Numerical Simulation of Coalescence-Induced Jumping of Multidroplets on Superhydrophobic Surfaces: Initial Droplet Arrangement Effect

The coalescence-induced droplet jumping on superhydrophobic surfaces (SHSs) has attracted considerable attention over the past several years. Most of the studies on droplet jumping mainly focus on two-droplet coalescence events whereas the coalescence, of three or more droplets is actually more frequent and still remains poorly understood. In this work, a 3D lattice Boltzmann simulation is carried out to investigate the effect of initial droplet arrangements on the coalescence-induced jumping of three equally sized droplets. Depending on the initial position of droplets on the surface, the droplet coalescence behaviors can be generally classified into two types: one is that all droplets coalesce together instantaneously (concentrated configuration), and the other is that the initial coalesced droplet sweeps up the third droplet in its moving path (spaced configuration). The critical Ohnesorge number, Oh, for the transition of inertial-capillary-dominated coalescence to inertially limited-viscous coalescence is found to be 0.10 for droplet coalescence on SHSs with a contact angle of 160 degrees. The jumping droplet velocity for concentrated multidroplet coalescence at Oh <= 0.10 still follows the inertial-capillary scaling with an increased prefactor, which indicates a viable jumping droplet velocity enhancement scheme. However, the droplet jumping velocity is drastically reduced for the spaced configuration compared to that for the aforementioned concentrated configuration. Because Oh exceeds 0.10, the effects of initial droplet arrangements on multidroplet jumping become weaker as viscosity plays a key role in the merging process. This work will provide effective guidelines for the design of functional SHSs with enhanced droplet jumping for a wide range of industrial applications.