Numerical study of the interfacial fluctuation of a droplet levitating above a moving wall

We conducted a two-dimensional simulation of a droplet levitating above a wall moving at a constant velocity. The droplet is solved using the front-tracking method, and the moving wall is modeled with our discrete-forcing immersed boundary method. When the droplet approaches the moving wall with a relative velocity in the tangential direction, the droplet levitates due to the local pressure increase between the droplet and the moving wall. This pressure is in good agreement with the value of the pressure predicted by the lubrication theory. We report the effect of the geometry of the moving wall on the stability of the droplet. For the walls of larger curvature, the air-liquid interface of the droplet facing the moving wall was observed to ripple, which is also confirmed by our previous experimental studies. The simulation results for different Weber and Froud numbers are compared with the experimental results, and the dependence of each parameter on the unsteadiness of the droplet interface are discussed.