An interesting approach to the spray problem has been suggested by Chiu and Liu [30], who consider a quasi-steady vaporization and diffusion process with infinite reaction kinetics. They show the importance of a group combustion number (G), which is derived from extensive mathematical analyses and takes the form:

The value of G was shown to have a profound effect upon the flame location and distribution of temperature, fuel vapor, and oxygen. Four types of behaviors were found for different ranges of G. External sheath combustion occurs for the largest value; and as G is decreased, there is external group combustion, internal group combustion, and isolated droplet combustion.

Isolated droplet combustion obviously is the condition for a separate flame envelope for each droplet. Typically, a group number less that 10⁻² is required. Internal group combustion involves a core with a cloud where vaporization exists such that the core is totally surrounded by flame. This condition occurs for G values above 10⁻² and somewhere below 1. As G increases, the size of the core increases. When a single flame envelops all droplets, external group combustion exists. This phenomenon begins with G values close to unity. (Note that many industrial burners and most gas turbine combustors are in this range.) With external group combustion, the vaporization of individual droplets increases with distance from the center of the core. At very high G values (above 10²), only droplets in a thin layer at the edge of the cloud vaporize. This regime is called the external sheath condition.