Coalescence-induced jumping of micro-droplets on heterogeneous superhydrophobic surfaces

Abstract

The phenomenon of droplets coalescence-induced self-propelled jumping on homogeneous and heterogeneous superhydrophobic surfaces was numerically modeled using the volume of fluid method coupled with a dynamic contact angle model. The heterogeneity of the surface was directly modeled as a series of micro-patterned pillars. To resolve the influence of air around a droplet and between the pillars, extensive simulations were performed for different droplet sizes on a textured surface. Parallel computations with the OpenMP algorithm were used to accelerate computation speed to meet the convergence criteria. The composition of the air-solid surface underneath the droplet facilitated capturing the transition from a no-slip/no-penetration to a partial-slip with penetration as the contact line at triple point started moving to the air pockets. The wettability effect from the nanoscopic roughness and the coating was included in the model by using the intrinsic contact angle obtained from a previously published study. As the coalescence started, the radial velocity of the coalescing liquid bridge was partially reverted to the upward direction due to the counter-action of the surface. However, we found that the velocity varied with the size of the droplets. A part of the droplet kinetic energy was dissipated as the merged droplet started penetrating into the cavities. This was due to a different area in contact between the liquid and solid and, consequently, a higher viscous dissipation rate in the system. We showed that the effect of surface roughness is strongly significant when the size of the micro-droplet is comparable with the size of the roughness features. In addition, the relevance of droplet size to surface roughness (critical relative roughness) was numerically quantified. We also found that regardless of the viscous cutoff radius, as the relative roughness approached the value of 44, the direct inclusion of surface topography was crucial in the modeling of the droplet-surface interaction. Finally, we validated our model against existing experimental data in the literature, verifying the effect of relative roughness on the jumping velocity of a merged droplet.