Evaporation-burning equations for a single droplet

The behavior of a single droplet during burning is the foundation for understanding and analyzing the process. Barnard el al. 11361 proposed that, if a liquid droplet exceeds some critical size but less than about one millimeter in diameter, the combustion takes the form of a spherical diffusion flame round the droplet and the burning rate is determined by the vaporization from the surface of the droplet. The fact 

Let us consider the symmetrical burning of a spherical droplet with the radius rp in surroundings without convection. Assume that there is an infinitely thin flame zone from the surface of the droplet to the radial distance rn [137], which is much larger than the radius of the droplet, rp. The heat released from the burning is conducted back to the surface to evaporate liquid fuel for combustion. Because the reaction is extremely fast, there exists no oxidant in the range of rp r m while no fuel vapor is available at r rn. At a quasi steady state the mass flux through the spherical surface with the radius r ( rp), Mfv, can be obtained with Fick s law as 

From the continuity equation at the quasi steady state, we have 

Substituting Eqs. (8.1) and (8.2) into Eq. (8.3) and integrating the resulting equation from rp to rfl gives the flux of fiiel-buming, Aflvs, as 

On the other hand, the diameter of the droplet reduces continuously as the vaporization-burning proceeds. The variation of the droplet radius with time can be determined from the mass balance round the droplet itself  

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