Multi-physics modeling of air entrapment during drop impact onto solid hydrophobic surfaces*

Controlled drop deposition onto a dry surface is important for various technologies such as spray cooling/painting, inkjet printing/coating, pesticide deposition, etc. During these processes air might be entrapped between the liquid and the solid layers leading to detrimental effects. We have developed a multi-physics modeling approach based upon the phase-field modeling (PFM) and Navier-Stokes equations to simulated air bubble formation during the drop impact onto solid surfaces. The PFM is validated against our own experimental measurements in terms of maximum spreading and rebound height. Then, several cases with varying Weber and Froude numbers are considered to study air entrapment. The PFM results reveal that air may be entrapped under water droplet during the initial deposition as well as retraction after maximum spreading. The volume of the entrapped air bubble varies during both processes, significantly influencing drop spreading and rebound height. Furthermore, the simulation results reveal a significant pressure build up in the entrapped air (up to an order of magnitude higher than in the surrounding water phase), which has a detrimental influence on the process of drop impact and spreading. Based upon our predictions and experimental results a contour map (the Weber vs. the Froude numbers) of the air entrapment is created and discussed.