Droplet dynamics under an airflow: splitting versus depinning

Partially-wetting droplets under an airflow can exhibit complex behaviors that arise from the coupling of surface tension, inertia of the airflow, and the contact line dynamics. Recent experiments by Hooshanginejad et al. (2020) have demonstrated that a water droplet may split under the jet or escape the wind by depinning to one side, depending on the magnitude and position of the jet. To rationalize these observations, we develop a 2D lubrication model that incorporates the external pressure of the airflow and capillary pressure of the droplet. Distinct from the previous model, we simulate the motion of the contact line based on a precursor film and disjoining pressure, which is required to capture depinning. The resultant simulations qualitatively reproduce the onset of splitting and depinning regimes for varying parameters, in addition to the overall speed of the moving contact line. We also obtain analytical steady-state solutions and construct the minimum criteria for splitting and depinning, respectively.