Hydrodynamic phenomena of collision between a high-speed droplet and a rigid plane using second-order perturbation techniques

In this paper, the hydrodynamic phenomena of collision of a high-speed droplet with a rigid plane have been investigated by using perturbation techniques. Here, the velocity components, in contrast to other works, have been directly derived by solving Navier -Stokes equations. The ratio of initial droplet radius to the final droplet radius has been chosen as a perturbation parameter. Due to the interaction of a solid surface and moving fluid, a boundary layer forms and the field equations can be divided into two parts: inner and outer. By combining inner and outer solutions, we can determine velocity and pressure fields inside the droplet. As a result, final droplet radius, spreading rate, and final time up to the point that the droplet ceases to move will be determined. In the present study the problem is solved for high Reynolds numbers in which surface tension effects during the spreading process can be neglected. The results obtained agree well with other semi-analytic and also experimental studies which can be used for prediction of droplet impingement behavior.