Numerical simulation of self-propelled non-equal sized droplets

Abstract

In general, external energy is needed to remove a liquid from a solid wall during cooling by dropwise condensation. However, experiments have shown that in some cases, droplets can propel themselves from the wall, without any external energy, due to the coalescence-induced conversion of surface energy to kinetic energy. Several authors have reported scaling analysis combined with an energy balance of kinetic energy, surface energy, and viscous dissipation to estimate whether the droplets can be self-propelled or not. Here, we use numerical simulation to describe the coalescence and self-propelling for nonequal sized droplets based on a finite-volume/front-tracking method and the generalized Navier boundary condition to model the moving contact lines. We find that a slightly smaller contact angle (165°) will give a larger out-of-plane jumping velocity than a superhydrophobic surface (with a contact angle of 180°). Further decreasing the contact angles results in "immobile coalescence." The speed of the moving contact line does not influence the spontaneous removal process as long as it is large enough to let the contact areas detach. Nonequal sized drops are much more difficult to be spontaneously removed from a wall compared to equal-sized ones. Two spherical drops with a diameter ratio of 2.0 have 60% total usable energy compared to equal-sized ones, and only 0.5% of the total released energy can be effectively used for out-of-plane jumping.