Constitutive model overview

This chapter gave an overview of how to simplify complex processes sufficiently to allow the use of analytical models for their analysis and optimization. These models are based on mass, momentum, energy and kinetic balance equations, with simplified constitutive models. At one point, as the complexity and the depth of these models increases by introducing more realistic geometries and conditions, the problems will no longer have an analytical solution, and in many cases become non-linear. This requires the use of numerical techniques which will be covered in the third part of this book, and for the student of polymer processing, perhaps in a more advanced course. 

This Introductory Section was intended to provide the reader with an overview of the structure of quantum mechanics and to illustrate its application to several exactly solvable model problems. The model problems analyzed play especially important roles in chemistry because they form the basis upon which more sophisticated descriptions of the electronic structure and rotational-vibrational motions of molecules are built. The variational method and perturbation theory constitute the tools needed to make use of solutions of... 

Over the past four decades, RIS models for hundreds of polymer structures, and sometimes many different ones for one and the same macromolecule, have been developed and published. The casual user of RIS techniques, even one intimately familiar with the method and its foundation, is often faced with the task of finding RIS parameters from the literature for unfamiliar constitutions and configurations. It is this task that the present review is aimed at easing by providing a comprehensive overview of the published models available to date. While completeness cannot be claimed, care has been taken to find as many models as possible and to report them in as brief a space as practical. 

The second chapter by Wesolowski presents a general overview of the recent developments in Density Functional Theory (DFT), which currently constitutes the most popular tool for modeling molecular materials. Particular emphasis has been... 

FIG. 17. A schematic overview of Cso represented by a stick model, 3D and 2D contour plots of the electron density. In the 3D plot in the middle the single contour has been chosen to show how the electrons are distributed in the bonds. The 2D contour plot shows the electron density in a plane that includes the center of the molecule. We clearly see that there is a void, which means that Ceo constitutes a spherical shell. 

Polymeric fluids are the most studied of all complex fluids. Their rich rheological behavior is deservedly the topic of numerous books and is much too vast a subject to be covered in detail here. We must therefore limit ourselves to an overview. The interested reader can obtain more thorough presentations in the following references a book by Ferry (1980), which concentrates on the linear viscoelasticity of polymeric fluids, a pair of books by Bird et al. (1987a,b), which cover polymer constitutive equations, molecular models, and elementary fluid mechanics, books by Tanner (1985), by Dealy and Wissbrun (1990), and by Baird and Dimitris (1995), which emphasize kinematics and polymer processing flows, a book by Macosko (1994) focusing on measurement methods and a book by Larson (1988) on polymer constitutive equations. Parts of this present chapter are condensed versions of material from Larson (1988). The static properties of flexible polymer molecules are discussed in Section 2.2.3 their chemistry is described in Flory (1953). 

The science of mechanics constitutes a vast number of sub-disciplines commonly considered beyond the scope of the standard chemical engineering education. However, when dealing with kinetic theory-, granular flow- and population balance modeling in chemical reactor engineering, basic knowledge of the principles of mechanics is required. Hence, a very brief but essential overview of the disciplines of mechanics and the necessary prescience on the historical development of kinetic theory are given before the more detailed and mathematical principles of kinetic theory are presented. 

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