The spray equations have been studied and solved for many applications: single-component and multicomponent liquids, high-temperature and low-temperature gas environments, monodisperse and polydisperse droplet-size distributions, steady and unsteady flows, one-dimensional and multidimensional flows, laminar and turbulent regimes, subcritical and supercritical thermodynamic regimes, and recirculating (strongly elliptical) and nonrecirculating (hyperbolic, parabolic, or weakly elliptic) flows. The analyses discussed here will not be totally inclusive of all of the interesting analyses that have been performed; rather, only a selection is presented.

Spray flows can be classified in various ways. One important issue concerns whether the gas is turbulent or laminar. In this chapter, only laminar flows are considered; the turbulent situation is discussed in Chapter 10. Another issue concerns whether thermodynamic conditions are subcritical, on the one hand, or near critical to supercritical, on the other hand.

In the most general spray case, the gas and the droplets are not in thermal and kinematic equilibria, that is, the droplet temperature and the droplet velocity differ from those properties of the surrounding gas. Of course, heat transfer and drag forces result in the tendency to move toward equilibrium. The equilibrium case is sometimes described as a locally homogeneous flow. It is possible to have thermal equilibrium or kinematic equilibrium without the other. When thermal equilibrium exists, the analysis described in Chapter 7 is simplified because the droplet temperature Tl can be set equal to the gas temperature T and Eq. (7.82) or its alternative forms, Eq. (7.83) or Eq. (7.87), can be avoided.