Computer simulations of the growth of breath figures

We describe computer simulations of the growth of breath figures, the patterns formed when droplets condense on a cold surface. The focus is on the coalescence of droplets, which is an important growth mechanism, and the conditions for self-similar patterns, which are experimentally observed. It is assumed that individual droplets grow according to a power law; droplets that touch coalesce instantly and are replaced by a new droplet at the center of gravity of the coalescing pair. The average droplet radius, distribution of droplet sizes, surface coverage, and radial distribution function are determined as a function of the time for a variety of initial coverages and polydispersities. These quantities are compared to those determined by experiment, and our simple model is found to be in good accord with the observed behavior. It is observed that the process of coalescence induces spatial correlation between droplets.