Unsteady Effects in Droplet Evaporation and Combustion

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Abstract
An asymptotic analysis is presented for the problem of droplet vaporization in a stagnant atmosphere taking into account the unsteady effects in the gas phase. The ratio of the densities of the ambient gas and of the liquid is considered as a small parameter. The results of the classical quasi-steady theories are recovered in the first approximation, and corrections due to unsteady effects are obtained for the vaporization rate and for the droplet lifetime, which are found to be of the order of the square root of the density ratio The analysis is extended to cover the cases when the vaporization rate is enhanced by a fast irreversible reaction between the fuel vapor and an oxidizer in the ambient gas. While the quasi-steady theories predict the vaporization rate with relative errors of the order of the square root of the density ratio, the ratio of flame radius to droplet radius is found in many practical cases to vary significantly with time in agreement with experimental results.

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