Violent droplet impacts with non-flat surfaces

The application of Wagner theory to idealised two-dimensional inertially dominated droplet impacts is extended to incorporate non-flat substrates that are continuous functions of distance along the surface. Mixed boundary value problems are solved for the displacement and velocity potentials for both a single impact with an asymmetric substrate and a pair of impacts. The droplet free-surface position and the pressure on the wetted surface are calculated, along with the load and moment on the substrate. For double impacts a void may be formed between the substrate and the droplet free surface. Double impacts are compared with a single asymmetric impact with one half of the equivalent substrate geometry to assess how the free surface, loads and moments are affected by the separation between impact sites. Interactions between symmetric double impacts enhance the liquid penetration between the
impact sites and increase the load and moment on each substrate element compared to the corresponding single impact. The time taken for the void between droplet and substrate to become saturated is found assuming the gas pressure build-up and capillary forces are negligible, giving an estimate for the transition time from a partially wetted to a fully wetted surface close to the initial impact site. After the void becomes saturated, the subsequent free-surface evolution is determined and the effect of periodic roughness on the contact line
evolution is calculated. For surfaces formed of an array of asperities, secondary impacts which both traps further voids and completely wet the surface are found.