Polymer momentum transport properties

Unlike metals, in which momentum transport properties are generally limited to the molten state, and ceramics, in which momentum transport properties are primarily (but not always) described by the solution state, polymers can be found in either the solution or molten state. As a result, many of the principles that have been previously discussed apply to polymers, especially with regard to non-Newtonian behavior. There are, however, a few viscosity-related concepts, exclusive to polymers, that we will describe here. 

Given the vast number of possible matrix-reinforcement combinations in composites and the relative inability of current theories to describe the viscosity of even the most compositionally simple suspensions and solutions, it is fruitless to attempt to describe the momentum transport properties of composite precursors in a general manner. There are, however, two topics that can be addressed here in an introductory fashion flow properties of matrix/reinforcement mixtures and flow of matrix precursor materials through the reinforcement. In both cases, we will concentrate on the flow of molten polymeric materials or precursors, since the vast majority of high-performance composites are polymer-based. Fnrthermore, the principles here are general, and they apply to the flnid-based processing of most metal-, ceramic-, and polymer-matrix composites. 

The close interrelations among mass, momentum, and energy transport can be explained in terms of a molecular theory of monatomic gases at low density. The continuity, motion, and energy equations can all be derived from the Boltzmann equation for the velocity distribution function, from which the molecular expressions for the flows and transport properties are produced. Similar derivations are also available for polyatomic gases, monatomic liquids, and polymeric liquids. For monatomic liquids, the expressions for the momentum and heat flows include contributions associated with forces between two molecules. For polymers, additional forces within the polymer chain should be taken into account. 

Research areas where a chemical engineer can expect to make the most contributions are primarily in resist processing. Here, the major engineering considerations often entail basic conservation laws for mass, momentum and energy, polymer physics, thermodynamics, and transport properties in polymeric matrices. An excellent review has been written by Thompson and Bowden (3) to address the issues encountered in individual unit operations. A few of the many topics discussed in their review will be selected here for a more in-depth examination. Hardware parameters such as lens imperfections, source stability, mask quality and dimensions, contamination and mechanical stability do not fall in the scope of the present discussion. This paper will concentrate on events and research challenges require a firm understanding of material... 

This paper presents a mathematical model and numerical analysis of momentum transport and heat transfer of polymer melt flow in a standard cooling extruder. The finite element method is used to solve the three-dimensional Navier-Stokes equations based on a moving barrel formulation a semi-Lagrangian approach based on an operator-splitting technique is used to solve the heat transfer advection-diffusion equation. A periodic boundary condition is applied to model fully developed flow. The effects of polymer properties on melt flow behavior, and the additional effects of considering heat transfer, are presented. 

Multiparticle collision dynamics describes the interactions in a many-body system in terms of effective collisions that occur at discrete time intervals. Although the dynamics is a simplified representation of real dynamics, it conserves mass, momentum, and energy and preserves phase space volumes. Consequently, it retains many of the basic characteristics of classical Newtonian dynamics. The statistical mechanical basis of multiparticle collision dynamics is well established. Starting with the specification of the dynamics and the collision model, one may verify its dynamical properties, derive macroscopic laws, and, perhaps most importantly, obtain expressions for the transport coefficients. These features distinguish MPC dynamics from a number of other mesoscopic schemes. In order to describe solute motion in solution, MPC dynamics may be combined with molecular dynamics to construct hybrid schemes that can be used to explore a variety of phenomena. The fact that hydrodynamic interactions are properly accounted for in hybrid MPC-MD dynamics makes it a useful tool for the investigation of polymer and colloid dynamics. Since it is a particle-based scheme it incorporates fluctuations so that the reactive and nonreactive dynamics in small systems where such effects are important can be studied. 

What makes the fabrication of composite materials so complex is that it involves simultaneous heat, mass, and momentum transfer, along with chemical reactions in a multiphase system with time-dependent material properties and boundary conditions. Composite manufacturing requires knowledge of chemistry, polymer and material science, rheology, kinetics, transport phenomena, mechanics, and control systems. Therefore, at first, composite manufacturing was somewhat of a mystery because very diverse knowledge was required of its practitioners. We now better understand the different fundamental aspects of composite processing so that this book could be written with contributions from many composite practitioners. 

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