Drop impact onto wetted walls: an unsteady analytical solution for modelling crown spreading

An unsteady analytical solution is proposed to predict the spreading rate of crown generated by an impacting droplet onto wetted walls. The modelling strategy based on direct integration boundary layer correction into potential flow that leads well-established square-root time dependence. original has structure unsteady, stagnation point with decaying strength. For initial strengths $a_0 \geqslant 100\ {\rm s}^{-1}$ , we find a self-similar can also be obtained for in variables $\left (r \sqrt {a(t)/(\nu t)}, z t)} \right )$ . self-similarity enables straightforward estimation momentum losses during liquid along wall. approach yields excellent agreement experiments entire phase. Moreover, it smooth transition from inertia-driven shear-controlled regime propagation. In general, analysis shows arising viscous effects cannot neglected significant portion propagation, particularly thin wall films.