Expressions for the liquid phase in a multiphase material

Abstract

Like Chapter 9, this chapter focuses on a single phase in a multiphase material. In this case, the transport of “conserved” quantities that takes place predominantly (or only) through the liquid phase is considered. In doing so, of course, it is also necessary to account for the interphase exchange of “conserved” quantities through internal (interphase) boundary surfaces that the liquid phase shares with other phases in the (multiphase) material. Practical examples of such transport include filtration and infiltration processes, and drying, as well as certain corrosion processes--all of which involve the flow of a liquid, and possibly a reactive species, in a multiphase material. Further, Table 10-1 lists some liquid-containing dispersions that might be found in a materials synthesis or fabrication process, where it may be seen that some of the dispersions are relatively simple geometrically, while others are relatively more complex, both geometrically and topologically. For example, a mist consists of discrete (often spherical) liquid droplets that are dispersed in a continuous gas phase. If the number density, and size and shape of the liquid droplets are known, it is a relatively straightforward matter to determine such quantities as the volume fraction, intermaterial area density, and so on. In this, as well as the other “simple” dispersions, either analytical expressions or empirical correlations have been developed that describe their continuum-level behavior (e.g., flow, interphase mass exchange, effective “conductivity,” etc.) [1–3]. The more “complex” dispersions, on the other hand, are less easily dealt with, since it is often the topological features (particularly the connectivity) that play a key role in both the intraphase transport and the interphase exchange of “conserved” quantities in the material. As a result, this chapter will concentrate on describing expressions that are most useful for the so-called “complex” liquid-containing dispersions.