ANALYSIS OF EVAPORATION AND COMBUSTION OF RANDOM CLUSTERS OF DROPLETS BY A MODIFIED METHOD OF EXPANSION INTO IRREDUCIBLE MULTIPOLES

Interaction between evaporating or burning droplets in random clusters of droplets of different sizes is analyzed using quasi-steady approximation. A method of solution of the Laplace equation in a region exterior to N arbitrarily located spheres of different radii is suggested. The method is based on the expansion of the solution into irreducible multipoles. Results are presented in terms of a correction factor defined as the ratio of the burning rate of a droplet located inside a cluster of burning droplets to a single-droplet burning rate. The proposed method is validated by comparing the present results with those available in the literature. The method is applied to the analysis of droplet interactions in large random arrays of droplets of different sizes.