Numerical investigation of air cushioning in the impact of micro-droplet under electrostatic fields

Abstract

Air cushioning widely occurs when a droplet impacts onto a solid or fluid surface at low velocity, which is mediated by the lubrication pressure of a thin air layer. Such air cushioning phenomena for micro-sized droplets bear important implications for precision coating and inkjet printing. In this study, we investigate numerically the air cushioning in the micro-sized droplets of various sizes impacting on a solid surface based on the volume of fluid method as implemented in the OpenFOAM framework. We find that the critical impact speed for bouncing on the air cushion increases as the droplet radius decreases, while the Weber number remains in a narrow range from 1 to 4. The scaling law of the critical impact speed for bouncing is derived by balancing the lubrication pressure of the air cushion with the capillary pressure and droplet inertia. The impact mode transforms from bouncing to wetting with an electric field. A group of phase diagrams of the electric Bond number vs the Weber number is presented for various droplet sizes. The diagrams are consistent with the scaling law of the critical electric field for the wetting-without-bubble mode. The findings provide insights for applications based on micro-droplet deposition, such as inkjet/electrohydrodynamic printing and spray coating, to avoid the adverse effect of air cushioning or air entrapment.