With no absorption of ambient gas into the spherical liquid droplet, a general form of the governing equation for the change in the liquid fuel distribution is

(6–76)

where y _i is the mass fraction of component i in the liquid droplet, ρ _i is the mass density of the liquid fuel, R is the droplet radius, and is the vaporization rate per unit area of species i.

The change of liquid droplet energy is obtained from the conservation equation of energy for the two phase system consisting of the droplet and the surrounding gas mixture as

(6–77)

where c _v,l is the specific heat of the liquid fuel, q _i is the heat transfer rate from the droplet surface to the interior per unit area, and T _d and T _s are the average droplet temperature and surface temperature, respectively.