A new model for the bouncing regime boundary in binary droplet collisions

This work experimentally investigates binary collisions of identical droplets over a range of liquid viscosities, using 2%, 4%, and 8% of hydroxypropyl methylcellulose solutions in water. The collisions were captured by using a high-speed camera, and regime maps of collision outcomes were derived. The performance of existing models of the boundary of the bouncing regime was assessed and found to give poor predictions. This was attributed to assumptions and errors in the treatment of kinetic energy and the droplet shape factors used in these models. A new model was derived which addresses these issues: the definition of the kinetic energy that contributes to deformation was corrected; a new shape factor that accurately reflects the geometry of the droplet at maximum deformation was proposed, and, importantly, an empirical approach was implemented to account for the effect of the impact parameter on this shape factor. Moreover, the model includes an estimate of the viscous dissipation, which is calculated directly from the experimentally observed difference between the impact and the rebound kinetic energies and measurements of the post-collision droplet oscillations. The proposed model shows a striking improvement versus the existing models, reducing the mean absolute error by an order of magnitude.