Dynamics and thin film drainage of a deformable droplet moving towards a solid wall with finite inertia

Abstract

Direct numerical simulations of a deformable droplet approaching a planar solid wall through another fluid are performed to investigate the droplet dynamics and thin film drainage. The numerical approach solves the full Navier–Stokes equations and the interface is located by a moving mesh interface tracking method with high fidelity. Cases with Reynolds numbers of 25 and 50 and capillary numbers of 5 × 10⁻³ and 1 × 10⁻² are simulated for both head-on and oblique approaching scenarios. The front head of the droplet is flattened as the droplet nearly touches the wall, and a dimpled thin film is observed. Because of the great viscous forces of the flow inside the thin film, the droplet slows down dramatically which leads to a significant jump in the drag force. A detailed study of the thinning of the thin film is presented, and an asymmetric thin film is observed for the oblique approach. The numerical prediction on the central separation at which a dimple is formed agrees fairly well with previous analysis based on the lubrication theory. The simulated thinning rate is slower than the rate predicted by previous approximate models. The differences are mainly due to the finite Reynolds number of the simulated cases.