Growth with coalescence during condensation

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Abstract
This paper describes an analytical and computer-simulation study of the way in which a system of droplets evolves during the condensation of a vapor onto a lyophobic substrate. The derivation of a system of first-order differential equations leads to a prediction for the spread of the distribution of the droplet sizes. The resulting equation was vindicated for a wide range of possible growth laws using the simulation. Furthermore, elimination of the time dependence of the differential equations produces a derivation of a previous empirical equation proposed by Vincent [Proc. R. Soc. London, Ser. A 321, 53 (1971)]. The equation directly relates the fraction of the substrate covered by the droplets to the number of droplets per unit of substrate area.

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