Drop size distribution during condensation on superhydrophobic surfaces

With recent interest in condensation on superhydrophobic surfaces, several models to predict the heat transfer rate have been proposed. The models typically consist of expressions for the heat transfer rate to an individual drop multiplied by the drop size distribution; the product is then integrated over the range of drop sizes found on the surface to obtain the total heat transfer rate. Population balance modeling is frequently combined with an empirical expression in a piece-wise fashion to obtain the drop size distribution. However, this approach assumes that droplet coalescence does not occur until a specified radius. The current work proposes a model where randomly distributed drops grow based on published models for heat transfer to an individual drop. When growing drops overlap, they coalesce and potentially jump. As drops become sufficiently large, gravity sweeps them along the vertical surface, removing all other drops in its path. Good agreement is found between current and previous models when employing conditions consistent with published expressions for drop size distribution. With the assumptions removed, the simulation predicts a size distribution more consistent with physical observations, thus improving prediction of the overall heat transfer rate.