Impact of microphysics on the growth of one-dimensional breath figures

Droplet patterns condensing on solid substrates (breath figures) tend to evolve into a self-similar regime, characterized by a bimodal droplet size distribution. The distributions comprise a bell-shaped peak of monodisperse large droplets and a broad range of smaller droplets. The size distribution of the latter follows a scaling law characterized by a nontrivial polydispersity exponent. We present here a numerical model for three-dimensional droplets on a one-dimensional substrate (fiber) that accounts for droplet nucleation, growth, and merging. The polydispersity exponent retrieved using this model is not universal. Rather it depends on the microscopic details of droplet nucleation and merging. In addition, its values consistently differ from the theoretical prediction by Blackman and Brochard [Phys. Rev. Lett. 84, 4409 (2000)]. Possible causes of this discrepancy are pointed out.