A theoretical study on coalescence-induced jumping of partially wetted condensed droplets on nano-textured surfaces

Partially wetted (PW) droplets specially exist on textured surfaces with proper nano-structural parameters. Such tiny drops can depart from surfaces by coalescence-induced jumping, and become the main medium for dropwise condensation heat transfer. Therefore, it is of great importance to study the relationship between nano-structural parameters and PW drop post-merging jumping. In this study, the principle of minimum energy increasing during condensed droplets growth was used to judge if a condensed drop is in PW state. The initial shape of a coalesced droplet was determined based on the conservation of PW drop interface free energy and viscous dissipation energy before and after two or more PW condensed droplets merge. The dynamic equation describing the shape conversion of the post-coalescence droplet was then solved. Whether jumping or not of a merged drop was determined by whether the base radius of the droplet can reduce to 0 and if existing a up moving speed of drop gravity center at this moment. The calculation results show that PW droplets can form only on the textured-surfaces with certain nano-pillar height and relatively larger ratio between pillar diameter and pitch, d(n)/s, while completely wetted droplets easily form on the surfaces with low pillar height and d(n)/s less than 0.1. Meanwhile, post-coalescence jumping of PW droplets closely relates to nano-structural parameters. Not all PW drops can jump after merging. Instead, self-propelled jumping of PW drops takes place only on the surfaces with relatively higher nano-pillar height and suitable d(n)/s. Moreover, PW drop size and the scale ratio between two PW droplets to merge also have significant effect on the coalescence-induced jumping. It is difficult for a merged drop to jump spontaneously if the size of PW drops is too large or too small, or the scale ratio of two PW drops is too small. Finally, post-coalescence jumping of multi-droplets is easier than that of two drops since more surplus interface free energy exists in the former case. The calculation results of this model are well consistent with the experimental observations in literatures for whether the post-coalescence condensed drops jump on nano-textured surfaces, with accuracy of 95%. In conclusion, coalescence-induced jumping takes place only when PW droplets with suitable size on the textured surfaces with proper nano-structural parameters.