Kinematic Closure of Drop Impact

Existing models for droplet impact prescribe the spreading contact time and effective spreading velocity from asymptotic arguments, which prevents a self consistent prediction of the maximum spreading ratio across regimes. Here, the total spreading time and characteristic spreading velocity are formulated from the energy balance, with explicit capillary and viscous contributions. Multiplying this time and velocity to obtain the maximum spreading diameter yields a closed, unified scaling law for the maximum spreading ratio of wetting drops across inertio capillary and inertio viscous regimes. The resulting expression quantitatively collapses the present measurements and literature data over a wide range of Weber and Ohnesorge numbers, droplet sizes, and surface wettabilities without prefactors that need to be adjusted to a certain regime.