The problem of coalescence-induced self-propelled jumping of droplet is studied using three-dimensional numerical simulation. The focus is on the effect of inertia and in particular the effect of air density on the behavior of the merged droplet during jumping. A lattice Boltzmann method is used for two identical, static micro-droplets coalescing on a homogeneous substrate with contact angle ranging from 0◦ to 180◦. The results reveal that the effect of air density is significant on detachment of the merged droplet from the substrate at the later stage of the jumping process; the larger the air density, the larger the jumping height of the droplet. Analysis of streamlines and vorticity contours is performed for density ratios ranging from 60 to 800. These show a generation of vortical structures inside and around the droplet. The intensity of these structures gets weaker after droplet departure as the air inertia is decreased. The results are also presented in terms of phase diagrams of the merged droplet jumping for different Ohnesorge numbers (Oh) and surface wettabilities for both small and large density ratios. The critical value of contact angle where the merged droplet jumps away from the substrate is independent of density ratio and has a value around 150◦. However, the critical value of Oh depends on both density ratio and wettability of the surface for contact angles greater than 150◦. In this range of contact angle, the diagrams show two distinct dynamical regimes for different density ratios, namely, inertial and viscous regimes.
Farokhirad, Samaneh; Morris, Jeffrey F.; and Lee, Taehun, "Coalescence-Induced Jumping of Droplet: Inertia and Viscosity Effects" (2015). CUNY Academic Works.