The evolution of a 2D constrained growth system of droplets-breath figures

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Abstract
In the growth of a system of droplets (breath figures), the droplets increase in size by a combination of direct condensation of vapour at their surface, referred to as intrinsic growth, and by their coalescence. An analytical model is presented which predicts the transient response of this 2D constrained system of droplets to intrinsic growth that follows a simple scaling law, and, if required, to other growth laws as well. The model predicts the mean diameter of the droplets, the fraction of the substrate covered by the droplets, and the number of droplets per unit area, as functions of time. It is applicable from the onset of the condensation, during which the influence of coalescence on the growth process is small, up to and including the intermediate, self-similar regime, during which the influence of coalescence on the transient features of the growth system is significant. The model is validated by comparing its solution with results from computer simulations.

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