Droplet Impact and Maximum Spreading on Inclined Porous Substrates: Experiments and Modeling.

To better quantify the impact of wind-driven rain on buildings, the spreading behavior of water droplets impacting inclined porous surfaces is investigated, a key process in building physics with direct applications for façade durability and moisture management. At the droplet scale, the impact during spreading, thus not considering splitting, rebound, and splashing, is experimentally observed, and a model predicting the maximum spreading is proposed. The droplet spreading dynamics are recorded with high-speed cameras from two points of view. The droplet shape, spreading diameter, and contact angle versus time are documented. The water droplet impact angle and impact velocity are varied for two different natural stones. The effect of surface tension is examined by studying water and ethanol. An energy balance model is presented, considering impact parameters and fluid characteristics, to predict the transverse and longitudinal spreading ratios. The model assumes that the droplet deforms into an elliptical disk of constant height, elongated in the longitudinal direction along the inclined surface. To solve the energy balance equation, it is further assumed that the transverse spreading is equivalent to the spreading of a droplet impacting a flat surface with a droplet diameter reduced by the cosine to the impact angle. The effects of impact parameters, including impact velocity, impact angle, and liquid surface tension, are systematically analyzed. The model agrees well with the experiments, for both water and ethanol, with a slightly better fit obtained for water. Future work will extend the analysis to a wider range of impact conditions, including angles and velocities that produce splitting, rebound, or splashing, in order to establish a more complete description of droplet deposition.