On the Changing Size Spectrum of Particle Clouds Undergoing Evaporation, Combustion, or Acceleration

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Abstract
A theoretical treatment is given showing how the size distribution of a cloud of particles changes as the result of evaporation, combustion, or acceleration. The general differential equation governing the concentration of particles as a function of size, position, and time is formulated for one-dimensional duct-type flows. Solutions to the differential equation are then obtained for a number of special problems of interest to evaporation and combustion. When molecular transfers control, the equivalent mean diameter for evaporation or combustion of drops is found to be approximately constant with time. This suggests that the conventional model of a constant number of uniform drops of varying size be replaced by a new model having a varying number of uniform drops of constant size. The new model predicts a lower rate of evaporation or combustion than the conventional model.

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