TRANSPORT PHENOMENA IN POLYMER PROCESSING

So divinely is the world organized that every one of us, in our place and time, is in balance with everything else. 

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The thermal conductivity of polymeric fluids is very low and hence the main heat transport mechanism in polymer processing flows is convection (i.e. corresponds to very high Peclet numbers the Peclet number is defined as pcUUk which represents the ratio of convective to conductive energy transport). As emphasized before, numerical simulation of convection-dominated transport phenomena by the standard Galerkin method in a fixed (i.e. Eulerian) framework gives unstable and oscillatory results and cannot be used. 

In engineering applications it is often convenient to obtain integral representations which directly involve the field and its fluxes, rather than equations for single- or double-layer densities. This methodology is commonly called the direct method. For Poisson s equation this can be done using the Green s identities for scalar fields. As we already know, Poisson s equation is widely used in transport phenomena and polymer processing, and it is defined as,... 

The equations which govern the nonisothermal flow of a reactive fluid are derived in several texts on transport phenomena and polymer processing (e.g. refs. 1,2). Regarding velocity, temperature, and concentration of unreacted species as the fundamental variables, the governing equations can be written as ... 

This is not sufficient, however. In several cases of practical interest, charge transport has the characteristics of a thermally activated hopping process the importance of the diffusion of localized (soliton or polaron) states is elusive and band conduction seems to be an idealization. The description of transport phenomena in polymer materials will therefore require a thorough characterization of the structure in both crystalline and disordered ( amorphous ) regions, and a detailed picture of how these are dispersed and interconnected. 

The aim of the article is to introduce new observations of diffusive-convective phenomena in polymer chemistry. The processes discussed are of significance to those interested in transport phenomena. 

The transport of gas in polymers has been studied for over 150 years (1). Many of the concepts developed in 1866 by Graham (2) are still accepted today. Graham postulated that the mechanism of the permeation process involves the solution of the gas in the upstream surface of the membrane, diffusion through the membrane followed by evaporation from the downstream membrane surface. This is the basis for the "solution-diffusion model which is used even today in analyzing gas transport phenomena in polymeric membranes. 

The field of transport phenomena is the basis of modeling in polymer processing. This chapter presents the derivation of the balance equations and combines them with constitutive models to allow modeling of polymer processes. The chapter also presents ways to simplify the complex equations in order to model basic systems such as flow in a tube or Hagen-Poiseulle flow, pressure flow between parallel plates, flow between two rotating concentric cylinders or Couette flow, and many more. These simple systems, or combinations of them, can be used to model actual systems in order to gain insight into the processes, and predict pressures, flow rates, rates of deformation, etc. 

The composition of the structural material and the choice of the fabrication process are important in the preparation of controlled-release systems. Over the past decades, great advances have been made in the engineering of multicomponent, polymer-based, structural materials. These materials were designed to release active substances by different mechanisms (ref. 1) including diffusion, chemical control (polymer degradation) and solvent activation (swelling or osmotic pressure). In some cases, combinations of such mechanisms have been used. Experimental methods and theoretical analysis of mass transport phenomena in these materials have been developed (refs. 2,3). 

The emphasis changes in Electroactive Polymer Electrochemistry, Part 2 Methods and Applications, where methodology and applications is addressed. The volume begins (Chapter 5) with a contribution by Morton-Blake and Corish. These contributors have been very active in the area of atomistic simulation of matter transport phenomena in solid materials. In the present contribution they describe in a lucid manner the results of their recent work in applying the methodology of atomistic simulation to quantify dopant transport processes in electroactive polymers. The idea of simulation is continued in Chapter 6, where Cassidy carefully describes the application of digital simulation protocols to charge transport in... 

Although our own research has outlined a complete new theoretical concept, there is still a great need to invest further research into the fundamentals of blend technology, such as dispersion, interfacial phenomena, conductivity breakthrough at the critical concentration, electron transport phenomena in blends, and others. It is not the purpose of this section to review these aspects in greater depth than in Section 1.1 and Section 1.2. In the context of this handbook, it should be sufficient to summarize the basis of any successful OM (PAni) blend with another (insulating and moldable or otherwise process-able) polymer is a dispersion of OM (here PAni, which is present as the dispersed phase) and a complex dissipative structure formation under nonequilibrium thermodynamic conditions (for an overview, see Ref [50] for the thermodynamic theory itself, see Ref [15], for detailed discussions, cf Refs. [63,64]). Dispersion itself leads to the drastic insulator-to-metal transition by changing the crystal structure in the nanoparticles (see Section 1.1). 

During the past decade or so, the school in polymer science and engineering that was established in the chemical engineering division has made useful contributions in the area of transport phenomena in non-Newtonian fluids, analysis of polymerisation reactors, polymer processing and polymer crystallization behaviour. A notable feature again has been the blend of theory and practice in most of this work. 

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