We present a novel macroscopic model for head-on binary droplet collisions. This model modifies the Navier-Stokes equations to accurately account for the rarefied nature of the interdroplet gas film, and for the intermolecular Van der Waals force. It does not use any adjustable (empirical) parameters. It thereby encompasses the extreme range of length scales (more than $5$ orders of magnitude): from those of the external flow in excess of the droplet size (a few hundred $\mu{\rm m}$) to the effective range of the Van der Waals force around $10\ {\rm nm}$. A state of the art moving adaptive mesh method, capable of resolving all the relevant length scales, has been employed. Our numerical simulations are able to capture the coalescence-bouncing and bouncing-coalescence transitions that are observed as the collision intensity increases. The predicted transition Weber numbers
for tetradecane and water droplet collisions at different pressures show remarkably good agreement with published experimental values. Our study also sheds new light on the roles of gas density, droplet size and mean free path in the rupture of the gas film.