Model and experiments of a drop impinging on an immersed wall

We present a model describing the rebound of a drop impinging on a rigid plane wall immersed in water. This model is based on the resolution of the drop equation of motion in an unbounded fluid in which an additional pressure force is introduced accounting for the wall effect on the drop motion. This force is computed from a film drainage simulation model during the approach of the deformable particle to the wall. Results of the model have been compared with experimental trajectories of drops impinging vertically at terminal rise velocity against a horizontal wall immersed in water at rest. These trajectories have been obtained with the help of an image processing technique. A wide range of experimental conditions has been studied (drop diameter, interfacial tension, drop viscosity, and density). In most of the cases, the model predicts the experimental trajectories within a very good accuracy (height of bouncing, deformation, number of rebounds) even in the case of a significant deformation. The numerical results show that the rebound of a deformable inclusion against a wall in water is essentially governed by the balance between the added mass force and the film pressure force exerted on the drop during the impact. The model has also been successfully tested in the case of an impinging bubble at high particle Reynolds number, based on experimental data taken from Tsao and Koch [Phys. Fluids 9, 44 (1997)].