Size distribution theory for jumping-droplet condensation

Abstract

Jumping-droplet condensation is promising for various applications where the droplet size distribution plays a key role in the overall system performance. Despite being extensively studied in recent works, inconsistencies existed in previous size distribution models as the droplet growth and removal mechanisms were often not properly described. Here, we developed a theoretical framework where the contact and the coalescence of droplets were identified as the dominant mechanisms for instantaneous size distribution change. We found a critical droplet diameter comparable to the average nucleation site distance, beyond which the droplet population decreased rapidly. This result is analogous to the well-known Fermi-Dirac distribution due to the underlying exclusive principle. We also showed the effect of the contact angle, that is, larger droplets become more probable as surface hydrophobicity increases. The coalescence count distribution given by the current theory agrees well with experimental data. Furthermore, we demonstrated the use of the proposed model in predicting condensation heat transfer coefficients, which also shows good agreement with previous experiments. Our size distribution theory elucidates the fundamental process of droplet growth and interactions leading to an overall size distribution during jumping-droplet condensation, which can be generally applied to self-cleaning, anti-icing/frosting, power generation, and water harvesting.