Universal rescaling of drop impact on smooth and rough surfaces

The maximum spreading of drops impacting on smooth and rough surfaces is measured from low to high impact velocity for liquids with different surface tensions and viscosities. We demonstrate that dynamic wetting plays an important role in the spreading at low velocity, characterized by the dynamic contact angle at maximum spreading. In the energy balance, we account for the dynamic wettability by introducing the capillary energy at zero impact velocity, which relates to the spreading ratio at zero impact velocity. Correcting the measured spreading ratio by the spreading ratio at zero velocity, we find a correct scaling behaviour for low and high impact velocity and, by interpolation between the two, we find a universal scaling curve. The influence of the liquid as well as the nature and roughness of the surface are taken into account properly by rescaling with the spreading ratio at zero velocity, which, as demonstrated, is equivalent to accounting for the dynamic contact angle.