ABSTRACT
The two-fluid model is usually formed by applying an appropriate averaging technique to the local instantaneous conservation equations and jump conditions. As an introduction to the derivation of the balance equations, this chapter reviews the important concept of averaging of subcontinuum or molecular-scale variables and the resulting need for realistic constitutive equations to gain closure. It presents various two-phase flow modeling equations in increasing order of complexity. The chapter also presents the derivations and applications of constitutive equations and the details of trajectory modeling. The flow mixture models and particle trajectory models can be regarded as special cases of the two-fluid model. There are two types of materials or media which may fall into the category of homogeneous equilibrium models: truly homogeneous, although possibly multicomponent, fluids such as air; and actually nonhomogeneous fluids that are treated as "homogeneous" mixtures, such as bubbly flows and other well-dispersed particle flows.
