Transmittance of transparent windows with non-absorbing cap-shaped droplets condensed on their backside

Abstract

This study aims to quantify systematically the effect of non-absorbing cap-shaped droplets condensed on the backside of transparent windows on their directional-hemispherical transmittance and reflectance. Condensed water droplets have been blamed to reduce light transfer through windows in greenhouses, solar desalination plants, and photobioreactors. Here, the directional-hemispherical transmittance was predicted by Monte Carlo ray-tracing method. For the first time, both monodisperse and polydisperse droplets were considered, with contact angle between 0 and 180°, arranged either in an ordered hexagonal pattern or randomly distributed on the window backside with projected surface area coverage between 0 and 90%. The directional-hemispherical transmittance was found to be independent of the size and spatial distributions of the droplets. Instead, it depended on (i) the incident angle, (ii) the optical properties of the window and droplets, and on (iii) the droplet contact angle and (iv) projected surface area coverage. In fact, the directional-hemispherical transmittance decreased with increasing incident angle. Four optical regimes were identified in the normal-hemispherical transmittance. It was nearly constant for droplet contact angles either smaller than the critical angle θcr (predicted by Snell’s law) for total internal reflection at the droplet/air interface or larger than 180°-θcr. However, between these critical contact angles, the normal-hemispherical transmittance decreased rapidly to reach a minimum at 90° and increased rapidly with increasing contact angles up to 180°-θcr. This was attributed to total internal reflection at the droplet/air interface which led to increasing reflectance. In addition, the normal-hemispherical transmittance increased slightly with increasing projected surface area coverage for contact angle was smaller than θcr. However, it decreased monotonously with increasing droplet projected surface area coverage for contact angle larger than θcr. These results can be used to select the material or surface coating with advantageous surface properties for applications when dropwise condensation may otherwise have a negative effect on light transmittance.