Background and definition of the problem

A variety of phenomena are exhibited by the burning of a spherical fuel particle in an infinite oxidizing atmosphere. Here we shall consider one of the simplest situations, the quasisteady, spherically symmetrical burning of a liquid fuel that vaporizes and reacts in a gas-phase flame, producing gaseous products that flow and diffuse to infinity. However, at the outset it is of interest to indicate some of the complexities that may arise in other situations. Because of the diversity of high-temperature oxidation mec-anisms of solids [24], [46], these complexities often are associated with the burning of solid fuels. 

If reaction products are less volatile, then their condensation can influence the combustion mechanism. For example, although boron is less volatile than B2O3, this oxide is sufficiently nonvolatile for its liquid phase to play a role in the combustion of boron particles under many circumstances [54]. Relatively volatile fuels with nonvolatile combustion products, such as magnesium and aluminum, practically always exhibit burning mechanisms influenced by product condensation. In the presence of product condensation, there are a number of possible modes of quasisteady burning. Condensed products may accumulate on the surface of the particle, may accumulate in a shell at a reaction sheet located at some distance from the surface of the particle, may accumulate in a shell at a condensation sheet located outside a thin primary gas-phase reaction sheet, or may flow and diffuse to infinity in the form of fine particles. The last of these processes may be enhanced by thermophoretic motion (see Section E.2.5) of fine particles away from the hottest reaction zone under the influence of the temperature gradient [55]. Many theoretical analyses of the various types of combustion processes have been published [55]-[62]. Law s models [60], [61] of different 

FIGURE 3.4. Diagrams of experiments on the burning of a fuel droplet in an oxidizing atmosphere, (a) Porous sphere, (b) Suspended droplet, (c) Falling droplet. 

In experiment (a) it is observed that the total mass per second that must be supplied to the sphere in order to maintain steady burning is 

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