Momentum Transport Properties of Materials

In this section, we will examine the microscopic origins of viscosity for each material type, and we will see how viscosity is much more complex than simply serving as a proportionality constant in Eq. (4.3). Ultimately, we will find that viscosity is not a constant at all, but a complex function of temperature, shear rate, and composition, among other things. 

1 Momentum Transport Properties of Metals and Alloys Inviscid Systems 

Most metallic systems above their melting point have very low viscosities, typically less than about 100 poise. Liquids with viscosities below this level are generally termed inviscid, that is, they are water-like in their fluidity. This is a relative statement, of course, since their viscosities are distinctly nonzero, but for all practical purposes the pressure required to cause these fluids to flow or overcome surface tension forces. 

For liquids, even simple monatomic liquids such as molten metals, this link between molecular interactions and a bulk property such as viscosity is still there, in principle, but it is difficult to derive a relationship from fundamental interaction energies that is useful for a wide variety of systems. Nonetheless, theoretical expressions for liquid viscosities do exist. Some are based on statistical mechanical arguments, but the model that is most consistent with the discussion so far is that of nonattracting hard spheres 

Notice the similarity between the relationship for liquid viscosity [Eq. (4.7)] and that for gaseous viscosity [Eq. (4.6)]. They both have a square root dependence on temperature and molecular weight and depend on the inverse square of the collision diameter [can you prove this for Eq. 4.7) ]. So, at least in principle, there is a fundamental relationship between the structure of a liquid and its viscosity. 

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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. 

THERMAL CONDUCTIVITY. The proportionality constant A is a physical property of the substance called the thermal conductivity. It, like the newtonian viscosity ft, is one of the so-called transport properties of the material. This terminology is based on the analogy between Eqs. (3.4) and (10,2). In Eq. (3.4) the quantity xg,. is a rate of momentum flow per unit area, the quantity du/dy is the velocity gradient, and jx is the required proportionality factor. In Eq. (10.2), q/A is the rate of heat flow per unit area, dTIdn is the temperature gradient, and k is the proportionality factor. The minus sign is omitted in Eq. (3.4) because of convention in choosing the direction of the force vector. 

Of the three general categories of transport processes, heat transport gets the most attention for several reasons. First, unlike momentum transfer, it occurs in both the liquid and solid states of a material. Second, it is important not only in the processing and production of materials, but in their application and use. Ultimately, the thermal properties of a material may be the most influential design parameters in selecting a material for a specific application. In the description of heat transport properties, let us limit ourselves to conduction as the primary means of transfer, while recognizing that for some processes, convection or radiation may play a more important role. Finally, we will limit the discussion here to theoretical and empirical correlations and trends in heat transport properties. Tabulated values of thermal conductivities for a variety of materials can be found in Appendix 5. 

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... 

Momentum transport The flow patterns mainly depend on the velocities of both phases, the surface tension (hquid, gas and reaction plate material properties) and on the channel dimensions (width, depth, length, diameter, etc.). We encounter the following parameters ... 

The ability to model the detailed chemistry of ignition and combustion of energetic materials requires the simultaneous treatment of the chemical kinetics behavior of large chemical reaction systems combined with convective and diffusive transport of mass, momentum, and energy. Such models require the evaluation of equations of state, thermodynamic properties, chemical rate expressions, and transport properties. The computer software used to evaluate these quantities is referred to as the Chemkin package.33-35 includes an interpreter for the chemical reactions, a thermochemical data base, a linking file, and gas-phase subroutine libraries. The interpreter reads in the list of elementary chemical reactions. The forward reaction rates are given in the form of the Arrhenius rate expression... 

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