Breath figures are the complex patterns that form when water vapor condenses into liquid droplets on a surface. The primary question concerning breath figures is how the condensing vapor is allocated between the growth of existing droplets and the nucleation of new ones. Although numerous studies have concentrated on scenarios resulting in highly polydisperse droplet ensembles, we experimentally [1] and theoretically [2] demonstrate that nearly monodisperse patterns can be achieved on defect-free substrates in a diffusion-controlled regime.

Specifically, we investigate the nucleation, growth, and coalescence of droplets on soft substrates consisting of crosslinked polymer networks. We discover that, following a short nucleation phase, the number of droplets remains constant over an extensive range of timescales due to collective effects mediated by the diffusion of vapor. The spatial extent of these diffusive interactions is identified through asymptotic matching, based on which we provide an accurate description of breath figures through a mean-field model (Fig. 1). In the experiments, we observe an algebraic sensitivity of the number of droplets on substrate elasticity, which is unexpected since nucleation occurs at a scale where the polymer network resembles a melt. Breath figures thus offer a macroscopic probe of the microscopic characteristics of the polymer surface, and suggest a surprisingly low-energy pathway for soft nucleation.

Contributors

Jacco H. Snoeijer(1), Ambre Bouillant(1),(2), Christopher Henkel(3), Uwe Thiele(3), Bruno Andreotti,(4)

(1)Physics of Fluids Group, University of Twente, 7500 AE Enschede, Netherlands

(2)MSC, UMR 7057 CNRS, UPC, 10 rue A. Domon et L. Duquet, 75013, Paris, France

(3)Institut für Theoretische Physik, Universität Münster, W.Klemm-Str. 9, 48149 Münster, Germany

(4)LPENS, UMR 8550 CNRS, ENS, UPCit´e, SU, 24 rue Lhomond, 75005 Paris, France

References

[1] A Bouillant, C Henkel, U Thiele, B Andreotti and JH Snoeijer, arXiv:2407.07624.

[2] A Bouillant, JH Snoeijer and B Andreotti, arXiv:2407.07608, to appear in Phys. Rev. Fluids.