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

TL;DR

This paper introduces a numerical model for droplet growth on fibers, revealing that the size distribution's polydispersity exponent depends on fiber thickness and interaction details, differing from previous theoretical predictions.

Contribution

The study develops a new numerical model for 3D droplet growth on 1D fibers, showing the non-universality of the polydispersity exponent and highlighting factors influencing it.

Findings

Polydispersity exponent depends on fiber thickness and droplet interactions.

The model's exponent values differ from Blackman's theoretical predictions.

Droplet size distribution exhibits a non-universal, non-trivial scaling law.

Abstract

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 non-trivial 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 thickness of the fiber and on details of the droplet interaction leading to merging. In addition, its values consistently differ from the theoretical prediction by Blackman (Phys. Rev. Lett., 2000). Possible causes of this discrepancy are pointed out.