Constructal theory of droplet impact geometry

In this paper we rely on the constructal law of maximization of flow access in order to construct a theory of geometry generation (selection, evolution) during molten droplet impact. We show that immediately after impact the liquid spreads inviscidly as a ring with a radial velocity that scales with the initial impact velocity. If the initial droplet is small and slow enough, the ‘splat’ comes to rest (dies) viscously, as a disc. If the droplet is large and fast enough, the ring splashes and is continued outward by needles that grow radially until they are arrested by viscous effects. We optimized the number of needles such that the total splash time is minimum. The theoretical dimensionless group that governs the selection of geometry (G) is the ratio of two lengths, the final radius of the disc that dies viscously, divided by the radius of the still inviscid ring that just wrinkles. Splats form when G ⩽ O(1) and splashes are favored when G ⩾ O(1). Experimental measurements reported in the literature confirm several of the features of the constructal development of splat vs. splash flow architecture.