Modeling the Maximum Spreading of Liquid Droplets Impacting Wetting and Nonwetting Surfaces

Droplet impact has been imaged on different rigid, smooth, and rough substrates for three liquids with different viscosity and surface tension, with special attention to the lower impact velocity range. Of all studied parameters, only surface tension and viscosity, thus the liquid properties, clearly play a role in terms of the attained maximum spreading ratio of the impacting droplet. Surface roughness and type of surface (steel, aluminum, and parafilm) slightly affect the dynamic wettability and maximum spreading at low impact velocity. The dynamic contact angle at maximum spreading has been identified to properly characterize this dynamic spreading process, especially at low impact velocity where dynamic wetting plays an important role. The dynamic contact angle is found to be generally higher than the equilibrium contact angle, showing that statically wetting surfaces can become less wetting or even nonwetting under dynamic droplet impact. An improved energy balance model for maximum spreading ratio is proposed based on a correct analytical modeling of the time at maximum spreading, which determines the viscous dissipation. Experiments show that the time at maximum spreading decreases with impact velocity depending on the surface tension of the liquid, and a scaling with maximum spreading diameter and surface tension is proposed. A second improvement is based on the use of the dynamic contact angle at maximum spreading, instead of quasi-static contact angles, to describe the dynamic wetting process at low impact velocity. This improved model showed good agreement compared to experiments for the maximum spreading ratio versus impact velocity for different liquids, and a better prediction compared to other models in literature. In particular, scaling according to We(1/2) is found invalid for low velocities, since the curves bend over to higher maximum spreading ratios due to the dynamic wetting process.