the Radial Functions Method that has shown to deliver excellent results for highly non-linear problems. This method has recently applied to model and simulate polymer processing problems by Lopez, Osswald, Estrada [2,3,4] and Mai-Duy [9] An additional motivation in this work is the... 

Pittman, J. F. T., 1989. Finite elements for field problems. In Tucker, C. L. Ill (ed.), Computer Modeling for Polymer Processing, Chapter 6, Hanser Publishers, Munich, pp. 237- 331. 

Iterative solution methods are more effective for problems arising in solid mechanics and are not a common feature of the finite element modelling of polymer processes. However, under certain conditions they may provide better computer economy than direct methods. In particular, these methods have an inherent compatibility with algorithms used for parallel processing and hence are potentially more suitable for three-dimensional flow modelling. In this chapter we focus on the direct methods commonly used in flow simulation models. 

Achieving steady-state operation in a continuous tank reactor system can be difficult. Particle nucleation phenomena and the decrease in termination rate caused by high viscosity within the particles (gel effect) can contribute to significant reactor instabilities. Variation in the level of inhibitors in the feed streams can also cause reactor control problems. Conversion oscillations have been observed with many different monomers. These oscillations often result from a limit cycle behavior of the particle nucleation mechanism. Such oscillations are difficult to tolerate in commercial systems. They can cause uneven heat loads and significant transients in free emulsifier concentration thus potentially causing flocculation and the formation of wall polymer. This problem may be one of the most difficult to handle in the development of commercial continuous processes. 

Finite element methods are one of several approximate numerical techniques available for the solution of engineering boundary value problems. Analysis of materials processing operations lead to equations of this type, and finite element methods have a number of advantages in modeling such processes. This document is intended as an overview of this technique, to include examples relevant to polymer processing technology. 

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